Quality and Reliability Methods - SAS

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224 Lifetime Distribution Chapter 13 Additional Examples of the Life Distribution Platform Figure 13.11 Nonparametric Estimates with a Fréchet Probability Scale nonparametric estimates Using a Fréchet scale, the nonparametric estimates approximate a straight line, meaning that a Fréchet fit might be reasonable. 4. Select SEV in the Scale column. The nonparametric estimates no longer approximate a straight line (Figure 13.12). You now know that the SEV distribution is not appropriate.
Chapter 13 Lifetime Distribution 225 Statistical Details Figure 13.12 Nonparametric Estimates with a SEV Probability Scale Statistical Details This section provides details for the distributional fits in the Life Distribution platform. Meeker and Escobar (1998, chaps. 2-5) is an excellent source of theory, application, and discussion for both the nonparametric and parametric details that follow. The parameters of all distributions, unless otherwise noted, are estimated via maximum likelihood estimates (MLEs). The only exceptions are the threshold distributions. If the smallest observation is an exact failure, then this observation is treated as interval-censored with a small interval. The parameter estimates are the MLEs estimated from this slightly modified data set. Without this modification, the likelihood can be unbounded, so an MLE might not exist. This approach is similar to that described in Meeker and Escobar (1998, p. 275), except that only the smallest exact failure is censored. This is the minimal change to the data that guarantees boundedness of the likelihood function. Two methods exist in the Life Distribution platform for calculating the confidence intervals of the distribution parameters. These methods are labeled as Wald or Profile (profile-likelihood) and can be selected in the launch window for the Life Distribution platform. Wald confidence intervals are used as the default setting. The computations for the confidence intervals for the cumulative distribution function (cdf) start with Wald confidence intervals on the standardized variable. Next, the intervals are transformed to the cdf scale (Nelson, 1982, pp. 332-333 and pp. 346-347). The confidence intervals given in the other graphs and profilers are transformed Wald intervals (Meeker and Escobar, 1998, chap. 7). Joint confidence intervals for the parameters of a two-parameter distribution are shown in the log-likelihood contour plots. They are based on approximate likelihood ratios for the parameters (Meeker and Escobar, 1998, chap. 8).
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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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References 413 Nelson, W.B. (2003),
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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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Index 423 Weibull Plot 360 Westgard
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