Practical applications of mixture models to complex time-to-failure data

Statistical time-to-failure analysis is a very powerful and versatile analytical tool available to reliability engineers and statisticians for understanding and communicating the failure risk and reliability of a component, device, or system. The typical approach to characterizing time to failure involves fitting a parametric distribution, such as a Weibull probability function, using historical data on sales and records of failure incidents since the launch of a product. However, such modeling assumes that each deployed unit has an equal chance of failing by any specified age. Such assumptions are often violated when two or more subpopulations exist but cannot be identified and analyzed separately. For example, production process changes, defects generated during component manufacturing, errors in the assembly process, variation of consumer behavior, and variation of operating environmental conditions can all result in significant heterogeneity in performance best described by multiple time-to-failure distributions. Available information does not always exist to separate such subpopulations. Neglecting to account for differences in time-to-failure distributions can lead to erroneous interpretations and predictions. Weibull mixture models can characterize such complex reliability data in situations when segregating subpopulations is impractical. This paper presents three case studies that successfully applied mixture modeling to field reliability data that could not be adequately modeled by standard time-to-failure distributions for homogeneous product populations.