The Constant Shape Parameter Assumption in Weibull Regression

Abstract

The usual assumption in Weibull regression is that the scale parameter is a function of the predictor variables, and the shape parameter is constant. We consider the problem of estimating parameters in the presence of a nonconstant shape parameter and the effect of assuming a constant shape parameter when it really is not constant. We consider both classical and Bayesian methods of estimation. The misspecification of a constant shape parameter can lead to a loss of power for tests regarding the slope parameters. We find that prediction intervals can be inaccurate when the shape parameter is incorrectly assumed to be constant.

Lower Percentile Estimation of Accelerated Life Tests with Nonconstant Scale Parameter

“…In ALT, higher stress levels may induce failure mechanisms that are never experienced at lower stress levels. This indicates that the scale parameter is a function of the stresses. A large number of researcher have studied on the nonconstant scale parameter assumption for (log) location‐scale distribution.…”

“…Balakrishnan et al concluded that the shape parameter of the one‐shot device was affected by stress levels. Mueller and Rigdon concluded that it could yield misleading prediction intervals under the constant shape parameter assumption when the shape parameter depends on the stresses. In this paper, we follow the nonconstant scale parameter assumption as discussed by many researchers in the SEV distribution.…”