Some recent results for series system reliability

Asymptotic properties of key test results ate obtained. Some further results on the Lindstrom-Madden method are given, including a binomial-Poisson inequality, together with some numerical examples. Simplified proofs of some results of Pledger and Proschan (1971) and Nevius, Proschan and Sethuraman (1977) are provided and the listing of a FORTRAN program to calculate a lower bound to the 1-α lower confidence limit on the system reliability is given.     

Distribution theory and inference for polynomial-normal densities

This paper considers a class of densities formed by taking the product of nonnegative polynomials and normal densities. These densities provide a rich class of distributions that can be used in modelling when faced with non-normal characteristics such as skewness and multimodality. In this paper we address inferential and computational issues arising in the practical implementation of this parametric family in the context of the linear model. Exact results are recorded for the conditional analysis of location-scale models and an importance sampling algorithm is developed for the implementation of a conditional analysis for the general linear model when using polynomial-normal distributions for the error.     

On Hacking's fiducial theory of inference

Fisher's theory of fiducial inference is known to lead to mathematical inconsistencies. Hacking (1965) puts forward a new basis for fiducial inference. In this paper we have presented Hacking's theory retaining his original terminology but replacing his notation by more usual mathematical notation. His condition of irrelevance is derived in an explicit mathematical form, making it more comprehensible to statisticians. Further an example is constructed to show that Hacking's theory also leads to mathematical inconsistencies.     

An alternative approach to reliability analysis of cold standby systems

ABSTRACT

An alternative approach is applied for reliability analysis of standby systems on the basis of matrix renewal function. In this regard, a single-server, two identical unit cold standby systems with an imperfect switch is considered as a three-state semi-Markov process. Several important reliability measures such as availability, mean time to failure, expected number of failures, etc., are obtained for general lifetime distributions. Also, the main results have been treated to the case of exponential lifetimes and explicit formulas obtained for this case in addition of some numerical illustrations. This approach can easily be extended to more general standby systems with different configurations.     

A unified approach to binomial-type distributions of order k

In this paper, we consider the distribution of the number of "1"-runs of length k in a sequence of {0,1}-valued random variables of length n by using a new (unified) counting scheme called l-overlapping counting. Here, k and n are positive integers with k ≦ and l is an integer less than k. We obtain the prohabi!ity generating function of the distribution of the number of eoverlapping "in-runs of iength k in the sequence, even when the underiying sequence is a dependent sequence such as a highcr order Markov chaic.     

Properties of systems with two exchangeable Pareto components

The life lengths of the units in a system can be modelled by a bivariate distribution. In this paper, we suppose that the joint distribution of the units is a symmetric bivariate Pareto (Lomax) distribution. For this model, we obtain basic reliability properties for series and parallel systems. J. M. Ruiz Partially Supported by Ministerio de Ciencia y Tecnologia under grant BFM2003-02947 and Fundacion Seneca under grant 00698/PI/04.     

Limit Theorems for Semi-Markov Queues and Their Applications

We begin by definition of semi-Markov flow and discussion of its properties. Asymptotic behavior of multi-server and single-server queueing systems is studied under assumption of time-compression or service time growth. The results obtained are used for calculation of large systems reliability. Statistical estimates of parameters involved are also provided.     

An application of negative binomial distribution of order k in sensitive surveys

This article is an attempt to generalize some of the recent papers on randomized response techniques by using the negative binomial distribution of order k to randomize the responses in the randomization design where respondents can report outcome of one of two binary devices depending upon their actual status. The relative efficiency results are observed to be better than those of many recent and relevant randomized response techniques. The results are also better than those of the base line model used in this study, providing the sensitive attribute is rare. An extra advantage of the proposed technique is that it does not require any additional sampling and administrative cost.     

A note on estimating the common mean of k normal distributions and the stein problem

An unbiased estimator for the common mean of k normal distributions is suggested. A necessary and sufficient condition for the estimator Lo have a smaller variance than each sample mean is given. In the case of estimating the common mean vector of k p-variate (p ≤ 3) normal distributions a combined unbiased estimator may be used. We give a class of estimators which are better than the combined estimator when the loss is quadratic and the restriction of unbiasedness is removed.     

