Productivity and Quality Journal

IAPQR Transactions
DURING 2005 TO 2010

2005 (Volume 30, No. 1)

Improving the variability function in case of a uniform distribution
Wolfgang Sans, Dmitri Stübner, Surath Sen, Xiaomin Zhi
Institute of Applied and Statistics, Würzburg, Germany and
Elart von Collani
Institute of Economics, Würzburg, Germany

In [2] the set of all probability measures suitable for describing real worked random structures is divided into disjoint families according to the complexity of the random structure. A more complex structure needs more information to select an appropriate probability distribution. Once the family has been identified by easy-to-check qualitative properties, the family member has to be determined using quantitative information. A general method is developed for shortening the selected range of variability of a random variable X and applied to the family of uniform probability measures.

Change point detection of failure rate functions
M.Z. Anis
ISI, Kolkata, India
Sujit K Basu
Viswa Bharati, Santineketan, India
Murari Mitra
B.E. College, Shibpur, India
The theory of change point analysis finds applications in diverse areas such as stock market analysis, industrial quality control and reliability studies. However, in this paper, which is largely expository in nature, we focus on inference problems concerning change points of hazard rate function in the context of reliability analysis. The typical models used by the different authors are critically examined. The models under parametric and non-parametric set ups as also complete and censored data are reviewed. The use of different statistical techniques such as weak converge theory, the theory of L-statistics, TTT transform methods, etc. have been highlighted. The applicability of change point models in analyzing certain medical studies data is discussed. Possible directions of further research are indicated.
Reliability test plan for parallel systems having stochastic failure rates S.V. Sabnis
IIT Bombay, India and
Hariharan Nair
Household-HSBC, U.S.A.

Consider a parallel system consisting of k components with lifetimes assumed to be independent random variables having exponential distribution with parameters ?j, j=1,2,…,k. This paper generalizes the construction of component level reliability test plans for parallel systems in the sense that ?j’s are assumed to be random variables having a specific distribution.

On the robustness of the reliability characteristics of a discrete lifetime model in view of prior variations K.K. Sharma, Bhupendra Singh and Shubhi Rathi
C.C.S. University, Meerut, India

Prior distributions represent random variations in the parameters of lifetime distributions. This prior knowledge is updated by using experimental data in the Bayesian framework. However, updating the basic lifetime distribution in respect of these parametric variations is another important aspect to be considered in reliability analysis. Using this concept, the study considers the analysis of the reliability characteristics of a discrete lifetime distribution when prior variations in its parameter are suspected.
Volume 30, No. 2
On a family of apportionment indices and its limiting properties
Bikas K. Sinha
ISI, Kolkata, India and
Laura Koskela and Tapio Nummi
University of Tampera, Finland
In the harvesting technique prevailing in Scandinavia, tree stems are converted into smaller logs immediately at harvest. Modern sawmills attempt to operate according to customers’ special needs rather than simply minimize production costs. Since the annual production of saw timber in Scandinavia is in tens of millions of cubic meters, proper measurement of the goodness of the bucking outcome is of crucial importance. The outcome of the bucking operation can be considered as a multidimensional tale of tree species, quality grades, prices and length and diameter classes. The prevailing method of measuring the outcome is the so-called Apportionment Index (Al), which is calculated from the relative properties of the observed and target tables. Recently, some statistical properties of the Al have been studied and alternative means of measuring the ducking outcome have been suggested (Nummi et al., 2004 and Sinha et al., 2004). In this article we extend the definition of Al and examine its limiting properties.
Bayesian estimation of traffic intensity
S.P. Mukherjee and Shovan Chowdhury
Calcutta University, Calcutta, India
Bayes estimators of the traffic intensity ? in an M/M/1 queue have been derived based on the number of customers present at a finite number of time points in the steady state. In the first section independent gamma priors for arrival and service rates have been considered to eventually yield a truncated beta prior for ?. Bayes estimator and Bayes risk with squared error loss have been derived. A beta prior for ? and a linex loss function have also been used to obtain the Bayes estimator and its risk. Estimation of parameters of mixed geometric failure models from type-I progressively censored sample M.N. Patel
Gujarat University, India and
Nandita W. Patel
St. Xavier’s College, Navrangpura, India
Mixtures of distributions are important in the area of life testing and reliability analysis. The paper considers the problem of estimation of parameters in mixed geometric failure models from Type-I progressively censored sample with parameters changing at each stage of censoring. Asymptotic standard errors of the estimates are also derived. A numerical example is given to illustrate the results. Perishable inventory model with finite rate of replenishment having Weibull lifetime and price dependent demand J. Lakshminarayana, K. Srinivasa Rao
Andhra University, Visakhapatnam, India and
R. John Mathew
Raghu Engineering College, Visakhapatnam, India
In this paper we develop and analyze an inventory model for deteriorating items with Weibull rate of decay, having finite rate of replenishment and selling price dependent demand and allowing shortages. The sensitivity of the model with respect to the parameters is discussed through numerical illustration. It is observed that the deteriorating parameters have a tremendous influence on the optimal selling price and ordering quantity.
Estimating the common parameter of several exponential distributions
P. Yageen Thomas and N.K. Sajeev Kumar
University of Kerala, Trivandrum, India
In this work, using the theory of order statistics of independent non-identically distributed (inid) random variables, we have proposed a new estimator of the common parameter of several exponential distributions. The efficiency of the proposed estimator relative to some of the well-known estimators is studied. It is seen that the proposed estimator has better performance than that of other known estimators in all small sample cases covered in this work.
A study of roboustness of reliability sampling plans
S.B. Bagchi
Burdwan University, Burdwan, India
The paper attempts to study criterion as well as inference robustness of some reliability demonstration plans.
Designing of TNT sampling scheme involving crossover point K.K. Suresh and K. Barathan
Bharathiar University, Coimbatore, India
Normally, in situations involving costly or destructive testing, an acceptance number zero and a small sample size are employed. This paper concerns selection of tightened – Normal – Tightened schemes TNT (n; 0,1) indexed with various parameters involving crossover point of the composite OC curve.
2006 (Volume 31, No. 1)

Hidden projection property for 4'2'' non-regular fractional factorial designs M.L. Aggarwal
University of Memphis, Memphis, USA
S. Roy Chowdhury
Lady Shri Ram College for Women, University of Delhi, India
Anita Bansal
Ramjas College, University of Delhi, India and
Neena Mital
Ram Lal Anand College, University of Delhi, India
Hamada and Wu [12] studied 16-run and 24-run Plackett-Burman designs for estimation of some two-factor interactions along with main effects. We study hidden projections for 4'2'' (n=3,4) non-regular fractional factorial designs using 16-run and 24-run non-regular Hadamard matrices. On the distribution of the number of failed components in a consecutive k-out-of-n : F system R.L. Shinde
North Maharashtra University, India and M.M. Mahale
University of Pune, India
In a consecutive-k-out-of-n : F system. Papastavridis [6] obtained the distribution of W, the number of failed components at the moment of system failure. This paper derives two exact formulae for the pmf of W using an urn model and minimal i-cutsequence approach.
Computational study of the transient solution of m/m/1 queue by takacs J.L. Jain and A. Jiran Meitei
University of Delhi, India
In this note we discuss computational efficiency of the Takacs expression for the transient solution to M/M/1 Queuing System, for different values of the parameters in comparison with the other expressions using the Mathematics 4-Package.
On estimation of P(X'<'Y) for discrete distributions useful in life testing Sudhansu S. Maiti
Visva-Bharati University, India
Estimation of R=P(X'<'Y) has been considered when X and Y follow discrete distributions (like Geometric, Poisson). Both UMVUE of R and estimator of R using ML estimators of parameters involved have been found out. Simulation has been conducted to examine the MSE’s of these two estimators.
Parametric and non-parametric estimation for right truncated exponential distribution M. Masoom Ali
Ball State University, Muncie, USA
Jungsoo Woo
Yeungnam University, Gyongsan, South Korea
Saralees Nadarajah
University of Nebraska, USA
For a right truncated exponential distribution, the estimation of the truncation parameter, mean parameter, right tail probability and the left tail probability are considered. Various parametric and non-parametric estimators are used and their performance compared in terms of the mean squared error.

