Bayesian Inference Based on Multiply Type-II Censored Samples of Sequential Order Statistics from Pareto Distribution

Abstract In this paper we are concerned with the reliability properties of two coherent systems having shared components. We assume that the components of the systems are two overlapping subsets of a set of n components with lifetimes X1,...,Xn. Further, we assume that the components of the systems fail according to the model of sequential order statistics (which is equivalent, under some mild conditions, to the failure model corresponding to a nonhomogeneous pure-birth process). The joint reliability function of the system lifetimes is expressed as a mixture of the joint reliability functions of the sequential order statistics, where the mixing probabilities are the bivariate signature matrix associated to the structures of systems. We investigate some stochastic orderings and dependency properties of the system lifetimes. We also study conditions under which the joint reliability function of systems with shared components of order m can be equivalently written as the joint reliability function of systems of order n (n>m). In order to illustrate the results, we provide several examples.

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Univariate and multivariate stochastic orderings of residual lifetimes of live components in sequential (𝑛-𝑟+ 1)-out-of-𝑛 systems

Journal of Applied Probability ◽

10.1017/jpr.2018.53 ◽

2018 ◽

Vol 55 (3) ◽

pp. 834-844

Author(s):

Ghobad Barmalzan ◽

Abedin Haidari ◽

Narayanaswamy Balakrishnan

Keyword(s):

Order Statistics ◽

Exponential Distribution ◽

Sufficient Conditions ◽

Sequential Order ◽

Stochastic Orderings ◽

Sequential Order Statistics ◽

Residual Lifetimes

Abstract Sequential order statistics can be used to describe the ordered lifetimes of components of a system when the failure of a component may affect the reliability of the remaining components. After a reliability system consisting of n components fails, some of its components may still be alive. In this paper we first establish some univariate stochastic orderings and ageing properties of the residual lifetimes of the live components in a sequential (n-r+1)-out-of-n system. We also obtain a characterizing result for the exponential distribution based on uncorrelated residual lifetimes of live components. Finally, we provide some sufficient conditions for comparing vectors of residual lifetimes of the live components from two sequential (n-r+1)-out-of-n systems. The results established here extend some well-known results in the literature.

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Model Selection Approaches for Predicting Future Order Statistics from Type II Censored Data

Mathematical Problems in Engineering ◽

10.1155/2018/3465909 ◽

2018 ◽

Vol 2018 ◽

pp. 1-29

Author(s):

Jyun-You Chiang ◽

Shuai Wang ◽

Tzong-Ru Tsai ◽

Ting Li

Keyword(s):

Model Selection ◽

Order Statistics ◽

Censored Data ◽

Model Misspecification ◽

Extreme Value Distribution ◽

Type Ii ◽

Underlying Distribution ◽

Censored Samples ◽

Scale Family ◽

Type Ii Censored Data

This paper studies a discriminant problem of location-scale family in case of prediction from type II censored samples. Three model selection approaches and two types of predictors are, respectively, proposed to predict the future order statistics from censored data when the best underlying distribution is not clear with several candidates. Two members in the location-scale family, the normal distribution and smallest extreme value distribution, are used as candidates to illustrate the best model competition for the underlying distribution via using the proposed prediction methods. The performance of correct and incorrect selections under correct specification and misspecification is evaluated via using Monte Carlo simulations. Simulation results show that model misspecification has impact on the prediction precision and the proposed three model selection approaches perform well when more than one candidate distributions are competing for the best underlying distribution. Finally, the proposed approaches are applied to three data sets.

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