Weibull accelerated life testing analysis with several variables using multiple linear regression

Abstract

In Weibull accelerated life test analysis (ALT) with two or more variables (X2, X3, ... Xk), we estimated, in joint form, the parameters of the life stress model r{X(t)} and one shape parameter β. These were then used to extrapolate the conclusions to the operational level. However, these conclusions are biased because in the experiment design (DOE) used, each combination of the variables presents its own Weibull family (βi, ηi). Thus the estimated β is not representative. On the other hand, since (βi, ηi) is determined by the variance of the logarithm of the lifetime data σt2 , the response variance σy2 and the correlation coefficient R2, which increases when variables are added to the analysis, β is always overestimated. In this paper, the problem is statistically addressed and based on the Weibull families (βi, ηi) a vector Yη is estimated and used to determine the parameters of r{X(t)}. Finally, based on the variance σy2 of each level, the variance of the operational level σop2 is estimated and used to determine the operational shape parameter βop. The efficiency of the proposed method is shown by numerical applications and by comparing its results with those of the maximum likelihood method (ML).