Abstract
This paper discussed the estimation of stress-strength reliability parameter 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.
Highlights
In the context of the mechanical reliability of a system or materials, it is very important to study the system performance referred to as the stress–strength parameter
The point and interval estimation of R was discussed; these include the maximum likelihood estimation of R and its asymptotic confidence interval, percentile bootstrap and student’s bootstrap confidence interval; Bayes estimation of R is computed under the square error loss function, absolute error loss function, linear exponential error loss function, generalized entropy error loss function, and maximum a posteriori, the credible interval based on the square error loss function is obtained
We examine by simulation studies the proposed point and interval estimates, and they work very well for various samples sizes as discussed by their mean square error (MSE) and the confidence intervals; the MSE decreases as the sample increases in both techniques, and based on the simulation result we recommend the use of the bootstrap for estimating the confidence interval of very small size
Summary
In the context of the mechanical reliability of a system or materials, it is very important to study the system performance referred to as the stress–strength parameter. [33] consider the estimation of R for the Weibull random variable case on progressively type-II censored data, ref. [35] investigate the estimation of R based on Burr type XII distribution under hybrid progressive censored samples, ref. We are aiming at the estimation of the stress–strength parameter R from independent random variables with a PHLD distribution, the classical maximum likelihood method and Bayesian estimation techniques were discussed and analyzed numerically by simulation studies. The rest of the paper follows: In Section 2, we provide the estimation of R in the general case and its maximum likelihood estimation, asymptotic distribution, and confidence interval, the bootstrap confidence interval is considered.
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