Estimation of the Guarantee Time in an Exponential Failure Model

The location parameter ¿ in a 2-parameter exponential failure model is often termed the guarantee time since no failure can occur until the life exceeds ¿. Several point estimators of ¿ are compared by examining each estimator´s risk corresponding to a loss function which features a greater penalty for overestimating than for underestimating ¿. The estimators considered in this fashion are: maximum likelihood, minimum variance unbiased, best invariant, and median unbiased. A new estimator of ¿ is derived which has smaller risk under our assumptions than any of the aforementioned estimators. A 2-fold pairwise comparison technique is then used which examines a) the odds in favor of the new estimator´s being closer to ¿ than is a competitor, and b) each estimator´s risk not only when it is closer to ¿ than is the other but also when it is not.