Bicriteria in nxm flowshop problem Laxmi Narain
University of Delhi, India and P.C. Bagga
Moti Lal Nehru College (E), Delhi, India
This paper provides the procedure for obtaining sequence(s) in special nxm flowshop problems which gives minimum possible mean flowing while minimizing total elapsed time. A gamma frailty regression model in bivariate survival data David D. Hanagal
University of Pune, India
We propose maximum likelihood estimation procedure for a bivariate fraility regression model in which dependence is generated by a gamma distribution. We assume that the bivariate survival data follow bivariate Weibull of Hanagal (1996) and distribution of censoring variable is independent of the two life times. There are some interesting situations like survival times in genetic epidemiology, survival times of dental implants of patients and survival times of twin births (both monozygotic and dizygotic) where genetic behavioujr (which is unknown and random) of patients follows gamma frailty distribution. These are the situations which motivate to study this particular model. Multivariate process capability using relative importance of quality characteristics K.G. Khadse
M.J. College, Jalgaon, India and
R.L. Shinde
School of Mathematical Sciences, North Maharashtra University, Jalgaon, India We propose probability based multivariate process capability indices (MPCIs) which take into account relative importance of quality characteristics. Two approaches based on (i) modified specification region and (ii) modified process regions, are used to incorporate relative importance. Estimation of the scale parameter of linear exponential distribution using order statistics N.V. Sreekumar and P. Yageen Thomas
University of Kerala, Trivandrum, India
In this paper we have developed an estimator for the scale parameter of linear exponential distribution using an appropriate U-statistic defined by the Best Linear Unbiased Estimator (BLUE) based on order statistics in a random sample of size 2 as the kernel. A comparison of our estimator with the maximum likelihood estimator is also made. Optimum mixture designs for the estimation of the slope of a response surface along component axes Manisha Pal and Nripes Kumar Mandal
University of Calcutta, India
The paper attempts to find optimum mixture designs for the estimation of slopes along the component axes in a second degree model. In the case of two – and three-component mixtures, it has been shown that the optimum design necessarily belongs to the class of Weighted Centroid Designs. The optimum designs have been explicitly derived in these cases.
A two non-identical unit parallel system with geometric failure and repair time distributions Rakesh gupta and Gaurav Varshney
Ch. Charan Singh University, Meerut, India
The paper deals with the cost-benefit analysis of a two non-identical unit parallel system. Both the units function independently. The failure and repair times of each unit are also taken as independent random variables of discrete nature having the geometric distribution with different parameters. The results are also analyzed graphically.
Construction of QQTSORD using central composite designs
R.N. Panda and Soma Roy
Kalyani University, India
In standard response surface designs all factors are quantitative in nature, vide, e.g., Box and Draper [3] and Khuri and Cornell [6]. But there are situations where factors may be both quantitative and qualitative. Adhikary and Panda [2] introduced the quality-quantity type second order rotatable designs (QQTSORD) to cope with such situations. The analysis and method of construction of such designs were considered by them and the method was explained by means of an example with (k,v)=(3,2), where k and v were the number of quantitative and qualitative factors respectively. The design was an orthogonal design. In this paper we have constructed QQTSORD with lesser number of design points. A list of QQTSORD (both orthogonal and non-orthogonal) has been prepared for 3=k=7 and 2=v=5.

A note on the loss of information due to censoring – the Weibull case A.B. Aich
Presidency College, Calcutta
This article is concerned with the loss of information that arises due to Type 1 censoring while discriminating between two Weibull populations. The discrepancy criterion used is due to Kullback and Leibler. An expression for the loss of information is derived.

2007 (Volume 32, No. 1)
Multi-attribute modified group runs control chart to identify process deterioration M.P. Gadre
Mudhoji College, Phaltan, India and
R.N. Rattihalli
Shivaji University, Kolhapur, India
Gadre and Rattihali (2006) proposed a control chart called the ‘Modified Group Runs (MGR) control chart’ to identify increase in fraction non-conforming. In this article, we extend the concept of MGR chart to a multi-attribute case to detect process deterioration. It is shown that in the multi-attribute case also, the MGR chart gives a significant reduction in out-of-control ‘Average Time to Signal’ (ATS) as compared to the other matched multi-attribute control charts (MACCs). In the steady state also, the performance of ‘Multi-Attributes MGR’ (MA-MGR) chart is better. The procedure of identifying the attribute causing signal is also described.
Shrinkage estimation for logarithm of variance of a normal distribution under linex loss function Gyan Prakash
Harishchandra P.G. College, Varanasi, India and B.N. Pandey
Banaras Hindu University, India In the present paper, we study the performance of some shrinkage testimators for logarithm of variance of a Normal distribution when a prior point guess value is available, under the invariant version of the LINEX loss function. Comparison has been made with improved estimator. Prediction interval for the Rayleigh distribution S.P. Mukherjee
Calcutta University, India and N. Dasgupta
Lady Brabourne College, Kolkata, India The paper attempts to find a prediction interval based on type-II censored sample from the Rayleigh distribution that will contain at least m out of k future sample observations.
The normal posterior Bessel distribution M. Masoom Ali
Ball State University, USA and
Saralees Nadarajah
University of Manchester, UK A posterior distribution for the shape parameter of the Bessel function distribution is obtained by deriving the distribution of the ratio X/Y, when X and Y are normal and Bessel function random variables distributed independently of each other.
Bayesian reliability analysis of certain types of systems with discrete failure time Ketan A. Gajjar, K.K. Shah Jarodwala
Mainagar Science College, Ahmedabad, India and M.N. Patel
Gujrat University, India
When lifetime data on a complete system are not available, it is desirable to make use of the operational data on its components. Pursuing this approach, Bayesian reliability analysis of a k-out of n-system and a cold standby system are considered when failure time is discrete. Some simulated results are discussed for illustration.

2007 (Volume 32, No. 2)
On estimation of parameters of consecutive-k-out-of-n : F system with weibully distributed component lifetimes R.L. Shinde
North Maharashtra University, India and M.M. Mahale
University of Pune, India We discuss the estimation of parameters of consecutive-k-out-of-n : F system when lifetimes of components have Weibull distribution with shape parameter ß and scale parameter s. We assume that the system lifetime (T) as well as the number of failed components at the moment of system failure (W) are observable. We obtain estimators of ß and s by using Gadambe’s theory of optimal estimating function. We establish the consistency and asymptotic normality of estimators based on conditional distribution of Ts given W’s. We compare these estimators with the estimators suggested by Aki and Hirano. A probabilistic inventory model for deteriorating items under condition of permissible delay in payment Sanjoy Kumar Ghosh
Vivekananda Mahavidyalaya, Burdwan, India
In many inventory situations, the purchaser is permitted to pay back the cost of purchased goods within a stipulated time, without paying any interest. Depending on the length of that period, the purchaser can earn interest on the sales of the inventory. In this paper, a probabilistic order-level inventory model has been developed for deteriorating items under permissible delay in payment. The model has been illustrated with a numerical example.
A power variance function frailty regression model in vibariate survival data David D. Hangal
University of Pune, India
We propose maximum likelihood estimation procedure for a bivariate frailkty regression model, in which dependence is generated by a power variance function distribution. We assume that the survival data follow bivariate Weibull of Hanagal [6] and distribution of censoring variable is independent of the two life times. Price adjusting sampling plans by variables under double specification scheme Banibrata Roy Maharaja Sayajirao University of Baroda, Vadodara, India This paper tries to study the price adjusting sampling plans for variables when the items are subjected to double specification with respect to a variable for the conformance to quality. The plan parameters are obtained under more general assumptions on the distribution of the variable, using three different methods.
Distribution of quality adjusted life of a product that can exist in three states S.P. Mukherjee and Manisha Pal
University of Calcutta, India
The paper considers a product which can be in three states, viz. ‘functioning’, ‘partially functioning’ and ‘failed’. It can pass from the functional to the failed state directly with probability 1-a(0< a<1) and can pass through a partly functional state before failing with probability a. The times to pass from the functional to the partly functional state and partly functional to the failed state have been assumed to be jointly distributed as bivariate exponential with different means, and they are distributed independently of the time to pass directly from the functional to the failed state, which is assumed to have an exponential distribution. A quality-adjusted life (QAL) has been defined as a weighted total of these durations. The distribution of QAL has been derived and some of its properties studied. Estimation of parameters of the distribution has been carried out and some numerical examples cited.