The New Zenga curve in the context of reliability analysis

ABSTRACT

In this article, we look into the properties and characterizations of the New Zenga curve. The relationship of the curve with other measures of inequality as well as some reliability concepts are examined. Classification of lifetime distributions using the Zenga curve and an illustration for the behaviour of the curve using a survival data are also provided.     

Estimation and testing procedures for the reliability functions of a general class of distributions

We consider here the general class of distributions proposed by Sankaran and Gupta (2005) by zeroing in on two measures of reliability, R(t) = P(X > t) and P = P(X > Y). Thereafter, we develop point estimation for R(t) and ‘P’ and develop uniformly minimum variance unbiased estimators (UMVUES). Then we derive testing procedures for the hypotheses related to different parametric functions. Finally, we compare the results using the Monte Carlo simulation method. Using real data set, we illustrate the procedure clearly.     

Applications of a general propagation algorithm for probabilistic expert systems

A probabilistic expert system provides a graphical representation of a joint probability distribution which can be used to simplify and localize calculations. Jensenet al. (1990) introduced a flow-propagation algorithm for calculating marginal and conditional distributions in such a system. This paper analyses that algorithm in detail, and shows how it can be modified to perform other tasks, including maximization of the joint density and simultaneous fast retraction of evidence entered on several variables.     

Analysis of non-repairable cold-standby systems in Bayes theory

ABSTRACT

In this paper, we seek to analyse the reliability of k-out-of-n cold-standby system with components having Weibull time-to-failure distribution in view of Bayes theory. At first, we review the existing methods exhaustively and find that all these methods have not considered Bayes theory. Then we modify the simplest method and propose new methods based on Monte Carlo simulation. Next, we combine all the information to derive the posterior distribution of Weibull parameters. A robust and universal sample-based method is proposed according to the Monte Carlo Markov Chain method to draw the sample of parameters to obtain the Bayes estimate of reliability. The drawn samples are proved to be rather satisfactory. Conducting a simulation study to compare all the methods in terms of accuracy and computational time, we have presented some useful recommendations from the simulation results. These conclusions would provide insight on the application for k-out-of-n cold-standby system.     

A family of measures to evaluate scale reliability in a longitudinal setting

Summary.  The concept of reliability denotes one of the most important psychometric properties of a measurement scale. Reliability refers to the capacity of the scale to discriminate between subjects in a given population. In classical test theory, it is often estimated by using the intraclass correlation coefficient based on two replicate measurements. However, the modelling framework that is used in this theory is often too narrow when applied in practical situations. Generalizability theory has extended reliability theory to a much broader framework but is confronted with some limitations when applied in a longitudinal setting. We explore how the definition of reliability can be generalized to a setting where subjects are measured repeatedly over time. On the basis of four defining properties for the concept of reliability, we propose a family of reliability measures which circumscribes the area in which reliability measures should be sought. It is shown how different members assess different aspects of the problem and that the reliability of the instrument can depend on the way that it is used. The methodology is motivated by and illustrated on data from a clinical study on schizophrenia. On the basis of this study, we estimate and compare the reliabilities of two different rating scales to evaluate the severity of the disorder.     

Signatures of series and parallel systems consisting of non disjoint modules

System signature is a useful tool to analyze coherent systems. In reliability theory, a large number of systems is actually the composition of disjoint subsystems (modules). However, in real life, there are situations in which the subsystems have common components. In this article, we consider the problem of obtaining signatures as well as minimal signatures of series and parallel systems that are composed of subsystems sharing a component. That is, these subsystems are no longer disjoint. Computational results are also presented to illustrate our findings.     

Equivariant estimation for the parameters of location-scale multivariate exponential models and its application in reliability analysis

ABSTRACT

By considering an absolutely continuous location-scale multivariate exponential model (Weier and Basu, 1980), we obtain minimum risk equivariant estimator(s) of the parameter(s). Given a location-scale multivariate exponential random vector, it is shown that the normalized spacings associated with the random vector are independent standard exponential. The distribution of the complete sufficient statistic is derived. We derive the performance measures of standby, parallel, and series systems and also obtain the minimum risk equivariant estimator of the mean time before failure of the three systems. Some of the results of this article are extensions of those of Chandrasekar and Sajesh (2010).