Estimation of system components reliabilities using masked data

摘要

Consider a system of m independent and non-identical components connected in series. Such system fails whenever at least one of the components has failed. Due to the cost and time constraints, however, the exact cause of system failure might be unknown. Instead, it is assumed that the cause of system failure may be due to a component that belongs to a subset of the m components. Such type of observation is referred to as being masked. Confronted with this phenomenon, we use the maximum likelihood procedure to estimate the parameters indexed to the lifetime distributions of the system components. Further the system component reliabilities at a specified time will be estimated. We focused on series systems with two and three components. The system components lifetimes are assumed to be Weibull distributed. We show that closed-form solutions for the maximum likelihood estimates can be obtained under certain assumptions. Further, numerical simulation study is presented.