A method for specifying critical threshold of Wiener degradation process

Degradation data are widely used in the field of reliability analysis and remaining useful lifetime estimation. Usually, a critical threshold must be defined before both reliability analysis and lifetime estimation is executed. In this paper, we present a method to specify a critical threshold for Wiener degradation process, based on both historical lifetime data and degradation data. The lifetime, defined as the first passage time of the Wiener process crossing a constant threshold, is changed to the first passage time of a standard Brownian motion passing a time dependent boundary. After fit a suitable distribution to the lifetime data and estimate parameters in the degradation path using the degradation data, this boundary, which is a function of the critical threshold, can be acquired approximately by solving an inverse first passage time problem. And the critical threshold is obtained accordingly through the function modelling the relationship between the threshold and the time dependent boundary. A numerical example is provided to illustrate and demonstrate the proposed method.