Variance Corrected Proportional Hazard Model for the Analysis of Recurrent Multiple Failure Modes

Abstract

Automobiles do fail repetitively owing to different types of failures. Modeling of such products should concern dissimilar recurrent failure types. Failure types are habitually correlated to each other. This study has utilized variance corrected proportional hazard models (VCPH) for modeling multiple failure occurrences of different failure types of automobiles taking into account the correlated nature of the failures. Though original Cox proportional hazard (PH) models require failure events to be independent, VCPH can handle non independency. In this study, this model is utilized for the analysis of multi-type, multiple occurrences of failures in automobiles, where the assumption of independence among failure times is violated. The VCPH model obtains parameter estimates by first fitting a Cox PH model that ignores the dependence structure and then replaces the naive standard errors with estimates from empirical sandwich variance estimation in order to incorporate the non-independence of times between failures. This study applies the Prentice, Williams and Petersen (PWP) models to model multiple occurrences of different failures in automobiles as proportionality among failure events were well demonstrated when risk interval is taken as ‘gap time’ and since PWP models are specified with a gap time risk interval. The Information Matrix (IM) test of White is applied for the checking of the PH model specification with multivariate failure time data. White’s paper on inference from missspecified models presented the IM test as a test for correct model specification. The objective of the study was to find out how automobile type and type of failure affect the time to failure. Applying the best suitable VCPH model to the data, it was revealed that both automobile and failure type have an impact on timing of failure however this effect doesn’t change over multiple failure occurrences of the automobile.