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

In Weibull accelerated life test analysis (ALT) with two or more variables (X₂, X₃, ... X_k), 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 (β_i, η_i). Thus the estimated β is not representative. On the other hand, since (β_i, η_i) is determined by the variance of the logarithm of the lifetime data σ_t² , the response variance σ_y² 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 (β_i, η_i) a vector Y_η is estimated and used to determine the parameters of r{X(t)}. Finally, based on the variance σ_y² of each level, the variance of the operational level σ_op² is estimated and used to determine the operational shape parameter β_op. The efficiency of the proposed method is shown by numerical applications and by comparing its results with those of the maximum likelihood method (ML).