Crow AMSAA with Modified MLE

The Reliability Growth platform can fit a Crow-AMSAA model with a modified maximum likelihood estimate (MLE). In the Crow-AMSAA model, the MLE of β is biased. This option fits a Crow-AMSAA model where β is adjusted for bias.

Note: This option is available only when the data are entered in the launch window as a single Time to Event or Timestamp column. It is not available for interval-censored data.

Figure 11.15 shows a Crow-AMSAA with Modified MLE fit to the data in TurbineEngineDesign1.jmp.

Figure 11.15 Crow-AMSAA with Modified MLE Report 

The formula for the bias-corrected estimate of β depends on whether the test is failure terminated or time terminated. See Parameter Estimates for Crow-AMSAA with Modified MLE.

When the Crow-AMSAA with Modified MLE option is selected, the Cumulative Events Plot updates to display this model. The Model List also updates. The Crow-AMSAA with Modified MLE report opens to show the MTBF plot, Estimates, and Covariance Matrix for the Crow-AMSAA with Modified MLE fit; this plot is described in the section MTBF Plot.

In addition to Show MTBF plot, available options are Show Intensity Plot, Show Cumulative Events Plot, Show Profilers, Achieved MTBF, and Goodness of Fit. These reports are described under Crow AMSAA. For more information about how the modified MLEs are used to construct these reports, see Parameter Estimates for Crow-AMSAA with Modified MLE. Details about the Goodness of Fit and Achieved MTBF reports specific to the modified MLE option are given below.

Goodness of Fit

Because the Crow-AMSAA with Modified MLE option is available only when the data are entered as a single Time to Event or Timestamp column, the Goodness of Fit test is a Cramér-von Mises test. Because the estimate of β is used in this test is bias-corrected, the test results are identical to those of the Goodness of Fit test for the Crow-AMSAA model.

Achieved MTBF

The achieved MTBF is estimated using the modified MLEs. However, the confidence interval for the achieved MTBF uses the true MLE and is identical to the interval given by the Crow AMSAA model.