A Proportional Intensity Model with Frailty for Missing Recurrent Failure Data

Abstract

AbstractIn some practical circumstances, data are recorded after the systems have begun operations, and data collection is stopped at a predetermined time or after a predetermined number of failures. In such circumstances, incompleteness of various types exists in the aspect of the missing number of failures and their occurrence times beyond the duration of the pilot study. Additionally, multiple repairable systems may present system-to-system variability caused by differences in the operating environments or working loads of individual systems. With respect to left-truncated and right-censored recurrent failure data from multiple repairable systems, we propose a reliability model based on a proportional intensity model with frailty. The frailty model explicitly models unobserved heterogeneity among systems. Covariates incorporated into the proportional intensity model additionally account for the heterogeneity between different operating conditions. To estimate the model parameters for the left-truncated and right-censored recurrent failure data, a Monte Carlo expectation maximization algorithm is proposed. Details of the estimation of the model parameters and the construction of their confidence intervals are examined. A real-world example and simulation studies under various scenarios show prominent applications of the proportional intensity model with frailty to left-truncated and right-censored multiple repairable systems for reliability prediction.1Index Terms: Monte Carlo expectation maximization (MCEM) algorithmnonhomogeneous Poisson processrecurrent failure dataproportional intensity modelrepairable systemDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also.