Dynamic Systems with Baseline Exponential Distribution Based on Sequential Order Statistics Under a Power Trend for Hazard Rates

Abstract

This paper deals with analyzing dynamic engineering systems consisting of independent components. The failure of a components causes more load on the surviving components. This property is modeled by a power trend conditionally proportional hazard rates. For modeling system lifetimes, the theory of sequential order statistics can be used. Sequential order statistics coming from heterogeneous exponential distributions are considered. The maximum likelihood and Bayesian estimates of the parameters are obtained in different cases. The generalized likelihood ratio and the Bayesian tests are also derived for testing homogeneity of the baseline exponential component lifetimes arising from s independent engineering systems.

Evaluation of evidences for dynamic systems based on Bayes factors with an application

“…, which are, respectively, the well-known ML and the Bayes estimates of the exponential parameters on the basis of a random sample of size n; see, e.g., (Lawless, 2003) and (Hashempour and Doostparast, 2016b). Proposition 3.2.…”

“…Hashempour and Doostparast (2016a) assumed that the lifetimes of the components are IID with an exponential distribution. We considered two simple hypothesis tests based on the ML estimate of the σ in (15). Also, we ran the SOS example for r = 3, 4 and s = 3, 4, 5.…”