2008 (Volume 33, No. 1)
Bayesian estimation of change point in inverse Weibull distribution Mayuri M. Pandya and Prabha V. Jadav
Bhavnagar University, Bhavnagar, India
A sequence of independent lifetimes X1,…,Xm, Xm+1,…,Xn was observed from Inverse-Weibull (IW) distribution with reliability R1(t0) at time t0 but later it was found that there was a change in the system at some point of time m and it is reflected in the sequence after Xm by change in reliability R2(t0) at time t0. The Bayes estimators of m under asymmetric loss functions are derived. The Bayes estimators and posterior medians of Reliability R1(t0) and R2(t0) are also derived. The effects of correct and wrong prior information on the Bayes estimates are studied.
A test based on gauging for improvement in process variability under normal model Biswanath Das and Asim Sankar Nag
Presidency College, Kolkata, India
A test for improvement in process variability is essentially a left-tailed test for the process standard deviation. When the underlying distribution is normal with known mean, the UMP test for H0 : s=s0 against H1 : s'<'s0 is the one based on the sum of squares of deviations about the population mean. Another test often used in this situation is based on standardized sample range. Both the tests require actual measurements to be taken on the sample.
In this paper, an alternative test based on the number of observations in the sample falling outside a suitably chosen symmetrical pair of gauges has been suggested, and numerically derived for sample size n=2(1) 25 and test size a=0.05, 0.025, 0.01 and 0.005. The suggested test has a distinct edge over its two rivals in that here inspection can be carried out simply on a go-no-go basis, which will often result in a substantial saving in the testing material, as also in testing time. This feature is particularly appealing when inspection itself is time-consuming and/or destructive in nature, e.g., in life-testing. The test has been compared for power with its two rivals referred to above for selected situations. The proposed test has been found to have favourable performance compared with not only the one based on range, but also with the UMP test.
A Curtailed Inverse Sampling Scheme (CISS) has been suggested for carrying out the proposed test, under which the test can be terminated, even before inspecting the entire sample, resulting in somewhat saving in the amount of inspection. Average amount of inspection for the test has been worked out for selected situations. It has been pointed out that although the two rival tests, too, are amenable to operation under CISS, even on this count the proposed test enjoys a distinct edge over its rivals.
Sampling procedure for Sieve analysis of NPK : 17-17-17 fertilizer D.K. Manna and A.K. Biswas
SQC & OR Unit, Indian Statistical Institute, Chennai, India and
T.S. Arthanari
Department of Information Systems & Operations Management, The University of Auckland, Auckland, New Zealand An important quality requirement of NPK 17-17-17 fertilizer is its particle size distribution. This is inspected through Sieve Analysis as per the specification and procedure of FCO (Government of India). In this article, we reviews the existing sampling procedure with regard to Sieve Analysis at the behest of one particular producer who has been drawn to the court of law on alleged noncompliance. Analysis of relevant clauses reveals inadequacy of the procedure that seeks a revision of FCO. We also provide certain guidelines for evolving sampling procedure on the light of particulate nature of the fertilizer.
Certain results and tables relating QSS-1 with conditional RGS plan K.K. Suresh and V. Kaviyarasu
Bharathiar University, Coimbatore, Tamil Nadu, India
This paper presents procedures and tables for the construction and selection of Quick Switching System with Conditional Repetitive Group Sampling Plan as reference plan indexed with Acceptable Quality Level (AQL), Limiting Quality Level (LQL), Indifference Quality Level (IQL) and its various operating ratios.
On Marshall-Olkin generalized exponential distribution R.V. Parikh
Department of Statistics, Bhavnagar University, Bhavnagar, India D.K. Ghosh
Department of Statistics, Saurashtra University, Rajkot, India and K. Muralidharan
Department of Statistics, M.S. University of Baroda, Vadodara, India
By adding a new parameter, Marshall and Olkin [6] proposed a new family of distributions with applications to the exponential and Weibull families. Such families are theoretically shown to be flexible to apply for accelerated life models and proportional hazards model. The introduction of the new parameter thus makes the model a covariate model in general. We study the inferential problems of Marshall-Olkin generalized exponential model.

2008 (Volume 33, No. 2)
Estimation under progressive type-II censoring for Legth biased exponential distribution G.C. Bhimani
Saurashtra University, Rajkot, India Sumeet H. Arora
Nirma University of Science and Technology, Ahmedabad, India and M.N. Patel
Gujarat University, Ahmedabad, India
Estimation related to parameters of the length biased exponential distribution has been discussed, based on progressively Type II censored samples. Maximum likelihood estimators as well as approximate Bayes estimators of the parameters are developed. A simulation study is considered for different patterns of censoring. A synthetic T2 chart with adaptive sample sizes
V.B. Ghute
K.B.P. Mahavidyalaya, Pandharpur, Solapur, India and
D.T. Shirke
Shivaji University, Kolhapur, India

Recent studies have shown that the synthetic T2 control chart detects process shifts faster than the Hotelling’s T2 chart. In this paper we extend these studies to process that are monitored with variable sample sizes. Simulation results show that the synthetic T2 VSS chart is quicker than the synthetic T2 and the Hotelling’s T2 charts in detecting almost all shifts in the process mean vector. A non-parametric estimate for PR(X'<'Y) Saralees Nadarajah
University of Manchester, Manchester, UK
Georgi K. Mitov
University of Sofia, Sofia, Bulgaria and
Kosto V. Mitov
National Military University, Pleven, Bulgaria
In this paper, we propose a non-parametric estimate of R=PR(X'<'Y) based on a simple property of the uniform distribution. We illustrate the use of the estimate with bootstrap confidence intervals for four commonly known distributions (normal, exponential, gamma and beta). Bayes estimators for the parameters of poisson type-exponential class model using non-informative priors
Rajesh Singh and N.W. Andure
Amravati University, Amravati, India
This paper deals with the estimation of parameters of Poisson type exponential class model for software evaluation. Estimators of the number of failures and failure rate have been proposed under squared error loss function using non-informative priors. These estimators have been compared with corresponding maximum likelihood estimators using Monte Carlo simulation.

