Weibull accelerated life testing analysis with several variables using multiple linear regression
In Weibull accelerated life test analysis (ALT) with two or more variables (<em>X<sub>2</sub>, X<sub>3</sub>, ... X<sub>k</sub></em>), 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<sub>i</sub>, η<sub>i</sub>). Thus the estimated β is not representative. On the other hand, since (β<sub>i</sub>, η<sub>i</sub>) is determined by the variance of the logarithm of the lifetime data σ<sub>t</sub><sup>2</sup> , the response variance σ<sub>y</sub><sup>2</sup> and the correlation coefficient R<sup>2</sup>, 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<sub>i</sub>, η<sub>i</sub>) a vector Y<sub>η</sub> is estimated and used to determine the parameters of r{X(t)}. Finally, based on the variance σ<sub>y</sub><sup>2</sup> of each level, the variance of the operational level σ<sub>op</sub><sup>2</sup> is estimated and used to determine the operational shape parameter β<sub>op</sub>. The efficiency of the proposed method is shown by numerical applications and by comparing its results with those of the maximum likelihood method (ML).
