Reliability analysis of Weibull multicomponent system with stress‐dependent parameters from accelerated life data

Abstract

In this paper, reliability estimation of multicomponent system under a multilevel accelerated life testing. When the lifetime of components follows Weibull distribution, the problem of point and interval estimates are discussed from different perspectives. Under a general life-stress assumption that there are multiple nonconstant and stress-dependent scale and shape parameters, the maximum likelihood estimates of unknown parameters along with associated existence and uniqueness are established. Approximate confidence intervals are constructed correspondingly via expected Fisher information matrix. Furthermore, some pivotal quantities are constructed and alternative generalized point and interval estimates are also proposed for comparison. In addition, predictive intervals for the lifetime of the multicomponent system are discussed under classical and generalized pivotal approaches, respectively. The results show that the proposed generalized estimates are superior to the conventional likelihood approach in terms of the accuracy. A real data example is carried out to illustrate the implementations of the proposed methods.

Parametric Distributions for Survival and Reliability Analyses, a Review and Historical Sketch

“…Figure 3 shows the hazard functions with the increasing (α > 1), constant (α = 1), and decreasing (α < 1) shapes. A number of papers adopted the Weibull distribution for accelerated life data [27,[56][57][58][59], left-truncated data [60,61], breast/colorectal/ovarian cancer data [6,[62][63][64], the AIDS data [65], and others. The Weibull distribution is also useful for creating multivariate survival distributions [66].…”