Multicomponent Stress-strength Model Research Articles

Reliability of a Coherent System in a Multicomponent Stress-Strength Model

SYNOPTIC ABSTRACT The problem of finding system reliability is difficult in a multicomponent stress-strength model because the strengths of different components may be different, and they may experience the same or different stress levels. In a single-component stress-strength model, reliability of a component is the probability of its strength being greater than the stress imposed on it. In a multicomponent stress-strength model, we must take into account the structure function of the system and respective stress and strength levels of the components while determining the system reliability. In this article we show how the stress-strength reliability of a multicomponent system, at least its lower bound, can be derived. The stress-strength reliability of a system is expressed here as a function of the stress-strength reliabilities of its individual components. This generalized expression helps evaluate the stress-strength reliability of different coherent systems, regardless of the dependent or independent nature of the stress and strength variables.

Estimation of Reliability in Multi-Component Stress-Strength Model Following Exponentiated Pareto Distribution

Estimation of Reliability in Multi-Component Stress-Strength Model Following Exponentiated Pareto Distribution

Consecutive k-Out-of-n : G System in Stress-Strength Setup

A consecutive k-out-of-n: G system consists of n linearly ordered components functions if and only if at least k consecutive components function. In this article we investigate the consecutive k-out-of-n: G system in a setup of multicomponent stress-strength model. Under this setup, a system consists of n components functions if and only if there are at least k consecutive components survive a common random stress. We consider reliability and its estimation of such a system whenever there is a change and no change in strength. We provide minimum variance unbiased estimation of system reliability when the stress and strength distributions are exponential with unknown scale parameters. A nonparametric minimum variance unbiased estimator is also provided.

Estimation of reliability in a multicomponent stress-strength model

This paper draws inferences regarding the reliability in a multicomponent stress-strength system when both stress and strength are independently identically Burr random variables. Maximum likelihood (ML) and Bayes estimators of the system reliability are considered. A numerical example is presented on the basis of a Monte Carlo simulation.

Reliability estimation of an system with non-identical component strengths: the Weibull case

Abstract A multi-component stress-strength model of an s- out-of -k system is considered. Johnson (Handbook of Statistics, vol. 7. Elsevier Science Publishers, 1988, pp. 27–54) introduced the generalization of such a system by considering a non-identical component's strength distribution and also found the maximum likelihood estimate (mle) by considering an exponential distribution of stress and strength. Bayes estimate of such a system's reliability function is obtained by using the Lindley's method of approximation (Trabajos de Estadisticay Investiracion Operative, 31 (1980) 232–245). The component strengths follow independent but not all identical Weibull distributions. It is further assumed that all the components are subjected to a common random stress which is also distributed as a Weibull random variable. A squared error loss function is used. A numerical example is presented in which comparison is made with the mle obtained by a Monte Carlo study of efficiency and Pitman nearness probability.

Estimation of reliability in multi-component stress-strength model following a Burr distribution

This paper draws inferences about the reliability in a multi-component stress-strength system when both stress and strength are independently identically distributed (idd) Burr random variables. We consider both maximum likelihood and Bayes estimators of the system reliability. The two estimators are compared numerically by obtaining empirical efficiencies with respect to the maximum likelihood estimator (MLE) by generating 1000 random samples by a Monte Carlo simulation. It is found that the Bayes estimators are better than the corresponding MLEs for small samples ( n i ≤ 7; i = 1, 2). Moreover, the robustness of the Bayes estimators to the change of the prior parameters is also considered.

Estimation of Reliability in a Multicomponent Stress-Strength Model

Estimation of Reliability in a Multicomponent Stress-Strength Model

Estimation of Reliability in a Multicomponent Stress-Strength Model

Abstract A stress-strength model is formulated for s of k systems consisting of identical components. We consider minimum variance unbiased estimation of system reliability for data consisting of a random sample from the stress distribution and one from the strength distribution when the two distributions are exponential with unknown scale parameters. The asymptotic distribution is obtained by expanding the unbiased estimate about the maximum likelihood value and establishing their equivalence. Performance of the two estimates for moderate samples is studied by Monte Carlo simulation. Uniformly most accurate unbiased confidence intervals are also obtained for system reliability.