Quality and Reliability Methods - SAS

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402 Reliability and Survival Analysis II Chapter 20 Nonlinear Parametric Survival Models Figure 20.25 Nonlinear Fit Results To use the Weibull loss function with two parameters or the extreme value loss function, again select Nonlinear and choose the loss function you want. Use starting values of 1 for the alpha and beta parameters in the Weibull function and for delta and lambda in the extreme-value function. The results are shown above. Note: Be sure to check the Loss is Neg LogLikelihood check box before you click Go. Lognormal Loss Function Example The Locomotive.jmp data in the Reliability sample data folder can be used to illustrate a lognormal loss. The lognormal distribution is useful when the range of the data is several powers of 10. The logNormal column in the table has the formula:
Chapter 20 Reliability and Survival Analysis II 403 Nonlinear Parametric Survival Models The lognormal loss function can be very sensitive to starting values for its parameters. Because the lognormal is similar to the normal distribution, you can create a new variable that is the log 10 of Time and use Distribution to find the mean and standard deviation of this column. Then, use those values as starting values for the Nonlinear platform. In this example the mean of log 10 of Time is 2.05 and the standard deviation is 0.15. Run this example as described in the previous examples. Assign lognormal as the Loss function. In the Nonlinear Fit Control Panel give Mu and Sigma the starting values 2.05 and 0.15 and click Go. After the Solution is found, you can click Confidence Limits on the Control Panel and see the table shown here. Figure 20.26 Solution Report Note: Remember to Save Estimates before requesting confidence limits. The maximum likelihood estimates of the lognormal parameters are 2.2223 for Mu and 0.3064 for Sigma (in base 10 logs). The corresponding estimate of the median of the lognormal distribution is the antilog of 2.2223 (10 2.2223 ), which is approximately 167. This represents the typical life for a locomotive engine.
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Quality and Reliability Methods - SAS

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