Dealing with real field reliability data: circumventing incompleteness by modeling and iteration

It is desired to estimate the parameters of the lifelength distribution of a given component. The observations on which inference is to be based are field data which are incomplete in some fashion. Thus, for example, the reported lifelength may include a period of unknown duration during which the component is not in use; the lifelength distribution may be affected by an unobserved environmental factor; or the component may be part of larger system, and failure mode analysis reveals only the module containing the failed component, not the identity of the latter. In each case, the estimation may be reformulated as a two-stage iterative procedure: at each iteration, we alternately estimate the missing information and the parameters of interest. Such a procedure is a special case of the expectation maximisation algorithm, or one of its variants, and hence, under fairly general conditions, the sequence of estimates of the unknown parameters converges to the maximum likelihood estimate of the latter