Weibull component reliability-prediction in the presence of masked data

Analysts are often interested in obtaining component reliabilities by analyzing system-life data. This is generally done by making a series-system assumption and applying a competing-risks model. These estimates are useful because they reflect component reliabilities after assembly into an operational system under true operating conditions. The fact that most new systems under development contain a large proportion of old technology also supports the approach, In practice, however, this type of analysis is often confounded by the problem of masking (the exact cause of system failure is unknown). This paper derives a likelihood function for the masked-data case and presents an iterative procedure (IMLEP) for finding maximum likelihood estimates and confidence intervals of Weibull component life-distribution parameters. The approach is illustrated with a simple numerical example.