Mixture models for analyzing product reliability data: a case study

In the case of manufactured products, there are situations where some components of a product are produced over a period of time by collecting items from different vendors, using different raw materials, machines, and manpower. The physical characteristics and the reliabilities of such components may be different, but sometimes it is difficult to distinguish them clearly. In such situations, mixtures of distributions are often used in the analysis of reliability data for these components. Here a twofold Weibull–Weibull mixture model is applied to analyze product reliability data that consist of both failure and censored lifetimes. The Expectation–Maximization (EM) algorithm is used to find the maximum likelihood estimates of the model parameters. As a case study, it analyses an Aircraft component (Windshield) failure data and various characteristics of the mixture model, such as the reliability function, B10 life, mean time to failure, etc., are estimated to assess the reliability of the component. Simulation studies are performed to investigate the properties and uses of the proposed method.