On analysis of incomplete field failure data

TL;DR

This paper develops a stochastic expectation-maximization algorithm to analyze incomplete field failure data with unknown sales dates, improving reliability estimates for products with warranty limits.

Contribution

It introduces a novel SEM algorithm for estimating sales lag and product lifetime distributions in the presence of missing sales data, enhancing analysis accuracy.

Findings

SEM algorithm performs well in simulations

Outperforms previous imputation methods

Validated with three real-world examples

Abstract

Many commercial products are sold with warranties and indirectly through dealers. The manufacturer-retailer distribution mechanism results in serious missing data problems in field return data, as the sales date for an unreturned unit is generally unknown to the manufacturer. This study considers a general setting for field failure data with unknown sales dates and a warranty limit. A stochastic expectation-maximization (SEM) algorithm is developed to estimate the distributions of the sales lag (time between shipment to a retailer and sale to a customer) and the lifetime of the product under study. Extensive simulations are used to evaluate the performance of the SEM algorithm and to compare with the imputation method proposed by Ghosh [Ann. Appl. Stat. 4 (2010) 1976-1999]. Three real examples illustrate the methodology proposed in this paper.