Analysis of Censored Aggregate Failure-time Data Using Phase-type Distributions

Field failure time data provide ample sources of valuable information for product reliability estimation. However, actual failure times of individual units are usually not reported in many engineering applications. Instead, aggregate failure time data that give cumulative failure times of multiple units are collected and sometimes implemented with censoring. This raises big challenges in reliability estimation using those popular failure-time models and statistical methods. So far, only a few probability distributions have been utilized to handle aggregate failure time data while many widely used probability distributions (e.g., Weibull, Lognormal) are intractable. In this work, a statistical method using Phase-type (PH) distributions is proposed for analyzing censored aggregate failure-time data for the first time. Specially, a censored aggregate failure-time model based on the Coxian distribution is proposed, and an Expectation-Maximization (EM) algorithm for maximum likelihood (ML) estimation is developed for model parameter estimation. A simulation study and a real-world example illustrate the superior capability of the proposed method. Indeed, by mimicking the true underlying distributions that are incapable of handling such data, the proposed method provides practitioners with a flexible tool to overcome this challenge.