A General Proportional Model and Modelling Procedure

• Published in: Quality and reliability engineering international Vol. 28; no. 6; pp. 634 - 647
• Main Author: Jiang, Renyan
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.10.2012
• Subjects: accelerated factor; covariate; degradation; general proportional model; life estimate; maintenance optimization
• ISSN: 0748-8017; 1099-1638
• DOI: 10.1002/qre.1394

This paper presents a unified representation for the Cox model and its extensions (e.g. proportional intensity model, proportional wear‐out model and accelerated life testing model) and calls it the general proportional model. A multi‐step procedure is proposed to sequentially determine the three parts of the model (i.e. baseline, covariate and stochastic parts). The basic idea of the proposed approach is to use an optimization method to estimate the ‘accelerated factor’ associated with each ‘stress’ (i.e. covariate) level. The estimated accelerated factors are fitted to an adequate model as a function of the stress level. The fitted accelerated factor model is used to transform the observed sample into an equivalent (or mixed) sample, which corresponds to a specified reference stress level. The main advantages of the proposed approach are that it makes the modelling process flexible and transparent, avoids making possibly unrealistic assumptions on the forms (or distribution family) of relevant functions (or random variable) and fully utilizes all the observations for modelling. The appropriateness and usefulness of the model and modelling approach are illustrated through a detailed analysis for two real‐world examples published in the literature. Copyright © 2012 John Wiley & Sons, Ltd.