Estimating a Service-Life Distribution Based on Production Counts and a Failure Database

Problem: A manufacturer wanted to compare the service-life distributions of two similar products. These concern product lifetimes after installation (not manufacture). For each product, there were available production counts and an imperfect database providing information on failing units. In the real case, these units were expensive repairable units warrantied against repairs. Failure (of interest here) was relatively rare and driven by a different mode/mechanism than ordinary repair events (not of interest here). Approach: Data models for the service life based on a standard parametric lifetime distribution and a related limited failure population were developed. These models were used to develop expressions for the likelihood of the available data that properly accounts for information missing in the failure database. Results: A Bayesian approach was employed to obtain estimates of model parameters (with associated uncertainty) in order to investigate characteristics of the service-life distribution. Custom software was developed and is included as Supplemental Material to this case study. One part of a responsible approach to the original case was a simulation experiment used to validate the correctness of the software and the behavior of the statistical methodology before using its results in the application, and an example of such an experiment is included here. Because of confidentiality issues that prevent use of the original data, simulated data with characteristics like the manufacturer\u27s proprietary data are used to illustrate some aspects of our real analyses. We note also that, although this case focuses on rare and complete product failure, the statistical methodology provided is directly applicable to more standard warranty data problems involving typically much larger warranty databases where entries are warranty claims (often for repairs) rather than reports of complete failures