Bayesian estimation and optimal designs in partially accelerated life testing

TLDR

Life testing can be conducted either in a standard environment or under stress. The paper proposes a partially accelerated life‑testing method and aims to estimate the lifetime parameter θ and stress factor α while optimizing the test design via Bayesian decision theory. The design fixes a stress level and a cut‑off time x; items are tested normally until x, then under stress with lifetime multiplied by α, producing a piecewise lifetime distribution where T is exponential with parameter θ.

Abstract

Abstract A method of life testing is proposed which combines both ordinary and accelerated life‐testing procedures. It is assumed that an item can be tested either in a standard environment or under stress. The amount of stress is fixed in advance and is the same for all items to be tested However, the time x at which an item on lest is taken out of the standard environment and put under stress can be chosen by the experimenter subject to a given cost structure. When an item is put under stress its lifetime is changed by the factor α. Let the random variable T denote the lifetime of an item in the standard environment, and let γ denote its lifetime under the partially accelerated test procedure just described. Then Y = T if T ≦ x , and Y = x + α ( T > x ) if T > x . It is assumed that T has an exponential distribution with parameter θ. The estimation of θ and α and the optimal design of a partially accelerated life test are studied in the framework of Bayesian decision theory.