2009 (Volume 34, No. 1)
On testing exponentiality against new better than used alternatives Parameshwar V. Pandit
Bangalore University, India and
C.M. Math
K.L.E.’s G.H. College, Haveri, India
In this paper, classes of test statistics for testing exponentiality based on U-statistics and combinations of U-statistics are proposed against new better than used alternative. Asymptotic distributions of the proposed test statistics are studied. Performance of the tests is studied in terms of Pitman asymptotic relative efficiency in comparison with their competitors. The estimated cut off ponts are computed using a simulation study. The power of each proposed test is also evaluated using Monte-Carlo simulation. A simple approach to solve multi-objective shortest path problem K. Karthikeyan
VIT University, Vellore, India
V.S. Sampath Kumar
SRM University, Kattankulathur, India and
P. Pandian
VIT University, Vellore, India
In this paper, we propose a new algorithm to obtain Properly Pareto optimal path from one node to another in a multi-objective shortest path problem using Geoffrion technique.
Pareto distribution in acceptance sampling based on truncated life tests Rosaiah K. and Kantam, R.R.L.
Acharya Nagarjuna University, Nagarjunanagar, India and
Sujbba Rao, R.
Shri Vishnu Engineering College for Women, Bhimavaram, India
Pareto distribution is considered as a life-testing model. The problem of acceptance sampling when the life test is truncated at a pre-assigned time is discussed with a known shape parameter. For various acceptance numbers, various confidence levels and various values of the ratio of the fixed experimental time to the specified mean life, the minimum sample size necessary to assure a specified mean life time worked out. The operating characteristic functions of the sampling plans are obtained. Producer’s risk is also discussed. A table for the ratio of true mean life to a specified mean that ensures acceptance with a pre-assigned probability is provided. Characterization of phase-type distribution under Poisson shock models
M. Manoharan and K. Aneesh Kumar
University of Calicut, India
A phase-type distribution is the distribution of the absorption time (or killing time) in a finite-state Markov Chain and is a generalization of many well-known life distributions. In this article we consider the life distribution H(t) of a device subject to shocks governed by a homogenous Poisson process. It is established that {Pk} – the probability that the device fails on the kth shock-follows a discrete phase-type (DPH) distribution is a necessary and sufficient condition for H(t) to have a continuous phase-type (CPH) distribution, under certain mild conditions. In particular, we prove that H(t) follows exponential (µ) distribution, if and only if {Pk} is a geometric distribution, under the homogeneous Poisson (?) shock model, when ?>µ. Further the result is established under a mixed Poisson model, proving the converse of the theorem given in Manoharan et al. [4]. Some shrinkage testimators for the scale parameter of Weibull distribution Gyan Prakash and D.C. Singh
Department of Statistics, Harish Chandra P.G. College, Varanasi, India
In this paper, the problem of estimation of the scale parameter for the two-parameter Weibull distribution is considered. Some shrinkage testimators are suggested for the scale parameter utilizing the knowledge of prior point guess value. Properties of the proposed testimators have been studied in terms of the relative efficiency. Properties of a Bayes shrinkage estimator are also studied. Inventory policy for a product with price and time dependent seasonal demand and an alternative market Snigdha Banerjee
School of Statistics, Devi Ahilya University, Indore, India and Ashish Sharma
Department of Mathematics, G.L.A. Institute of Technology and Management, Mathura, India
In this paper, we discuss the problem of determining jointly the order quantity and pricing policy for a seasonal commodity, with demand arising in two different markets at different points of time. Demand is price and time dependent, with increasing, constant and declining phases within each demand season in both the markets. After completion of the season at the first market, the distribution can transfer the remaining inventory and sell it in the alternative market having a similar demand pattern, which is repeated with random time between two successive seasons. Partial time dependent backlogging is considered. Concavity of the net profit function is discussed. Numerical examples and sensitivity analysis are presented.
Bayesian analysis of parameter of geometric life time model under multiple type II censorying
J.B. Shah
Department of Statistics, R.J. tibrewal College, Ahmedabad, India and
M.N. Patel
Department of Statistics, Gujrat University, Ahmedabad, India

In this paper, we derive some Bayes estimators of the parameter of geometric life time model under squared error loss, minimum expected loss and linex loss functions for a non-information as well as a beta prioe from multiple Type II censored data. A real life example is considered to demonstrate the results. A simulation study is carried out to study the performance of the Bayes estimator under different choice of prior parameters.

2009 (Volume 34, No. 2)
A deteriorating inventory model for reducing excessive stock by returns and special sales allowing shortages Sanjay Jain, Mukesh Kumar
Government College, Kishangarh, India and
Priya Advani
Government Women Engineering College, Ajmer, India
A deterministic inventory model for infinite time – horizon, incorporating deterioration and shortages is developed. The salient feature of the model is the introduction of two different costs corresponding to returning and selling of items, so as to suit some real life situations. It has been assumed that a certain amount of inventory is returned and the remaining is disposed of through sales at reduced price. Sensitivity analysis is carried out to show the interdependence of the amount to be returned and/or sold with the costs involved. Some new asymmetric orthogonal arrays from lengthened BCH codes Seema Gupta
Ram Lal Anand College, New Delhi, India
This paper presents a method for the construction of some new asymmetric orthogonal arrays of higher strength through extended or lengthened BCH codes using some fundamental results from coding theory.
An interference model with number of stresses a Poisson process J. Gogoi, M. Borah and G.L. Sriwastav
Tezpur University, India
In this paper an n-standby S-S system is considered where the number of impacts of stresses faced by the system is a Poisson process. The expression for reliability of the system Rn is given for n<4. In particular when both stress and strength follow either exponential or gamma or normal or Weibull distribution, expressions of reliability have been worked out. Some numerical results have also been presented. Single sampling plan based on generalized exponential distribution
M.R. Sindhumol
University of Madras, Chennai, India
Generalized Exponential Distribution (GED) is considered as a model for lifetime random variable. The dproblem of developing a Single Sampling Plan when the life test is truncated at a pre-assigned time is discussed. The Operating Characteristicd (OC) function is studied by considering Consumer’s risk and Producer’s risk. Tables are provided for the selection of plan parameters.
Construction and selection of quick switching multiple sampling system-sample size tightening S. Devaraj Arumainayagam
Government Arts College, Coimbatore, India and
G. Uma
PSG College of Arts and Science, Coimbatore, India
A sampling inspection system involving normal and tightened plans is presented procedures and tables are given for the selection of Quick Switching System with Multiple Sampling Plan as the reference plan. Advantages of the system are highlighted.
Count of runs of length two in binary sequences M.P. Gadre
University of Pune, Pune, India and
R.N. Rattihalli
Shivaji University, Kolhapur, India
In this note we derive some results related to the number of counts of different types of runs of length two in binary sequences. These results are useful to develop attribute control charts based on a single attribute under Markovian dependence.

2010 (Volume 35, No. 1)
Optimum designs in accelerated life testing problems : a Bayesian approach Manisha Pal and Nripen Kumar Mandal
Department of Statistics, Calcutta University, India

In accelerated life testing experiments, the life of an item is affected by the stress on it, which may be caused by a number of factors. In this paper we use exponential regression model to represent the lifetime of an item as a function of the stress factors and attempt to find the optimum choice of factors levels using D-optimality, assuming a suitable prior for the regression parameters. Bayes estimation of residual entropy function from classical Pareto model containing spurious observations E.I. Abdul-Sathar
University of Kerala, Trivananthapuram, India
E.S. Jeevanand
Union Christian College, Ahurva, India and
g. Rajesh
D.B. College, Perumala, India
We consider the problem of estimation of residual entropy function of the presence of outliers for the classical Pareto distribution. Bayes estimates are derived for exchangeable and identifiable cases. Bayes estimators have been developed under squared error loss function as well as under LINEX loss functions. The estimators are applied to datas on tournament earnings data. Monte Carlo simulation is carried out to compare the bias and the expected loss of proposed estimators.
On characterization of uniform distribution using reliability concepts P. Yageen Thomas and Minimol, S.
Department of Statistics, University of Kerala, India
In this paper we consider some characterization results of uniform distribution based on certain reliability concepts such as reversed hazard rate and past entropy. We define a new concept called conditional measure of uncertainty in the past life and a new class of distributions based on this.
Reliability of a system with varying workload and fast repair by using Weibull failure and repair time distribution Kirti Arekar
K.J. Somaiya Institute of Management Studies and Research, Mumbai, India
Reliability model with varying workload and fast repair is studied. Initially, one unit is operative and other is kept as standby. When workload increases a fast repair facility is available. Study has been made about two-identical-unit deteriorating standby system when workload increases arbitrarily for some random duration. Failure time distributions of the units are assumed to be exponential with different parameters, while repair time distributions are arbitrary i.e. time dependent. Using regenerative point technique, measures of reliability are obtained.
On optimal replacement of a multi-state deteriorating system K. Aneesh Kumar and M. Manoharan
University of Calicut, Kerala, India
A multi-state system subjected to homogenous Poisson shocks gets deteriorated according to the magnitude of shocks received. With a known distribution of shock magnitude, the life distribution of the system is modeled under Phase Type distribution assumption. A numerical illustration narrates the method even if the probability distribution of the shock magnitude is unknown. An optimal preventive replacement time for the system which minimizes the long run cost per unit time is discussed. Discrete Birnbaum-Saunders distribution and its properties related to reliability analysis Subhradev Sen
Pondicherry University, Pondicherry, India Mithu Dey
Asansol Engineering College, Kanyapur, India and
Sudhansu S. Maiti
Visva-Bharati University, Santiniketan, India
The continuous two parameter Birnbaum-Saunders distribution (BSd) has several applications in reliability science and engineering. It can be successfully applied to model failure times of metals under fatigue. We come across situations where lifetime of a device is considered to be a discrete random variable. In this article, discrete Birnbaum-Saunders distribution (dBSD) has been defined following the discrete concentration approach. Some reliability characteristics of this distribution have been studied. Maximum Likelihood Estimation procedure for estimation of parameters has been mentioned. Data sets have been analyzed using this distribution.

