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362 Reliability and Survival Analysis Chapter 19 Univariate Survival Analysis Save Estimates creates a data table containing survival and failure estimates, along with confidence intervals, and other distribution statistics. Fitting Distributions For each of the three distributions JMP supports, there is a plot command and a fit command. Use the plot command to see if the event markers seem to follow a straight line. The markers tend to follow a straight line when the distributional fit is suitable for the data. Then use the fit commands to estimate the parameters. Figure 19.15 Exponential, Weibull, and Lognormal Plots and Tables
Chapter 19 Reliability and Survival Analysis 363 Univariate Survival Analysis The following table shows what to plot that makes a straight line fit for that distribution: Table 19.1 Straight Line Fits for Distribution Distribution Plot X Axis Y Axis Interpretation Exponential time -log(S) slope is 1/theta Weibull log(time) log(-log(S)) slope is beta Lognormal log(time) Probit(1-S) slope is 1/sigma Note: S = product-limit estimate of the survival distribution The exponential distribution is the simplest, with only one parameter, which we call theta. It is a constant-hazard distribution, with no memory of how long it has survived to affect how likely an event is. The parameter theta is the expected lifetime. The Weibull distribution is the most popular for event-time data. There are many ways in which different authors parameterize this distribution (as shown in Table 19.2 on page 364). JMP reports two parameterizations, labeled the lambda-delta extreme value parameterization and the Weibull alpha-beta parameterization. The alpha-beta parameterization is used in the Reliability literature. See Nelson (1990). Alpha is interpreted as the quantile at which 63.2% of the units fail. Beta is interpreted as follows: if beta>1, the hazard rate increases with time; if beta
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INDIRECT OR CONSEQUENTIAL DAMAGES O
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Chapter 1 Learn about JMP 17 Book C
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Chapter 11 Pareto Plots The Pareto
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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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Quality and Reliability Methods - SAS

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