Quality and Reliability Methods - SAS

Chapter 18 Reliability Growth 335
Fit Model Options
Figure 18.13 Goodness of Fit Report - Cramér-von Mises Test
Chi-Squared Goodness of Fit Test for Interval-Censored Failure Times
When the data are entered in the launch window as two Time to Event or Timestamp columns, a
chi-squared goodness of fit test is performed. The chi-squared test is based on comparing observed to
expected numbers of failures in the time intervals defined. Large values of the test statistic lead to rejection
of the null hypothesis and the conclusion that the model does not fit.
In the Reliability Growth platform, the chi-squared goodness of fit test is intended for interval-censored
data where the time intervals specified in the data table cover the entire time period of the test. This means
that the start time of an interval is the end time of the preceding interval. In particular, intervals where no
failures occurred should be included in the data table. If some intervals are not consecutive, or if some
intervals have identical start and end times, the algorithm makes appropriate accommodations. But the
resulting test will be only approximately correct.
Fixed Parameter Crow AMSAA
This option enables you to specify parameter values for a Crow-AMSAA fit. If a Crow-AMSAA report has
not been obtained before choosing the Fixed Parameter Crow-AMSAA option, then both a Crow-AMSAA
report and a Fixed Parameter Crow-AMSAA report are provided.
When the Fixed Parameter Crow-AMSAA option is selected, the Cumulative Events Plot updates to display
this model. The Model List also updates. The Fixed Parameter Crow-AMSAA report opens to show the
MTBF plot for the Crow-AMSAA fit; this plot is described in the section “Show MTBF Plot” on page 338.
In addition to Show MTBF plot, available options are Show Intensity Plot, Show Cumulative Events Plot,
and Show Profilers. The construction and interpretation of these plots is described under “Crow AMSAA”
on page 329.
Estimates
The initial parameter estimates are the MLEs from the Crow-ASMAA fit. Either parameter can be fixed by
checking the box next to the desired parameter and then typing the desired value. The model is re-estimated
and the MTBF plot updates to describe this model. Figure 18.14 shows a fixed-parameter Crow-AMSAA fit
to the data in TurbineEngineDesign1.jmp, with the value of beta set at 0.4.