ESTIMATION FROM QUASI LIFE-TABLES

A large number of identical components are simultaneously set into operation at each of a regular sequence of times and, on failure, a component is instantaneously replaced. The functional form of the distribution of the component lifelength is assumed to be known and it is desired to estimate the parameters of this distribution. However, no observations of the lifelengths of individual components have been recorded: the, only information available is the numbers of components which fail between successive time points. It is shown how this information, in conjunction with the theory of recurrent events, may be used to construct a nonparametric estimator of the discretised lifelength distribution. The latter is then used to estimate the unknown parameters.