A Proportional Intensity Model with Frailty for Missing Recurrent Failure Data

Abstract

In 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.

KEYWORDS:

• Monte Carlo expectation maximization (MCEM) algorithm
• Nonhomogeneous Poisson process
• Proportional intensity model
• Recurrent failure data
• Repairable system

Supplementary Materials

Supplementary file.pdf: Supplement to “A Proportional Intensity Model with Frailty for Missing Recurrent Failure Data”. This file contains the proof of Theorem 3.1 in Section 3 and the plots of simulation study in Section 5.2.

Computer code.zip: This file contains R (x64 4.1.2) scripts to reproduce the tank failure data analysis in Section 4 and the simulation study in Section 5, and the data in data.RData. README file inside the .zip file describes the contents in detail.

Disclosure Statement

The authors report there are no competing interests to declare.