The R. A. Evans - P. K. McElroy Award for the 2008 Best Paper

Abstract

Warranty data is a valuable source of information for analyzing the failure characteristics of a product. Knowing the failure trends of a product provides an array of benefits, including the ability to predict future returns, to estimate warranty-related claim costs, and to monitor product quality. Typically, the failure distribution and its parameters are determined using product manufacturing data for each month of production and the corresponding monthly failure counts derived from the warranty claims. If the data is collected systematically, the product ages at the times of failure can be derived. Classical methods are then used to determine the failure time distribution and parameters. However, in many cases it may not be possible to know the failure ages of components. The information available each month might be limited to the volume of shipments and total claims or product returns. In such cases, the data hides the component age at the time of failure. In our paper, we show that when the failure history information is incomplete, the failure distribution of the product can be determined using Bayesian analysis techniques applicable for handling incomplete data. We apply the popular Expectation-Maximization (EM) algorithm to find the Maximum Likelihood Estimates (MLE) of the failure distribution parameters using incomplete data. The effectiveness of the EM algorithm is evaluated against classical methodology by using several sets of simulated complete/incomplete warranty data. We observed that the EM algorithm is powerful in capturing the hidden failure patterns from the incomplete warranty data.