2010 (Volume 35, No. 2)
Stochastic model for the cumulative effects of industrial accidents-SCBZ property t. Chitrakalarani
Kundhavai Naachiar, Government Arts College (W), Thanjavur, Tamil Nadu
In this paper the expected time to reach the breakdown point is obtained by assuming that the threshold variable is a random variable which satisfies the ‘setting the clock back to zero (SCBZ)’- property. Cost benefit analysis of two-unit parallel systems with correlated failure and repair times Rakesh Gupta and Shivakar
C.S.S. University, Meerut, India
The paper deals with the cost benefit analysis of two stochastic models, each consisting of two non-identical units connected in parallel. In each model it is assumed that a unit has two modes (Normal and Failed) and the repairman is not available always with the system. A general waiting time distribution is considered whenever a failed unit waits for the availability of repairman. Failure and repair time distributions of each unit are taken to be Bivariate Exponential in one model, whereas the distribution of life times of the units is assumed to be Bivariate Exponential in the other. Standby redundant system reliability with imperfect switching in discrete stress-strength model K.A. Gajjar
K.K.S.J. Maninagar Science College, Rambaug, Maninagar, Ahmedabad and M.N. Patel
School of Sciences, Gujarat University, Ahmedabad
The problem of estimating reliability under stress-strength model plays an important role in reliability analysis. In this article, we have considered an n-cold standby system with imperfect switches in stress-strength model. Each of the stand-by components has its own switching device. Under geometric stress and different types of strength reliability experiments are performed. Numerical values are also tabulated for different models. Cascade system with random attenuation factor C. Doloi, M. Borah and G.L. Sriwastav
Tezpur University, Assam
This paper deals with an n-cascade system for which the attenuation factor K is assumed to be a uniform random variable in (0,1). Here the unconditional reliability of the system is given by the expected value of Rn(K), where expectation is taken w.r.t the distribution of K. In particular when both stress-strength are either exponential or gamma or Weibull distributions the unconditional reliability is evaluated in each case. We also consider the case when stress follows gamma and strength follows exponential distribution. In some cases expressions could not be obtained in closed form. For such cases, some numerical integration methods are used to evaluated these reliabilities. For all the cases some numerical values of reliability are tabulated, for a few particular values of the parameters involved.
Construction and selection of Bayesian RGS plan through incoming quality levels K.K. Suresh, V. Sangeetha and M. Kavithamani
Department of Statistics, Bharathiar University, Coimbatore, Tamil Nadu
According to Sherman (1965), under Repetitive Group Sampling (RGS) plan, the number of defectives are counted, and then, according to a fixed criterion, the lot is either accepted, rejected or the sample is completely disregarded, and begin over again with a new sample. This is continued until the fixed criterion tells either to accept or reject the lot. One should not even keep track of how many times a sample is repeated. Bayesian Sampling Plan is that experimental or analytical study which can yield prior frequency distribution for the quality of the submitted lots and these ‘prior’ distributions can in turn be used to derive lot-by-lot sampling plans. In this paper, selection of Bayesian RGS plan is provided through various set of incoming quality levels. The average probability of acceptance function and the formula for overall average incoming quality level for Bayesian Repetitive Group Sampling Plan (BRGS) are derived and tables are given towards shop-floor industrial situations.


IAPQR Transactions

DURING 2011 TO 2015


2011 (Volume 36, No. 1)


A multivariate modified group runs control chart for process dispersion

M.P. Gadre

Department of Statistics, University of Pune, Pune, India

P.G. Dixit

Department of Statistics, Modern College, Pune


In this article, we propose the ‘Modified Group Runs’ (MGR) charts useful to detect a shift in the process variability in case of bivariate and multivariate normal data. It is verified that the proposed charts significantly reduce the out of control ‘Average Time to Signal’ (ATS) as compared to the most of the well-known control charts. The control charts considered for comparison are the standard S chart, adaptive sample size chart, the synthetic S chart (Ghute and Shirke, 2008) and the GR S chart.


Estimation of optimal order quantity in newsboy problem

S.P. Mukherjee

Department of Statistics, University of Calcutta

Ayan Chandra

Department of Statistics, St. Xavier’s Coollege, Kolkata


This paper deals with the estimation of optimal order quantity in the classical newsboy problem, with an exponential demand distribution. Apart from the parametric and non-parametric estimates, the Bayes’ estimates have also been worked out under Gamma prior for squared error loss function and loinex loss function. The corresponding cost estimates have also been obtained. Some numerical examples have also been worked out.


Inference on generalized process capability index

Sudhansu S. Maiti and Mahendra Saha

Visva-Bharati University, Santiniketan, India


Inferential and aspects of a generalized process capability index, i.e. the ratio of proportion of specification conformance to proportion of desired conformance, has been considered. Normal exponential (non-normal) and Poisson (discrete) processes have been taken into account. Under each distributional assumption, small sample as well as large sample properties of point estimators of the proposed index have been studied and lower confidence limits (lcls) have been constructed. A few data sets have been analyzed.


A stochastic inventory system with renewal demands and full backlogging

A. Shophia Lawrence, B. Sivakumar and G. Arivarignan

Madurai Kamraj University, Madurai, India


This article considers a continuous review inventory system with full backlogging of demands that occur during the stock out periods. The demand occurrence times are assumed to form a renewal process. A modified (s,S) ordering policy which allows placement of l orders each of size Q=S-s, where l is the largest positive integer less than or equal to S/Q, is considered. The lead times are independent and identically distributed as exponential. The inventory level distribution in the steady state is obtained and the results are illustrated numerically.


Conditional test for trend in Cox process

Rupal Shah and K. Muralidharan

Department of Statistics, Faculty of Science, The M.S. University of Baroda, Vadodara, India


The power law model is the most commonly used model in the class of nonhomogeneous Poisson process (NHPP), for the repairable systems. If the power law model is rejected by a goodness-of-fit test, other NHPP models can be fitted and tested. One such model was proposed by Cox and Lewis (1966) with intensity function l(t) = exp (a + bt). In this paper, we study some inference problems and propose a conditional test by exploiting the sufficient statistics for testing the shape parameter b, treating the other parameter as nuisance parameter. We have performed a simulation study to compute the power of the proposed test.



2011 (Volume 36, No. 2)


Perishable-inventory model under inflation and delay in payment allowing partial payment

Deepa H. Kandpal and Khimya S. Tinani

Department of Statistics, Faculty of Science, The M.S. University of Baroda


This paper develops a model to determine an optimal ordering policy for deteriorating items under inflation, permissible delay of payment and allowable shortage for future supply uncertainty. In this paper we have introduced the aspect of part payment. A part of the purchase cost is to be paid during the permissible delay period. We consider order quantity/reorder-point inventory models where the availability of supply is subject to random fluctuations. We use concepts from renewal reward processes to develop average cost objective function. In many inventory situations, purchasers are allowed a period to pay back for the goods bought without paying any interest. Depending on the length of that payment period, the purchaser can earn interest on the sales of the inventory. The effect of inflation period, the purchaser can earn interest on the sales of the inventory. The effect of inflation and time value of money was investigated under given sets of inflation and discount rates. Optimal solution is obtained using Newton Raphson method in R programming. Finally sensitivity analysis of the varying parameter on the optimal solution is done.


