Estimation of Reliability in a Multicomponent Stress–Strength System for the Exponentiated Moment-Based Exponential Distribution

Abstract

A multicomponent system of k components with independent and identically distributed random strengths X 1 , X 2 , . . . X k , with each component undergoing random stress, is in working condition if and only if at least s out of k strengths exceed the subjected stress. Reliability is measured while strength and stress are obtained through a process following an exponentiated moment-based exponential distribution with different shape parameters. Reliability is gauged from the samples using maximum likelihood (ML) on the computed distributions of strength and stress. Asymptotic estimates of reliability are compared using Monte Carlo simulation. Application to forest data and to breaking strengths of jute fiber shows the usefulness of the model.

Reliability Inference for the Multicomponent System Based on Progressively Type II Censored Samples from Generalized Pareto Distributions

“…This topic is beyond the goal of this paper and can be an open question for future study. Moreover, this paper can be a valuable addition to the works of Rezaei, et al [12] and Rezaei, et al [2], who considered the Pareto distribution, as well as Pak et al [8]; Mokhlis and Khames [19]; Rao [5]; and many others who considered reliability inference under various working assumptions. A comprehensive review of all published information regarding this topic should be compiled in the future in hopes of inferring generalized conclusions regarding the reliability of stress-strength systems.…”

“…In view of Tables 2-9, we find that the bias of ofδ s,k is close to 0 and the MSE ofδ s,k are also small for all simulation settings. The findings indicate the proposed maximum likelihood estimation method is reliable to obtain the point estimate of the model parameters; and then, the reliable point estimate,δ s,k , can be obtained by pluggingα 1 andα 2 into Equation (5).…”

“…Various researchers have studied the inference of δ s,k for the MSS system using different distributions. For example, Rao [5] studied δ s,k for the generalized exponential distribution; Rao et al [6] investigated δ s,k for the Burr-XII distribution; Hassan and Alohali [7] studied δ s,k for the generalized linear failure rate distribution; and Pak et al [8] investigated δ s,k for the power Lindley model. Readers can refer Kotz, et al [9] for a comprehensive review of the MSS.…”

Reliability Estimation in Multicomponent Stress-Strength Based on Inverse Weibull Distribution

“…Multicomponent stress-strength (MCSS) models have great applications range from communication and industrial systems to logistic and military systems. For examples, an aircraft generally contains more than one engine (k) and assume that for takeoff at least s (1 ≤ s ≤ k) engines are needed, see Hanagal [3], Turkkan and Pham-Gia [4], Serkan [5,6], Serkan and Funda [7], Shawky and Al-Gashgari [8], Pak et al [9,10], and Rao et al [11]. SS models have been discussed in the literature many a times.…”

Multicomponent stress-strength reliability estimation for the standard two-sided power distribution

“…In recent years, there has been growing interest for the s-out-of-k and related systems under different probability distributions. This type of multicomponent stress-strength reliability estimation studies is considered for log-logistic distribution by [24], generalized exponential by [23], PoissonWeibull models by [10], Weibull distribution by [16], Kumaraswamy distribution by [8], the general class of inverse exponential distributions by [14], Topp-Leone distribution by [1]. Furthermore, Kzlaslan [15] considered a multicomponent system when the underlying distributions belonging to the proportional reversed hazard rate model.…”