Hare Krishna

Original Articles: Reliability estimation in Lindley distribution with progressively type II right censored sample

In this paper we discuss one parameter Lindley distribution. It is suggested that it may serve as a useful reliability model. The model properties and reliability measures are derived and studied in detail. For the estimation purposes of the parameter and other reliability characteristics maximum likelihood and Bayes approaches are used. Interval estimation and coverage probability for the parameter are obtained based on maximum likelihood estimation. Monte Carlo simulation study is conducted to compare the performance of the various estimates developed. In view of cost and time constraints, progressively Type II censored sample data are used in estimation. A real data example is given for illustration.

Reliability estimation in generalized inverted exponential distribution with progressively type II censored sample

In this paper, a generalization of inverted exponential distribution is considered as a lifetime model [A.M. Abouammoh and A.M. Alshingiti, Reliability estimation of generalized inverted exponential distribution, J. Statist. Comput. Simul. 79(11) (2009), pp. 1301–1315]. Its reliability characteristics and important distributional properties are discussed. Maximum likelihood estimation of the two parameters involved along with reliability and failure rate functions are derived. The method of least square estimation of parameters is also studied here. In view of cost and time constraints, type II progressively right censored sampling scheme has been used. For illustration of the performance of the estimates, a Monte Carlo simulation study is carried out. Finally, a real data example is given to show the practical applications of the paper.

Reliability estimation in Maxwell distribution with progressively Type-II censored data

There may be situations in which either the reliability data do not fit to popular lifetime models or the estimation of the parameters is not easy, while there may be other distributions which are not popular but either they provide better goodness-of-fit or have a smaller number of parameters to be estimated, or they have both the advantages. This paper proposes the Maxwell distribution as a lifetime model and supports its usefulness in the reliability theory through real data examples. Important distributional properties and reliability characteristics of this model are elucidated. Estimation procedures for the parameter, mean life, reliability and failure-rate functions are developed. In view of cost constraints and convenience of intermediate removals, the progressively Type-II censored sample information is used in the estimation. The efficiencies of the estimates are studied through simulation. Apart from researchers and practitioners in the reliability theory, the study is also useful for scientists in physics and chemistry, where the Maxwell distribution is widely used.

Reliability estimation in Maxwell distribution with Type‐II censored data

Purpose – This paper seeks to focus on the study and estimation of reliability characteristics of Maxwell distribution under Type‐II censoring scheme.Design/methodology/approach – Maximum likelihood estimation and Bayes estimation methods have been used for the estimation of reliability characteristics. Monte‐Carlo simulation is used to compare the efficiency of the estimates developed by these estimation methods.Findings – With prior information on the parameter of Maxwell distribution, Bayes estimation provides better estimates of reliability characteristics; otherwise Maximum likelihood estimation is good enough to use for reliability practitioners.Practical implications – When items are costly, Type‐II censoring scheme can be used to save the cost of the experiment and the discussed methods provide the means to estimate the reliability characteristics of the proposed lifetime model under this scheme.Originality/value – The study is useful for researchers and practitioners in reliability theory and als...

A Bivariate Geometric Distribution with Applications to Reliability

This article studies a bivariate geometric distribution (BGD) as a plausible reliability model. Maximum likelihood and Bayes estimators of parameters and various reliability characteristics are obtained. Approximations to the mean, variance, and Bayes risk of these estimators have been derived using Taylors expansion. A Monte-Carlo simulation study has been performed to compare these estimators. At the end, the theory is illustrated with a real data set example of accidents.

Estimation in Maxwell distribution with randomly censored data

In many practical situations, complete data are not available in lifetime studies. Many of the available observations are right censored giving survival information up to a noted time and not the exact failure times. This constitutes randomly censored data. In this paper, we consider Maxwell distribution as a survival time model. The censoring time is also assumed to follow a Maxwell distribution with a different parameter. Maximum likelihood estimators and confidence intervals for the parameters are derived with randomly censored data. Bayes estimators are also developed with inverted gamma priors and generalized entropy loss function. A Monte Carlo simulation study is performed to compare the developed estimation procedures. A real data example is given at the end of the study.

Generalized inverted exponential distribution under progressive first-failure censoring

This article deals with progressive first-failure censoring, which is a generalization of progressive censoring. We derive maximum likelihood estimators of the unknown parameters and reliability characteristics of generalized inverted exponential distribution using progressive first-failure censored samples. The asymptotic confidence intervals and coverage probabilities for the parameters are obtained based on the observed Fishers information matrix. Bayes estimators of the parameters and reliability characteristics under squared error loss function are obtained using the Lindley approximation and importance sampling methods. Also, highest posterior density credible intervals for the parameters are computed using importance sampling procedure. A Monte Carlo simulation study is conducted to analyse the performance of the estimators derived in the article. A real data set is discussed for illustration purposes. Finally, an optimal censoring scheme has been suggested using different optimality criteria.

On Randomly Censored Generalized Inverted Exponential Distribution

SYNOPTIC ABSTRACT Life testing experiments are conducted to collect lifetime information on patients in survival analysis. The subjects of testing in reliability theory are electronic, electrical, and mechanical devices. Because of time and cost constraints, it is difficult to collect lifetime data on all items, and therefore, the experiment is terminated before its completion. Various types of censoring schemes are used by the practitioners. Random censoring is an important censoring scheme in which the time of censoring is not fixed but taken as random. In this article, we study the generalized inverted exponential distribution under random censoring. Maximum likelihood estimators of the parameters and expected Fisher information under random censoring model are derived. Bayes estimators of the parameters under squared error loss function are obtained using Lindleys approximation and importance sampling methods. Also, highest posterior density credible intervals of the parameters based on importance sampling procedure are constructed. A Monte Carlo simulation study is conducted to compare the performance of various estimators developed. A randomly censored real dataset illustrates the estimation procedures developed in this study.

Estimation of reliability characteristics of general system configuration

Purpose – The purpose of this paper is to consider a General System Configuration (GSC), whose particular cases are all the popular system configurations. In reliability engineering one comes across various system configurations, for example, series, parallel and k‐out of‐m system models, which consist of a number of components.Design/methodology/approach – The paper gives a general approach to express the reliability properties of the whole system in terms of component parameters. The reliability of a GSC is expressed as a polynomial of the component reliability. Lifetime data on components have been used to estimate the system reliability characteristics through classical and Bayes estimation procedures.Findings – The paper finds that the underlying distribution is assumed to be Weibull and, in view of cost constraints, Type‐II censored information has been used.Practical implications – The paper is useful for reliability practitioners as well as theoreticians. It provides an easy method to estimate the...

Estimation of P(Y < X) for progressively first-failure-censored generalized inverted exponential distribution

ABSTRACT In this article, we consider the problem of estimation of the stress–strength parameter δ = P(Y < X) based on progressively first-failure-censored samples, when X and Y both follow two-parameter generalized inverted exponential distribution with different and unknown shape and scale parameters. The maximum likelihood estimator of δ and its asymptotic confidence interval based on observed Fisher information are constructed. Two parametric bootstrap boot-p and boot-t confidence intervals are proposed. We also apply Markov Chain Monte Carlo techniques to carry out Bayes estimation procedures. Bayes estimate under squared error loss function and the HPD credible interval of δ are obtained using informative and non-informative priors. A Monte Carlo simulation study is carried out for comparing the proposed methods of estimation. Finally, the methods developed are illustrated with a couple of real data examples.