Classical and Bayesian stochastic analysis of an industrial system

Rakesh Gupta, Bhupendra Singh

Department of Statistics, C.C.S. University, Meerut (U.P.), India

Punam Phartyal

Department of Statistics, H.N.B. Garhwal University, Srinagar-Garhwal (U.K.)


The purpose of this study is to compute reliability and other measures of system effectiveness by classical and Bayesian approach of a milk packaging plant consisting of five sub-systems arranged in series. The functi9oning of all subsystems depends upon the electric power supply through main grid or cold standby generator. Failure time distributions of power supply, generator and all the five subsystems are considered as exponential. Repair time distributions of po9wer supply and generator are also taken exponential whereas the repair time distributions of all the five subsystems are assumed to be general. The maximum likelihood estimates (m.l.e) of reliability, mean time to system failure (MTSF), availability and net expected profit obtained. A. Bayesian approach is adopted to evaluate these measures by taking different priors. Monte Carlo Simulation is used to derive the posterior values of these measures.


Estimating the parameter m of the exponential distribution with known coefficient of variation using censored sample by order statistics

N.K. Sajeevkumar

Department of Statistics, Govt. College Kariavattom, Trivandrum, India

M.R. Irshad

Department of Statistics, University Library, University of Kerala, Trivandrum, India


In this paper, we have obtained an estimator of m of the exponential distribution E(m, c2m2) with known coefficient of variation ‘c’, using censored sample by order statistics. Efficiency76 comparisons are also made on the proposed estimators with some of the usual estimators of m.


Cumulative sum control chart for Gamma process variate

R.R.L. Kantam, K. Rosaiah

Department of Statistics, Acharya Nagarjuna University, Guntur, India

B. Sriram

Department of Mathematics and Statistics, AAR & BMR Degree College, Nunna, Vijayawada (Rural), India


Sequential probability ratio procedures are used in construction of a cumulative sum control chart for a variable process characteristic. The distribution of process variate is assumed gamma with shape parameter 2. The construction of mask and values of average run length are also presented. Such a chart is useful in early detection of shifts in the process average.


2012 (Volume 37, No. 1)


Identical stress for a warm standby system with imperfect switching

J. Gogoi and M. Borah

Tezpur University, India


A warm standby redundant system has been considered in which switching mechanism is not perfect. Strengths of different components and stresses on them are all independent random variables. Here exponential, gamma and normal distributions have been assumed for identical stresses. System reliability Rn is obtained n<3, when stress-strength of components and the switch follow particular distributions. System reliability Rn have been estimated based on the general expressions derived from different distributions viz. exponential, gamma and normal.


Minimization of unconstrained non-linear functions by numerical algorithms

K. Karthikeyan

School of Advanced Sciences, VIT University, Vellore 632 014, India


In this paper, we propose new iterative algorithms for minimization of unconstrained nonlinear functions, based on two-step quadrature. A comparative study among the two new algorithms and Newton’s algorithm has been established.


Second order response surface designs involving quantitative and qualitative factors under split-plot structure

Manohar Aggarwal

University of Memphis, Memphis, USA

Anita Bansal

Ramjas College, New Delhi, India

Sanjoy Roy Chowdhury

Lady Shri Ram College, New Delhi, India

Archana Verma

P.G.D.A.V. College, New Delhi, India


Draper and John [8] gave highly rotatable second order response surface designs uner split plot structure for quantitative factors. In this paper we develop response surface designs under split-plot structure involving both quantitative and qualitative factors using the designs given by Draper and John [8]. We have considered the qualitative factor as hard to change factor in all the designs.



An EOQ model for deteriorating items with variable rate of deterioration

Bala Srinivasan and E. Joanna Kezia

Madras Christian College, India


In this paper, an inventory model for items that deteriorate over time is considered. The demand at any instant of time t is assumed to be deterministic in nature. The rate of deterioration is a linear function dependent on time. Shortages are fully backlogged and there is no lead time. The optimum order quantity and the optimum time of placing the order are calculated for the model. Also numerical illustrations are provided to show the working of the model.


Reliability testing through acceleration – A new approach

R. Muthukumar

Centre for Reliability, Chennai

K. Senthamaraikannan

Manonmaniam Sundaranar University, Tirunelveli


Accelerated Reliability testing is adopted with the single purpose of quantifying life characteristics of products at normal use conditions by testing these products at elevated stress conditions. An acceleration model suitable to the failure mechanisms is combined with the normal distribution of time-to-failure and an attempt is made to assess reliability characteristics of a product.


2012 (Volume 37, No. 2)


A cascade model with random parameters

C. Doloi, M. Borah and G.L. Sriwastav

Department of Mathematical Sciences, Tezpur University, India


In this paper a 2-cazscade system is considered where stress and strength are exponential variates and one of the parameters (stress or strength) is assumed to be random with a known prior distribution, the other parameter remaining constant. Using the derived compound distribution, reliability of the 2-cascade system is obtained. Uniform and Two point distributions are taken as the prior distributions for the parameters concerned. For all the cases, some numerical values of reliability are tabulated at the end.


Forecasting daily workflow volumes for medical transcription process

Shri Ashok Sarkar

SQC & OR Unit, Indian Statistical Institute, Mumbai, India

Arup Ranjan Mukhopadhyay

SQC & OR Unit, Indian Statistical Institute, Kolkata, India

Sadhan Kumar Ghosh

Dept. of Mechanical Eng. Jadavpur University, Kolkata, India


Effective utilization of manpower is a vital issue in a service industry. It depends on the prediction accuracy of inflow work volume. For a transcription process, variation of inflow has been modeled by adopting four methods. It is found that the effect of annual holidays can be better explained through regression method. Consequently, a model has finally been developed by combining regression and seasonal ARIMA. It has been found that the model accuracy is much better compared to the method that prevails in this business vertical. Implementation of the proposed method establishes the potential for increased manpower utilization.


On G’ class of lifetime distributions and a test for geometricity against G’ class

K.K. Jose

St. Thomas College, Pala, India

K.V. Jayamol

Maharaja’s College, Ernakulam, India


Two new classes of life time distributions based on ordering of alternate probability generating function (apgf) are introduced. Some properties of these classes are discussed and various results are established. We propose tests for geometricity against G* class as a discrete counter part for the test of exponentiality versus L class.


Double stage shrunken testimators of the scale parameter of an exponential distribution under general entropy loss function

Rakesh Srivastava

Department of Statistics, M.S. University of Baroda, Gujarat, India

Tejal Shah

Acharya Motibhai Patel Institute of Computer Studies and Management, Gujarat, India


The present paper proposes two shrinkage testimators for the scale parameter of an exponential distribution when a double stage sample is available. The shrinkage factor being dependent on test statistics behaves as per the choice of level of significance. Recently many estimation/testimation procedures have been considered using General Entropy Loss Function (GELF). This study is an attempt to observe the performance of shrinkage testimators under GELF. Recommendations regarding its applications have been attempted.


Optimization of censoring strategies for life-testing under two-parameter exponential model

B. Das

Presidency College, Kolkata, India

S.P. Das

College of Textile Technology, Berhampore, W.B., India


For failure censored data, a minimax test based on the number r of failures, has been derived for the shape parameter of a 2-parameter exponential distribution for various (n,a) combinations in this study. A hybrid censoring scheme has been suggested in this situation, and a minimax test has been derived under this scheme as well for various (n,a) combinations. The tests have been compared for performance in terms of power, as well as cost in terms of average testing time (ATT). It appears that the two tests show almost identical performance, although the one based on hybrid censoring is better off in terms of ATT for small to moderate shifts, which are crucial, in addition to the simplified record-keeping and analysis involved.


