Quality and Reliability Methods - SAS

Chapter 19 Reliability and Survival Analysis 367
Estimation of Competing Causes
To use this feature, hold down the Shift key, click on the red triangle of the Product-Limit Survival Fit
menu, and then click on the desired fit. You may then enter a constrained value for the parameter as
prompted: theta for the exponential fit; beta for the Weibull fit; and sigma for the lognormal fit.
Estimation of Competing Causes
Sometimes there are multiple causes of failure in a system. For example, suppose that a manufacturing
process has several stages and the failure of any stage causes a failure of the whole system. If the different
causes are independent, the failure times can be modeled by an estimation of the survival distribution for
each cause. A censored estimation is undertaken for a given cause by treating all the event times that are not
from that cause as censored observations.
Nelson (1982) discusses the failure times of a small electrical appliance that has a number of causes of
failure. One group (Group 2) of the data is in the JMP data table Appliance.jmp sample data, in the
Reliability subfolder.
To specify the analysis you only need to enter the time variable (Time Cycles) in the Survival dialog. Then
use the Competing Causes menu command, which prompts you to choose a column in the data table to
label the causes of failure. For this example choose Cause Code as the label variable.
Figure 19.20 Competing Causes Window
The survival distribution for the whole system is just the product of the survival probabilities. The
Competing Causes table gives the Weibull estimates of Alpha and Beta for each failure cause. It is shown
with the hazard plot in Figure 19.21.
In this example, most of the failures were due to cause 9. Cause 1 occurred only once and couldn’t produce
good Weibull estimates. Cause 15 happened for very short times and resulted in a small beta and large
alpha. Recall that alpha is the estimate of the 63.2% quantile of failure time, which means that causes with
early failures often have very large alphas; if these causes do not result in early failures, then these causes do
not usually cause later failures.