Issue 30, August 2003

What is the "Use True 3-P MLE on Weibull" option on the Calculations page of the User Setup in Weibull++?

This option simply indicates how the parameters of the 3-parameter Weibull distribution are to be estimated when using maximum likelihood estimation (MLE). If this option is not selected, Weibull++ first determines the estimate of the location parameter by nonlinear regression. Once this estimate has been determined, Weibull++ uses MLE to estimate beta and eta. This methodology is generally more appropriate for the analysis of life data.

If this option is selected, then all three parameters are estimated simultaneously using MLE. However, a pure MLE solution on a 3-parameter Weibull distribution is problematic in certain regions of beta and may yield results that do not make sense in the context of life data analysis (e.g. very large negative values for gamma, etc.).

Why is rank regression not available as an analysis method in ALTA?

Although rank regression (graphical methods) is fairly simple, it is quite laborious. Furthermore, many issues surrounding its use require careful consideration. Some of these issues are presented next:

• What happens when no failures are observed at one or more stress level? In this case, plotting methods cannot be employed. Discarding the data would be a mistake since every piece of life data information is important. In other words, no failures at one stress level combined with observed failures at other stress level(s) are an indication of the dependency of life on stress. This information cannot be discarded.
• In the step at which the life-stress relationship is linearized and plotted to obtain its parameters, you must be able to linearize the function, which is not always possible.
• In real accelerated tests, the data sets are small. Separating them and individually plotting them and then subsequently re-plotting the results increases the underlying error.
• During initial parameter estimation, the parameter that is assumed constant will likely vary.

• Confidence intervals on all of the results cannot be ascertained using graphical methods.

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