A large number of identical components are simultaneously set into ope
ration at each of a regular sequence of times and, on failure, a compo
nent is instantaneously replaced. The functional form of the distribut
ion of the component lifelength is assumed to be known and it is desir
ed to estimate the parameters of this distribution. However, no observ
ations of the lifelengths of individual components have been recorded:
the, only information available is the numbers of components which fa
il between successive time points. It is shown how this information, i
n conjunction with the theory of recurrent events, may be used to cons
truct a nonparametric estimator of the discretised lifelength distribu
tion. The latter is then used to estimate the unknown parameters.