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