Quality and Reliability Methods - SAS

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346 Reliability Growth Chapter 18 Additional Examples of the Reliability Growth Platform Figure 18.23 Cumulative Events Plot with Crow AMSAA Model 8. From the red triangle menu at Reliability Growth, select Fit Model > Piecewise Weibull NHPP Change Point Detection. The Cumulative Events plot in the Observed Data report updates to show the piecewise model fit using change-point detection. Both models are shown in Figure 18.24. Though the data are rather sparse, the piecewise model appears to provide a better fit to the data.
Chapter 18 Reliability Growth 347 Statistical Details for the Reliability Growth Platform Figure 18.24 Cumulative Events Plot with Two Models Statistical Details for the Reliability Growth Platform Statistical Details for the Crow-AMSAA Report Parameter Estimates Profilers The estimates for λ and β are maximum likelihood estimates, computed as follows. The likelihood function is derived using the methodology in Meeker and Escobar (1998). It is reparametrized in terms of param = log(λ) and param 2 =log(β). This is done to enable the use of an unconstrained optimization algorithm, namely, an algorithm that searches from - ∞ to + ∞ . The MLEs for param 1 and param 2 are obtained. Their standard errors are obtained from the Fisher information matrix. Confidence limits for param 1 and param 2 are calculated based on the asymptotic distribution of the MLEs, using the Wald statistic. These estimates and their confidence limits are then transformed back to the original units using the exponential function. The estimates for the MTBF, Intensity, and Cumulative Events given in the profilers are obtained by replacing the parameters λ and β in their theoretical expressions by their MLEs. Confidence limits are obtained by applying the delta method to the log of the expression of interest.
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References Abernethy, Robert B. (19
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References 407 Carroll, R.J., Ruppe
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References 409 Haaland, P.D. (1989)
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References 411 Lawless, J.F. (1982)
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Index JMP Quality and Reliability M
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Index 419 Fit SEV 242 Fit Weibull 2
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Index 421 Q Quantiles table 356 R R
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Quality and Reliability Methods - SAS

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