2013 (Volume 38, No. 1)


A study of random walk approach in economic sampling plan

Banibrata Roy

Department of Statistics, Maharaja Sayajirao University of Baroda, India


A random walk approach has been considered in formulating the optimal plan parameters of a three class two decision price adjusting sampling plan in contrast to the trinomial distribution involving 3 parameters, with the items classified into three categories as good, marginal and bad. The relative advantages of the random walk model (RWM), its properties including producers and consumers risk and operating characteristic (O.C.) function are discussed. The plan parameters are determined by considering no loss-no gain approach in terms of unit pay off ratio, illustrated through a suitable case study to explain the advantage of using this RWM over the existing traditional method.


On a property of generalized record values arising from exponential distribution

Jerin Paul and P. Yageen Thomas

Department of Statistics, University of Kerala, India


In this paper we derive the Rényientropy of Generalized Record Values and hence we establish a characterization property of a exponential distribution function within a specified family of distributions considered.


Reliability approximation with extent of error for a hollow rectangular tube under the Weibull and Rayleigh setups

Sadananda Nayak

Ramakrishna Mission Vidyabhaban, W.B., India


Determination of reliability of a hollow rectangular tube under the stress-strength model is an analytically intractable problem. This paper aims at adopting a different approach for reliability approximation along with the idea of extent of error. Here, we have approximated reliability based on upper and lower bounds. The reliability bounds being both item and setup dependent, we have studied reliability bounds for a hollow rectangular tube under the well known Weibull model. We have also considered a particular case of Weibull distribution, i.e. the Rayleigh setup. Numerical analyses have also been worked out to study the usefulness of this bound-based reliability approximation. In the absence of analytical expression of reliability value, the proposed method will be very helpful to reliability planners during the early stages of product design in terms of the design parameters.


Confidential limits for stationary rate of disappointments of an intermittently used two unit standby system

P. Chandrasekhar

Department of Statistics, Loyola College, Chennai, India

A.. Vincent Raja

Department of Mathematics, Statistics & Physics, University of Guyana, Georgetown, South America


A two unit cold standby system meant for intermittent use with a single repair facility is considered, wherein the failure and repair rates of the unit are assumed to be constants. Also, failure rates during the need and no-need periods are assumed to be different constants. An expression for the stationary rate of disappointments, along with a CAN estimator and 100 (1-a) % asymptotic confidence interval for the same are obtained.


Estimating the mean of the normal distribution with known coefficient of variation by U-statistics

N.K.  Sajeevkumar

Department of Statistics, Govt. College Kariavattom, Trivandrum, India

M.R. Irshad

Department of Statistics, University of Kerala, Trivandrum, India


In this work we propose a technique of estimating the mean m of a normal distribution with known coefficient of variation by U-statistics constructed by taking best linear functions of order statistics as kernels. The efficiency comparison of the proposed estimators with respect to moment estimator is also made.


Construction and selection of one plan suspension system with repetitive deferred sampling

K. Indira and K.K. Suresh

Department of Statistics, Bharathiar University,  Coimbatore, India


This paper provides a new procedure for designing and Selecting a One Plan Suspension System with Repetitive Deferred Sampling Plan as the reference plan. Tables and procedures are also provided for the selection of parameters for the plan. Some numerical illustrations are also provided for shop-floor applications of these procedures.


2013 (Volume 38, No. 2)

 Estimating the common mean and common standard deviation of several distributions by ranked set sampling

R.S. Priya and P. Yageen Thomas

Department of Statistics, University of Kerala, Trivandrum, India


In this paper we propose a ranked set sampling procedure to estimate the common location and scaleparameters of several distributions. Efficiency comparison of the proposed estimators with some other standard estimators is illustrated for logistic and double exponential distributions.


On the distribution of the number of stranded customers in a M/M(b,b)/1 queuing system

Kuntal Bakuli and Manisha Pal

Department of Statistics, University of Calcutta, India


The paper studies a queuing model with Poisson arrival process and bulk service. The server serves the customers in batches of fixed size b, and the service time is assumed to be exponentially distribution. The model is analyzed to find the steady-state distribution of the number of customers stranded following each service. The approach adopted is based on discrete-time Markov chains, instead of Laplace transforms that is usually used in literature. A simulation study is carried out to estimate the expected number of stranded customers at any point of time, its variance and the downside risk for given values of the system parameters.


A discrete parametric Markov-chain model of a two unit warm standby system with rest period of repairman

Rakesh Gupta and Parul Bhardwaj

Ch. Charan Singh University, India


The paper deals with the profit analysis of a two-identical unit warm standby system assuming two modes – normal and total failure. A single repairman is always available with the system to repair a failed unit. The repairman goes for rest after working for a random period of time and, after taking rest, he again starts the repair of a failed unit. The random variables denoting the failures and repair times of a unit, working time and rest time of repairman are independent and have geometric distributions with different parameters. The various measures of system effectiveness are obtained by using regenerative point technique.


A discrete time inventory system with postponed demands and infinite pool

B. Sivakumar, C. Alexander and G. Arivarignan

Madurai Kamraj University, Madurai, India


This article considers a discrete time inventory system in which demand occurs according to a Bernoulli process. The inventory is replenished according to an (s,S) inventory policy and the replenishing times are assumed to have a geometric distribution. Demands that occur during the stock-out period either enter a pool of infinite capacity or are considered to be lost. The demands in the pool are selected one by one according to first-come first-serve discipline, only when the replenished stock level is above S, so that the time interval between any two successive selections is distributed as Bernoulli. This system is modeled as a quasi birth and death process and the necessary and sufficient condition for stability of the system is derived. Using matrix geometric method, we derive the steady-state probability vector of this model. Various system performance measures in the steady state are derived and the total expected cost rate under a suitable cost structure is calculated. The results are illustrated numerically.


Concomitants of K-record values from Kibble’s bivariate Gamma distribution

Shy Mary, M. and Manoj Chacko

University of Kerala, Trivandrum, India


In this paper, we have obtained the means, variances and covariances of the concomitants of lower k-record values. Then, we use these moments to calculate the best linear unbiased estimator for the scale parameter of Kibble’s bivariate gamma distribution.


2014 (Volume 39, No. 1)

On R-norm past entropy measure

Minimol, S. and P. Yageen Thomas

Department of Statistics, University of Kerala, Trivandrum


We introduce the concept of R-norm entropy in past lifetime. Certain ordering and aging properties based on R-norm past entropy measure are discussed. Further, characterization problems using the proposed measure is also dealt with.


Reliability of a multi-component system under repeated attacks

K. Sandhya and T.S. Umamaheswari

Department of Mathematics, Kakatiya University, India


In this paper, a multi-component system has been taken when stress-strength of each component is assumed to be a mixture of two exponential distributions and the general expression for reliability is derived under repeated attacks. The time survival function of the system is obtained when attacks on the system occur as Poisson arrivals.


A nonparametric group runs control chart to detech shifts in the process median

M.P. Gadre

University of Pune, Pune, India


In this article, we propose a ‘Nonparametric ‘Group Runs’ (GR)’ control chart to detect shifts in the process median based on the signed-rank statistic. A nonparametric Shewhart-type synthetic control chart by Pawar and Shirke (2010) is also based on the signed-rank statistic. It is verified that, a Nonparametric ‘Group runs’ control chart gives a significant reduction in out-of-control ‘Average Time to Signal’ (ATS) as compared to a ‘Nonparametric Shewhart-type synthetic’ control chart as well a nonparametric Shewhart control chart when in-control ATS is not smaller than a certain number.


