Exponential, Weibull, and Lognormal Plots and Reports
 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
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 Various Weibull Parameters in Terms of JMP’s alpha and beta). 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<1, the hazard rate decreases with time; and if beta=1, the hazard rate is constant, meaning it is the exponential distribution.
 JMP Weibull alpha beta Wayne Nelson alpha=alpha beta=beta Meeker and Escobar eta=alpha beta=beta Tobias and Trindade c = alpha m = beta Kececioglu eta=alpha beta=beta Hosmer and Lemeshow exp(X beta)=alpha lambda=beta Blishke and Murthy beta=alpha alpha=beta Kalbfleisch and Prentice lambda = 1/alpha p = beta JMP Extreme Value lambda=log(alpha) delta=1/beta Meeker and Escobar s.e.v. mu=log(alpha) sigma=1/beta
 • Set the confidence level for the limits.
 •
 •
Confidence Contour Plot
 • Where there are few or no failures
 • There are existing historical values for beta
 • There is still a need to estimate alpha

Help created on 9/19/2017