Estimation subject to block censoring

A series system comprises n components arranged in decreasing order of likelihood of failure. The components are grouped into modules and, on system failure, the modules are replaced in sequence until the system is repaired. Thus, it is not known which component has failed, only which module contains the failed component. It is shown how, for a certain class of life-length distributions, prior information on the relative propensities of the components to fail can be incorporated to estimate the parameters of the life-length distributions of the components. The case where each component life-length is exponentially distributed is studied in detail