Weibull analysis with sequential order statistics under a power trend model for hazard rates

TL;DR

This paper develops a Weibull-based sequential order statistics model with a power trend for hazard rates, addressing non-iid component failures in engineering systems and providing estimation and hypothesis testing methods.

Contribution

It introduces the PTCPHM model as a generalization of iid assumptions and develops comprehensive inferential techniques for this new framework.

Findings

Maximum likelihood estimates obtained for the model

Statistical inference methods established for PTCPHM

Application to aircraft component failure data demonstrated model utility

Abstract

In engineering systems, it is usually assumed that lifetimes of components are independent and identically distributed (iid). But, the failure of a component results in a higher load on the remaining components and hence causes the distribution of the surviving components change. For modeling this kind of systems, the theory of sequential order statistics (SOS) can be used. Assuming Weibull distribution for lifetimes of components and conditionally proportional hazard rates model as a special case of the SOS theory, the maximum likelihood estimates of the unknown parameters are obtained in different cases. A new model, denoted by PTCPHM, as a generalization of the iid case is proposed, and then statistical inferential methods including point and interval estimation as well as hypothesis tests under PTCPHM are then developed. Finally, a real data on failure times of aircraft components, due to Mann and Fertig (1973), is analyzed to illustrate the model and inferential methods developed here.