Expectation-Maximization Algorithm for Failure Analysis Using Incomplete Warranty Data
Volume 5, Number 5, October 2009 - Paper 1 - pp. 403-417
SUPRASAD V. AMARI1, KAREN MOHAN1, BRAD CLINE1, LIUDONG XING2
1Relex Software Corporation, 540 Pellis Road, Greensburg, PA 15601, USA
2University of Massachusetts Dartmouth, 285 Old Westport Road, Dartmouth, MA 02747, USA
(Received on October 3, 2007, revised on April 29, 2008)
The use of warranty claims data to determine the failure characteristics of a product is well documented. Typically, existing techniques assume that the product ages at the times of failure are known or can be derived based on product manufacturing data for each month of production and the corresponding monthly failure counts derived from the warranty claims. However, our experience shows that, in many cases, it may not be possible to know the failure ages of components. The information available from each month might be limited to the volume of shipments and total claims or product returns. In these cases, the data hides the component age at the time of failure. In this 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. The popular Expectation-Maximization (EM) algorithm is applied to find the Maximum Likelihood Estimates (MLE) of the failure distribution parameters using incomplete data. The effectiveness of the EM algorithm is compared using several sets of incomplete warranty data generated using simulation. The EM algorithm is observed to be powerful in capturing the hidden failure patterns from the incomplete warranty data.
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