Inference on reliability of stress-strength model with Peng-Yan extended Weibull distributions

Abstract

In this paper we estimate R = PfX < Yg when X and Y are independent random variables following the Peng-Yan extended Weibull distribution. We find maximum likelihood estimator of R and its asymptotic distribution. This asymptotic distribution is used to construct asymptotic confidence intervals. In the case of equal shape parameters, we derive the exact confidence intervals, too. A procedure for deriving bootstrap-p confidence intervals is presented. The UMVUE of R and the UMVUE of its variance are derived and also the Bayes point and interval estimator of R for conjugate priors are obtained. Finally, we perform a simulation study in order to compare these estimators and provide a real data example.

Stress–Strength Reliability of the Type P(X < Y) for Birnbaum–Saunders Components: A General Result, Simulations and Real Data Set Applications

“…Using Theorem 1 with the parameters of Table 5, it was possible to obtain RMLE = 0.5390 from the fitted distributions, RNP = 0.5333 and Rboots = 0.5394 (M = 10 4 ) whose confidence interval is (0.3921, 0.6825) at a 95% significance level. It is important to highlight that the size of the bootstrap confidence interval was large, similar to the results obtained in [16] ( R = 0.57 and CI = (0.45, 0.69)). One can see the distribution of the bootstrap estimates in Figure 9.…”

“…An application of stress-strength probability R = P(X < Y) in the modelling and comparison of daily wind speeds (in 0.1 m/s units) in two Atlantic coastal cities, Coruña (Spain)-X-and Bergen (Norway)-Y-from 1 January 2010 till 31 December 2019, is presented. The data are presented below and were first analysed and studied in [16] Descriptive statistics for x (Coruña) and y (Bergen) are presented in Table 4. The boxplot in Figure 7 shows that the 50% highest y values appear to be larger and more dispersed than the 50% highest x values.…”

On the study of the stress-strength reliability in Weibull-$F$ Models

“…The stress-strength models in generalized Weibull-G family of distributions have been investigated by researchers such as [1,2,13]. We now study the stochastic ordering between Y and X.…”

Inference on the stress strength reliability with exponentiated generalized Marshall Olkin-G distribution

“…Maurya et al [16] introduced a reliability estimation in a multicomponent stress-strength model based on inverse Weibull distribution. Jovanovic et al [17] proposed an inference on reliability of stress-strength model with Peng-Yan extended Weibull distributions. Sabry et al [18] presented a Monte Carlo simulation of the stressstrength model and reliability estimation for extension of the exponential distribution.…”