Bayesian estimation of system reliability under asymmetric loss.

摘要

This research is concerned with estimating the reliability of a k-out-of-p system when the lifetimes of its p components are iid, when subjective beliefs about the behavior of the system's individual components are available, and when losses corresponding to overestimation and underestimation errors can be approximated by a suitable family of asymmetric loss functions. Point estimates for such systems are discussed in the context of Bayes estimation with respect to loss functions. A set of properties is proposed as being minimal properties that all loss functions appropriate to reliability estimation might satisfy. Several families of asymmetric loss functions that satisfy these minimal properties are discussed, and their corresponding posterior Bayes estimators are derived. One of these families, squarex loss functions, is a generalization of linex loss functions. The concept of loss robustness is discussed in the context of parametric families of asymmetric loss functions. As an application, the reliability of O-rings critical to the 1986 catastrophic failure of the Space Shuttle Challenger is estimated. Point estimation of negative exponential stress-strength k-out-of-p systems with respect to reference priors is discussed in this context of asymmetric loss functions.