Weibull Probability Plots with Corners and Doglegs
Data collection is often less than perfect. When the Weibull probability plot shows sharp corners or dogleg bends, the cause is likely to be the mixture of multiple failure modes or failure sources in the data set. For example, many hydro-mechanical components show infant mortality from production and quality problems, followed by wear-out later in life as competing failure modes. The resulting Weibull probability plot is likely to have a shallow slope followed by a steep slope.
Known as a classic bi-Weibull, results for both the infant mortality and wear-out failure mechanisms are shown on one probability plot. Such bi-Weibull probability plots often occur in the analysis of warranty data. Although failure and suspension times are identified, the modes of failure often are not. In such cases, the life data should be examined to determine the different failure modes that exist, and the failures from modes other than the one being plotted should be tagged as suspensions.
In cases where the failure modes cannot be physically separated, Weibull software often provides a technique for separating failure modes statistically by analysing the data for competing risks. This means that the software searches the data set for two possible failure modes by evaluating ordered combinations. Separate Weibull probability plots are then generated for each failure mode identified, with the failures from a second failure mode (B) treated as suspensions for the first failure mode under consideration (A).
When warranty data suffers from mixed failure modes, the Kaplan-Meier model can be used to predict life based on the age of the units. Or, the Crow-AMSAA model can be used to predict life based on test or calendar time. The Kaplan-Meier and Crow-AMSAA models are further described in Related Quantitative Models.
When a data set mixes many failure modes for a system or component, the doglegs disappear, the slope tends toward 1 and the Weibull distribution has a better fit. However, using a Weibull probability plot with a mixture of many failure modes is the equivalent of assuming that the exponential distribution applies. The best procedure is to perform careful analysis of the root causes for failure and avoid mixing failure modes together. An effort to categorise the data into separate, more accurate failure modes should be made.