On the variance of total warranty claims

A model for obtaining the expected value of total warranty claims is extended to derive the variance of their size. The model considers N items whose failure time distribution is gamma, the warranty policy is pro-rata or lump sum, and total discounted warranty claims are of interest. The paper focuses on the variance of this total which is computed both for the case when the parameters of the gamma distribution are known and for the case when one of the parameters, the mean, is unknown. (A Bayesian approach is used for parameter estimation.) It is shown that parameter uncertainty can have a considerable effect on the variance of total warranty claims.