Statistical analysis of marginal count failure data

Manufacturers want to assess the quality and reliability of their products. Specifically, they want to know the exact number of failures from the sales transacted during a particular month. Information available today is sometimes incomplete as many companies analyze their failure data simply comparing sales for a total month from a particular department with the total number of claims registered for that given month. This information--called marginal count data--is, thus, incomplete as it does not give the exact number of failures of the specific products that were sold in a particular month. In this paper we discuss nonparametric estimation of the mean numbers of failures for repairable products and the failure probabilities for nonrepairable products. We present a nonhomogeneous Poisson process model for repairable products and a multinomial model and its Poisson approximation for nonrepairable products. A numerical example is given and a simulation is carried out to evaluate the proposed methods of estimating failure probabilities under a number of possible situations.