Age-based warranty data analysis without date-specific sales information

Age-based analysis of warranty claim data forms the basis for the estimation, prediction, and comparison of claims across different product groups or across time. The age of a product means the elapsed calendar time since the product was sold or entered service. In this article, we develop a method to deal with situations when the information on date-specific sales amounts is not available but the total sales quantity can be determined from other sources. Date-specific sales amounts, i.e. the number of products sold on different dates, are difficult to determine for many products from many wholesalers and retailers around the world. We consider the problem of maximum likelihood estimation of the expected number of claims for repairable items based on a non-homogeneous Poisson process model, and of the probability of a claim for non-repairable items based on a multinomial model. These estimators derived for the above two cases are in a closed-form expression and are the same. We carry out numerical simulation to evaluate the effectiveness of these proposed estimators by comparing them with those obtained under the assumption that date-specific sales amounts are available.