Estimation of the Reliability of a Stress–Strength System from Poisson Half Logistic Distribution

Abstract

This paper discussed the estimation of stress-strength reliability parameter R=P(Y<X) based on complete samples when the stress-strength are two independent Poisson half logistic random variables (PHLD). We have addressed the estimation of R in the general case and when the scale parameter is common. The classical and Bayesian estimation (BE) techniques of R are studied. The maximum likelihood estimator (MLE) and its asymptotic distributions are obtained; an approximate asymptotic confidence interval of R is computed using the asymptotic distribution. The non-parametric percentile bootstrap and student’s bootstrap confidence interval of R are discussed. The Bayes estimators of R are computed using a gamma prior and discussed under various loss functions such as the square error loss function (SEL), absolute error loss function (AEL), linear exponential error loss function (LINEX), generalized entropy error loss function (GEL) and maximum a posteriori (MAP). The Metropolis–Hastings algorithm is used to estimate the posterior distributions of the estimators of R. The highest posterior density (HPD) credible interval is constructed based on the SEL. Monte Carlo simulations are used to numerically analyze the performance of the MLE and Bayes estimators, the results were quite satisfactory based on their mean square error (MSE) and confidence interval. Finally, we used two real data studies to demonstrate the performance of the proposed estimation techniques in practice and to illustrate how PHLD is a good candidate in reliability studies.

Exponentiated half‐logistic Weibull distribution with reliability inference

“…The 95% asymptotic confidence intervals (ACI), HPD CrIs, and the percentile bootstrap intervals (𝐵 𝑝 ) are assessed using average widths (A. Width) and CP. The simulation studies were conducted for 1000 replicates for various sample sizes, (𝑛, 𝑚)= (10,15), (20,25), (30,35), (50, 50), and (100,100). For each replication, 1000 bootstrap samples were used, and 10, 000 observations for MCMC algorithm were generated.…”

A New Extension of the Topp–Leone-Family of Models with Applications to Real Data

“…R has been discussed by many researchers in the literature through various perspectives. For example, let X and Y be an independent random variables, then: normal distribution (N) [ 41 , 42 ], Weibull (W) [ 43 – 45 ], exponential (E) [ 46 ], generalized exponential (GE) [ 47 ], beta-Erlang truncated exponential (BETE) [ 48 ], Poisson-odd generalized exponential family (POGE) [ 49 ], generalized logistic (GL) [ 50 ], Poisson-generalized half logistic (PGHL) [ 51 ], generalized exponential Poisson (GEP) [ 52 ], Poisson half logistic (PHL) [ 53 ], exponentiated sine Weibull (ESW) [ 54 ], extended cosine Weibull (ECSW) [ 55 ], among others.…”

A New Extended Cosine—G Distributions for Lifetime Studies

“…Parameter R s has been studied by many authors in the literature from various viewpoints. For example, for the study based on independent random variables X and Y that follow normal (N) distributions see [22,23], exponential (E) distributions see [24], generalized logistic (GL) distributions see [25], Weibull (W) distributions see [26][27][28], generalized exponential (GE) distributions see [29], generalized exponential Poisson (GEP) distributions see [30], beta-Erlang truncated exponential (BETE) distributions see [31], Poisson-generalized halflogistic (PGHL) distributions see [32], and Poisson half-logistic (PHL) distributions see [33], among others.…”