Quality and Reliability Methods - SAS

334 Reliability Growth Chapter 18
Fit Model Options
Figure 18.12 Achieved MTBF Report
There are infinitely many possible failure-time sequences from an NHPP; the observed data represent only
one of these. Suppose that the test is failure terminated at the n th failure. The confidence interval computed
in the Achieved MTBF report takes into account the fact that the n failure times are random. If the test is
time terminated, then the number of failures as well as their failure times are random. Because of this, the
confidence interval for the Achieved MTBF differs from the confidence interval provided by the MTBF
Profiler at the last observed failure time. Details can be found in Crow (1982) and Lee and Lee (1978).
When the test is failure terminated, the confidence interval for the Achieved MTBF is exact. However, when
the test is time terminated, an exact interval cannot be obtained. In this case, the limits are conservative in
the sense that the interval contains the Achieved MTBF with probability at least 1-α.
Goodness of Fit
The Goodness of Fit report tests the null hypothesis that the data follow an NHPP with Weibull intensity.
Depending on whether one or two time columns are entered, either a Cramér-von Mises (see “Cramér-von
Mises Test for Data with Uncensored Failure Times” on page 334) or a chi-squared test (see “Chi-Squared
Goodness of Fit Test for Interval-Censored Failure Times” on page 335) is performed.
Cramér-von Mises Test for Data with Uncensored Failure Times
When the data are entered in the launch window as a single Time to Event or Timestamp column, the
goodness of fit test is a Cramér-von Mises test. For the Cramér-von Mises test, large values of the test
statistic lead to rejection of the null hypothesis and the conclusion that the model does not fit adequately.
The test uses an unbiased estimate of beta, given in the report. The value of the test statistic is found below
the Cramér-von Mises heading.
The entry below the p-Value heading indicates how unlikely it is for the test statistic to be as large as what is
observed if the data come from a Weibull NHPP model. The platform computes p-values up to 0.25. If the
test statistic is smaller than the value that corresponds to a p-value of 0.25, the report indicates that its
p-value is >=0.25. Details about this test can be found in Crow (1975).
Figure 18.13 shows the goodness-of-fit test for the fit of a Crow-AMSAA model to the data in
TurbineEngineDesign1.jmp. The computed test statistic corresponds to a p-value that is less than 0.01. We
conclude that the Crow-AMSAA model does not provide an adequate fit to the data.