Multi Stress-Strength Reliability Based on Progressive First Failure for Kumaraswamy Model: Bayesian and Non-Bayesian Estimation

Abstract

It is highly common in many real-life settings for systems to fail to perform in their harsh operating environments. When systems reach their lower, upper, or both extreme operating conditions, they frequently fail to perform their intended duties, which receives little attention from researchers. The purpose of this article is to derive inference for multi reliability where stress-strength variables follow unit Kumaraswamy distributions based on the progressive first failure. Therefore, this article deals with the problem of estimating the stress-strength function, R when X,Y, and Z come from three independent Kumaraswamy distributions. The classical methods namely maximum likelihood for point estimation and asymptotic, boot-p and boot-t methods are also discussed for interval estimation and Bayes methods are proposed based on progressive first-failure censored data. Lindly’s approximation form and MCMC technique are used to compute the Bayes estimate of R under symmetric and asymmetric loss functions. We derive standard Bayes estimators of reliability for multi stress–strength Kumaraswamy distribution based on progressive first-failure censored samples by using balanced and unbalanced loss functions. Different confidence intervals are obtained. The performance of the different proposed estimators is evaluated and compared by Monte Carlo simulations and application examples of real data.

Reliability Analysis of the New Exponential Inverted Topp–Leone Distribution with Applications

“…The component fails if the applied stress exceeds its strength: . For more information about this model, see Abu El Azm et al [ 17 ], Sabry et al [ 18 ], Yousef and Almetwally [ 19 ], and Hassan et al [ 20 ]. Let and be two independent random variables with NEITL and NEITL distributions, respectively.…”

A new Topp-Leone Kumaraswamy Marshall-Olkin generated family of distributions with applications

“…However, it is crucial to carry out this procedure with care, avoiding overloading the model, to ensure relevant interpretation of results and appropriate generalization to new data. In this article, we will discuss a newly developed broad family of distributions that was produced by mixing the Topp-Leone distribution [1] , with other distributions as the Generated families of Kumaraswamy [2] , Kumaraswamy censored model [3] and Marshall-Olkin [4] . Typical instances of this family of distributions include the Marshall-Olkin Topp Leone-G [5] , [6] , type II half logistic [7] , exponentiated generalized Topp-Leone-G [8] , Garhy-G [9] , half-logistic odd Weibull-Topp-Leone-G [10] , truncated inverted Kumaraswamy-G [11] , Topp-Leone Kumaraswamy-G [12] , odd log-logistic Poisson-G [13] , Kumaraswamy-G [14] , type II power Topp-Leone-G [15] , Fréchet Topp-Leone-G [16] , Topp-Leone Gompertz-G [17] , Topp-Leone odd Lindley-G [18] , type II Topp-Leone-G [19] , Topp–Leone modified Weibull [20] , Marshall-Olkin extended Gompertz Makeham [21] , Marshall Olkin alpha power extended Weibull [22] , Marshall-Olkin alpha power inverse Weibull [23] , Marshall-Olkin alpha power Lomax [24] , [25] , a generalized Birnbaum-Saunders distribution [26] , Topp–Leone modified Weibull model [20] , a new version of Topp–Leone distribution with engineering applications [27] , reliability analysis of exponential distributions [28] , Marshall-Olkin improved Rayleigh distribution [29] , [30] .…”

Multi-component Reliability Inference in Modified Weibull Extension Distribution and Progressive Censoring Scheme

“…Also, Metwally et al [ 18 ] studied reliability analysis of the new exponential inverted Topp–Leone distribution with applications. About the multi- stress–strength reliability, Yousef and Almetwally [ 28 ] investigated multi- stress–strength reliability based on progressive first failure for Kumaraswamy model in Bayesian and non-Bayesian approaches. Also, Almetwally et al [ 3 ] studied optimal plan of multi-stress–strength reliability Bayesian and non-Bayesian methods for the alpha power exponential model using progressive first failure.…”