Classical and Bayesian Estimation of Reliability in Multicomponent Stress-Strength Model Based on Weibull Distribution

Kızılaslan, Fatih; Nadar, Mustafa

doi:10.15446/rce.v38n2.51674

Cited by 53 publications

(19 citation statements)

References 6 publications

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“…Another example may be a suspension bridge with m pairs of vertical cables such that the bridge survives when at least r number of vertical cables work. Inference on the reliability in MSS models when the stress and strength follow Weibull distribution is considered by Kizilaslan and Nadar (2015). Rao et al (2012Rao et al ( ,2014 conducted a series of studies to estimate the reliability of MSS models by assuming generalized exponential and Burr XII distributions for the components.…”

Section: Bshmentioning

confidence: 99%

Bayesian inference on reliability in a multicomponent stress-strength bathtub-shaped model based on record values

Pak

Khoolenjani

Rastogi

2019

Pak.j.stat.oper.res.

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In the literature, there are a well-developed estimation techniques for the reliability assessment in multicomponent stress-strength models when the information about all the experimental units are available. However, in real applications, only observations that exceed (or fall below) the current value may be recorded. In this paper, assuming that the components of the system follow bathtub-shaped distribution, we investigate Bayesian estimation of the reliability of a multicomponent stress-strength system when the available data are reported in terms of record values. Considering squared error, linex and entropy loss functions, various Bayes estimates of the reliability are derived. Because there are not closed forms for the Bayes estimates, we will use Lindleyâ€™s method to calculate the approximate Bayes estimates. Further, for comparison purposes, the maximum likelihood estimate of the reliability parameter is obtained. Finally, simulation studies are conducted in order to evaluate the performances of the proposed procedures and analysis of real data sets is provided.

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Section: Bshmentioning

confidence: 99%

Bayesian inference on reliability in a multicomponent stress-strength bathtub-shaped model based on record values

Pak

Khoolenjani

Rastogi

2019

Pak.j.stat.oper.res.

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“…The reliability in the MSS model based on a simple random sample has been developed in Kuo and Zuo [17] and Pandey and Uddin [18]. A considerable amount of the literature on the estimation of reliability in the multicomponent system for some lifetime distributions has been studied by several authors; see for examples; Rao [19], Rao et al [20], Rao [21], Kizilaslan and Nadar [22]. Recently, Pak et al [23] investigated Bayesian estimation of the reliability of an MSS system for the bathtub-shaped distribution when the available data are reported in terms of record values.…”

Section: Introductionmentioning

confidence: 99%

Estimation of multicomponent stress-strength reliability following Weibull distribution based on upper record values

Hassan

Nagy

Muhammed

et al. 2020

Journal of Taibah University for Science

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Stress-strength models are of special importance in reliability literature and engineering applications. This paper deals with the estimation problem of a stress-strength model incorporating multi-component system. The system is regarded as alive only if at least S out of k (S < k) strength components exceed the stress. The reliability of such system is obtained when strength and stress variables have Weibull distributions. Maximum likelihood estimator of R S,k and asymptotic confidence intervals are obtained based on upper record values. Bayesian estimator under squared error and linear exponential loss functions using gamma prior distributions and the corresponding credible intervals are obtained. Due to the lack of explicit forms for the Bayes estimates, the Markov Chain Monte Carlo (MCMC) method is employed. A simulation study is implemented to assess the performance of estimates. A real-life example is presented to show how the proposed model may be utilized in breaking strength of jute fibre data.

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“…Such structures are extensively utilized in industrial experiments, military radio networks, bridge construction, building communication networks, etc. In recent past, many scholars have studied multicomponent stress-strength models largely owing to the growing interest on this topic, see for instance, works of [20][21][22][23], Dey and Moala [24] and many others. Seadawy et al [25], Seadawy et al [26], Ahmad et al [27], Riaz et al [28], Abbasi et al [29] have also studied some complex structures.…”

Section: Introductionmentioning

confidence: 99%

Bayesian and non-Bayesian reliability estimation of multicomponent stress–strength model for unit Weibull distribution

Alotaibi

Tripathi

Dey³

et al. 2020

Journal of Taibah University for Science

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Mazucheli et al. introduced a new transformed model referred as the unit-Weibull (UW) distribution with uni-and anti-unimodal, decreasing and increasing shaped density along with bathtub shaped, constant and non-decreasing hazard rates. Here we consider inference upon stress and strength reliability using different statistical procedures. Under the framework that stress-strength components follow UW distributions with a known shape, we first estimate multicomponent system reliability by using four different frequentist methods. Besides, asymptotic confidence intervals (CIs) and two bootstrap CIs are obtained. Inference results for the reliability are further derived from Bayesian context when shape parameter is known or unknown. Unbiased estimation has also been considered when common shape is known. Numerical comparisons are presented using Monte Carlo simulations and in consequence, an illustrative discussion is provided. Two numerical examples are also presented in support of this study. Significant conclusion: We have investigated inference upon a stress-strength parameter for UW distribution. The four frequentist methods of estimation along with Bayesian procedures have been used to estimate the system reliability with common parameter being known or unknown.

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Classical and Bayesian Estimation of Reliability in Multicomponent Stress-Strength Model Based on Weibull Distribution

Cited by 53 publications

References 6 publications

Bayesian inference on reliability in a multicomponent stress-strength bathtub-shaped model based on record values

Bayesian inference on reliability in a multicomponent stress-strength bathtub-shaped model based on record values

Estimation of multicomponent stress-strength reliability following Weibull distribution based on upper record values

Bayesian and non-Bayesian reliability estimation of multicomponent stress–strength model for unit Weibull distribution

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