Estimation of Stress-Strength Reliability for Multicomponent System with Rayleigh Data

Abstract

Inference is investigated for a multicomponent stress-strength reliability (MSR) under Type-II censoring when the latent failure times follow two-parameter Rayleigh distribution. With a context that the lifetimes of the strength and stress variables have common location parameters, maximum likelihood estimator of MSR along with the existence and uniqueness is established. The associated approximate confidence interval is provided via the asymptotic distribution theory and delta method. Meanwhile, alternative generalized pivotal quantities-based point and confidence interval estimators are also constructed for MSR. More generally, when the lifetimes of strength and stress variables follow Rayleigh distributions with unequal location parameters, likelihood and generalized pivotal-based estimators are provided for MSR as well. In addition, to compare the equivalence of different strength and stress parameters, a likelihood ratio test is provided. Finally, simulation studies and a real data example are presented for illustration.

Inferences of the Multicomponent Stress–Strength Reliability for Burr XII Distributions

“…The monthly water capacity of the Shasta reservoir over the months of August, September, and December from 1980 to 2015, which was accessed on September 19, 2021, is used in this section for the illustration of the processes considered. The dataset was also considered by Wang et al [16] for the Rayleigh stress-strength model.…”

“…The s-out-of-k G system has attracted extensive attention and R s,k inference has been broadly investigated by numerous studies. These include multicomponent strength-stress models for Kumaraswamy distribution by Dey et al [7], based on Chen distribution by Kayal [8], based on general class of inverse exponentiated distribution and proportional reversed hazard rate distribution by Kizilaslan [9,10], based on bivariate Kumaraswamy distribution by Kizilaslan and Nadar [11], based on Marshall-Olkin bivariate Weibull distribution by Nadar and Kizilaslan [12], based on Rayleigh stress-strength model by Rao [13], based on Burr XII distribution by Rao et al [14], based on progressively Type-II censored samples from generalized Pareto distribution by Sauer et al [15], and based on Rayleigh stress-strength model by Wang et al [16].…”

The Reliability Inference for Multicomponent Stress–Strength Model under the Burr X Distribution

“…The monthly water capacities in the months of August, September, and December from 1980 to 2015, which were accessed on 19 September 2021, were utilized for the demonstration of the processes presented. The data set was also studied under the Rayleigh distribution and Burr XII one, respectively, by Wang et al [20] and Lio et al [18].…”

“…The work by Sauer et al [19] was based on progressively type II censored samples from generalized Pareto distributions. And the work by Wang et al [20] was based on type II censored strength and complete stress samples from Rayleigh stress-strength models.…”

Bayesian Estimation of Reliability for Multicomponent Stress-Strength Model Based on Topp-Leone Distribution

“…As well, Rasekhi et al in 2020 [24], Mezaal et al in 2020 [25], Lately in 2021, Kohansal and Shoaee in [26], reported the reliability of the system using the Weibull Distribution. And Wang et al in same year 2021 [27] published a paper to find the reliability of stress and strength of multicomponent system for Type II monitoring data where the stress and strength variables followed Rayleigh Distribution.…”