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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.

The correlation between contact fatigue failure and wear failure of rolling bearing is analyzed, and the reliability model of rolling bearing based on multi-correlation failure mode is established. Based on the improved linear fatigue cumulative damage theory and wear theory, the limit state equations of two failure modes are established, and the correlation of state functions of contact fatigue and wear failure modes is described by the mixed Copula function. The random sample data are generated by Monte Carlo method, and the unknown parameters are estimated by genetic algorithm based on the minimum deviation square criterion, then the dynamic reliability model of rolling bearing is established. The quadratic polynomial without cross-term is used as the implicit functional proxy model, then the Latin hypercube sampling method and least squares theory are employed to estimate parameters of mixed Copula function and finally, the reliability sensitivity analysis of multi-failure modes of bearing is presented by fourth-order moment estimation method. Taking a certain type of spherical roller bearing as an example, the bearing reliability analysis considering the correlation of failure modes is carried out. The results show that compared with the bearing reliability model based on the assumption of independent failure modes and the weakest link theory, the bearing reliability model based on multi-correlation failure is more consistent with the practical application.

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