Abstract
In this paper we study the reliability of a multicomponent stress-strength model assuming that the components follow power Lindley model. The maximum likelihood estimate of the reliability parameter and its asymptotic confidence interval are obtained. Applying the parametric Bootstrap technique, interval estimation of the reliability is presented. Also, the Bayes estimate and highest posterior density credible interval of the reliability parameter are derived using suitable priors on the parameters. Because there is no closed form for the Bayes estimate, we use the Markov Chain Monte Carlo method to obtain approximate Bayes estimate of the reliability. To evaluate the performances of different procedures, simulation studies are conducted and an example of real data sets is provided.
Highlights
Stress-strength models have attracted the attention of statisticians for many years due to their applicability in diverse areas such as medicine, engineering, and quality control, among others
The interest of this paper is to provide classical and Bayesian inferences on the reliability of r-out-of-m: G models when the strength and stress components are independent random variables distributed as power Lindley model
Once the maximum likelihood estimate of the reliability parameter is obtained, we can use the asymptotic normality of the MLEs to compute the approximate 100(1 − α)% condence intervals (CI) of the reliability Rr,m as follows: Rr,m
Summary
Stress-strength models have attracted the attention of statisticians for many years due to their applicability in diverse areas such as medicine, engineering, and quality control, among others. Pak, Khoolenjani & Jafari (2014) developed inference procedures for the stress-strength parameter R in bivariate Rayleigh model They studied dierent estimation methods by using the ML and bootstrap techniques. The interest of this paper is to provide classical and Bayesian inferences on the reliability of r-out-of-m: G models when the strength and stress components are independent random variables distributed as power Lindley model. Considering squared error loss function and using gamma priors on the parameters, an expression is provided as the Bayesian estimate of the reliability parameter Since this expression can not simplied to a nice closed form, we employ a Markov Chain Monte Carlo (MCMC) procedure to obtain random samples from the posterior distributions and in turn use them to derive the Bayes estimate and highest posterior density (HPD) credible interval of the reliability.
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