Statistical analysis for a two service point tandem queue with varying service rate

Paul Savariappan

Luther College, Decorah, Iowa -   52101, USA

V.S. Vaidyanathan

Pondicherry University, Puducherry – 605 014, India

P. Chandrasekhar

Loyola College, Chennai – 600 034, India


A two service point tandem queue with zero queue capacity and with blocking is considered, where the arrivals occurs according to Poisson process and the service time is governed by the generalized Erlang distribution. An estimator based on sample moments, a consistent asymptotic normal (CAN) estimator and the asymptotic confidence interval for the expected service time per entity in the system are obtained. Numerical study is carried out to demonstrate the behavior of the expected service time per entity in the system by simulating samples from exponential distribution and from generalized Erlang distribution.


A study on statistical assessment of agreement

Montip Tiensuwan

Department of Mathematics, Faculty of Science, Mahidol University, Bangkok, Thailand

Bikas K. Sinha                        

Retired Faculty, Indian Statistical Institute, Kolkata, India


We propose to discuss briefly some aspects of assessment of agreement with reference to two actual studies conducted in Thailand and USA each. The first study dealt with extraction of some features of Diabetie, Retinopathy (DR) and Macular Edema (ME). Four different ‘expert’ groups were engaged in the process. The second study refers to a ‘gold standard’ instrument and two ‘competing’ instruments in the screening of carotid stenosis.


Moment type estimation in linear failure rate distribution

R.R.L. Kantam, M. Ch. Priya and M.S. Ravikumar

Department of Statistics, Acharya Nagarjuna University, Nagarjunanagar, India


The reparameterised Linear Failure Rate Distribution (LFRD) version as given in Sen [2] is used to develop moment type estimation. Though the estimates are implicit in nature, values of the estimates are calculated in an analytical way with the help of an exclusively developed auxiliary table. The information matrix is also constructed. Comparison of the proposed moment type estimates with the MLEs of the parameters is made.


2014 (Volume 39, No. 2)

An alternative solution to a simple inventory problem

S.P. Mukherjee and Ayan Chandra

Indian Association for Productivity, Quality & Reliability and

Department of Statistics, St. Xavier’s College, Kolkata

The optimum order quantity for a static inventory model with random demand as well as random supply varying around the order quantity have been worked out by minimizing the prior as also the posterior expected total cost. Exponential demand along with gamma prior and uniform as well as triangular distribution of supply have been used and some illustrative calculations provided.


Selection of quick switching system with repetitive deferred sampling plan through minimum angle method

K.K. Suresh, Anamiya Baby and Pradeepa Veerakumari

Department of Statistics, Bharathiar University, Coimbatore

This paper explains elaborately the designing of quick switching system with repetitive deferred sampling plan as reference plan of type QSRDSS-1 for i-2 through minimum angle method. Procedures and necessary tables are provided for the selection of sampling system through minimum angle criteria involving producer and consumer quality.


An approximation approach for evaluating reliability of resistor under stress-strength model

Sadananda Nayak

Ramakrishna Mission Vidyabhaban, Midnapore, India

Analytical expressions for reliability of complex systems are sometimes pretty involved. We have approximated system reliability based on bounds for Resistor. Taylor’s series expansion, Monte carlo simulation and discretization were used earlier approximating system reliability of complex engineering items. But these methods fail to provide an expression for the level of error. The present work offers level of error in terms of design parameters.


Ranked set sampling and extreme ranked set sampling in estimating a parameter of Morgenstern type bivariate logistic distribution with known coefficients of variation

N.K. Sajeevkumar1, Sumi, A.R2. and Irshad, M.R3.

1 & 3Department of Statistics, Govt. College Kariavattom, Trivandurm – 695 581

2 University Library, TVPM, University of Kerala

In this work we apply Ranked Set Sampling and Extreme Ranked Set Sampling to estimate a parameter of Morgenstern Type Bivariate Logistic Distribution (MTBLD) with equal (but known) coefficients of variation ‘c’. Using both the methods of ranked set sampling we propose estimators for the unknown parameter m2 of MTBLD based on the observations available and also make efficiency comparisons on the proposed estimators.


Inventory model for non-instantaneous deteriorating items with stock and time dependent demand, price discount and partial backlogging

Manisha Pal and Sujan Chandra

Department of Statistics, University of Calcutta, India and Haldia Govt. College, Haldia, India

In this paper we study a periodic review inventory model for non-instantaneous deteriorating items when demand is dependent on the stock on hand and time. To boost up the demand, the inventory manager offers a temporary discount on the selling price before the items start to deteriorate and a higher discount when the items begin to deteriorate. When the stock on hand is exhausted, a price discount is given to the customers who are willing to backorder their demand. The optimum policy is determined so as to maximize the total expected profit of a reorder interval. Numerical examples are cited to illustrate the model.


Properties and the use of half normal distribution in ROC curve analysis

R. Vishnu Vardhan and Kiruthika, A.C.

Pondicherry University, Puducherry

In this paper, an attempt is made to derive the properties of Half Normal Distribution in ROC analysis. A functional relationship between the accuracy measure AUC and Kullback – Leibler divergence (KLD) is established. Testing significance of the accuracy measure has also been addressed.


2015 (Volume 40, No. 1)

System reliability with imprecise constant failure rates of components

A.K. Shaw and T.K. Roy

Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah 711 103

In this paper we have considered that constant failure rate of the components are fuzzy in nature. Here the failure rate of components is taken as trapezoidal fuzzy number. The reliability function of system reliability is expressed in terms of fuzzy number of the components reliability. Simple reliability models are taken in fuzzy environment and then its reliability is analyzed. Fuzzy system reliability of series system, parallel system, k out of a system and cold standby system are approximated. Then the corresponding left and right divergences are computed, which are occurring due to approximation of system reliability. Numerical examples are given to illustrate the approaches.


Interval estimation for the measures of ROC curve underlying half normal and Rayleigh distributions

S. Balaswamy and R. Vishnu Vardhan

Department of Statistics, Pondicherry University, Pondicherry 605 014

In this paper, confidence intervals are constructed for Area under the ROC Curve and b along with this the importance and influence of the ratio b is also focused under the mixture of Half Normal and Rayleigh distributions. Further, inferential procedure for testing the AUC against random classification is also addressed. The proposed methodology is supported by simulation studies.


Role of least count of a gage in statistical process control

Department of Statistics, School of Mathematical Sciences

We have studied the impact of least count of a gaps in accordance with the goodness of fit test and capability analysis of the quality characteristic. We consider normal and exponential distributions as these are commonly encountering probability distributions in many processes. We observed that goodness of fit test for exponential distribution is severely affected by rounding resulted due to gage used, than for normal distribution. Impact of rounding is more severe in the case of goodness of fit test as compared to capability analysis based on part per million defectives. Simulations and computations are based on MATLAB programs.


Response surface designs involving qualitative factors using moment aberration designs

M.L. Aggarwal

Department of Mathematical Sciences, University of Memphis, Memphis, USA

Anita Bansal

Department of Statistics, Ramjas College, University of Delhi, India

S. Roy Chowdhury

Department of Statistics, Lady Shri Ram College, University of Delhi, India and

Neena Mital

Department of Statistics, ram Lal Anand College, University of Delhi, India

Response surface Methofology involving both qualitative and quantitative factors have been studied byDraper and John (1988), Wu and Ding (1998), aggarwal and Bansal (1998), Aggarwal, Gupta and Bansal (2000) and Aggarwal et al. (2006a), when quantitative factors are at five levels. Aggarwal et al. (2006b) developed second order response surface designs when quantitative factors are at three levels. Xu and Deng (2005) gave moment aberration criteria for ranking and classifying non-regular designs. In this paper, we have developed second order response surface designs when quantitative factors are at three/five levels using 16-run, 20-run and 27-run moment aberration designs.


Shared frailty models based on reversed hazard rate for modeling Australian twin data

David D. Hangal and Arvind Pandey

Department of Statistics, University of Pune, Pune 411 007, India

In this paper, we introduce the shared gamma frailty model and the inverse Gaussian frailty model with the reversed hazard rate and the generalized log-logistic distribution as the baseline distribution. We introduce the Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in the model. We present a simulation study to compare the true values of the parameters with the estimated values. Also we apply these proposed models to the Australian twin data set and suggest a better model.