  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.
