You have a fleet of 60 haul trucks. You have been told by the OEM that they allocate 5% of the purchase price to cover repairs during the warranty period. The rationale for this is that the warranty is meant to cover infant mortality failures, with the purpose of indemnifying the owner against manufacturing defects that would reveal themselves during the first year of operation. You would like to use data from this fleet to verify the manufacturer’s logic and the fairness of his warranty calculation.
In this fleet there were six failures. Can you, using the ages of these six failures, perform a Weibull analysis. Then by inspecting the resulting failure rate (hazard) plot could you get a measure of the period (if any) of infant mortality? Finally, might you use the survival curve to come to a judgment on the adequacy of the manufacturer’s 5% one year warranty allocation?
These are good questions because they drive home the concept of a “good” sample for analysis. A good sample is one that is unbiased. However, by entering only these six failure ages into your Weibull software application, you are definitely going to get a biased analysis. The reason is that the analysis ignores all the units that didn’t fail.
One of the best ways to get a good sample for reliability analysis is to use a time window defined by two calendar dates, say 3 or 4 years apart, such that your six failures occurred in that period. To make things simple, assume that the entire fleet was purchased after the sample start date. That gives you six complete life cycles and 60 partial life cycles, assuming that all 60 were in service and operating at the time the sample period ended.
Enter into your Weibull software application the six failure ages as well as the ages of each of the 60 operating units at the date marking the end of the calendar window defining the sample. We call these 60 “temporary suspensions”. Use the software to plot the hazard (aka failure rate function) and survival graphs. With those, and the estimated repair costs, draw your conclusions on the adequacy of the manufacturer’s warranty policy.
© 2011, Murray Wiseman. All rights reserved.