Figure 12.5 Exponential, Weibull, and Lognormal Plots and Reports
The alpha-beta parameterization, shown in the Weibull Parameter Estimates report, is widely used in the reliability literature (Nelson 1990). The alpha parameter is interpreted as the quantile at which 63.2% of the units fail. The beta parameter determines how the hazard rate changes over time. If beta > 1, the hazard rate increases over time; if beta < 1, the hazard rate decreases over time; and if beta = 1, the hazard rate is constant over time. A Weibull distribution with a constant hazard function is equivalent to an exponential distribution.
The lambda-delta extreme value parameterization is shown in the Extreme-Value Parameter Estimates report. This parameterization is sometimes desirable in a statistical sense because it places the Weibull distribution in a location-scale setting (Meeker and Escobar 1998, p. 86). The location parameter is lambda, and the scale parameter is delta. In relation to the alpha-beta parameterization, lambda is equal to the natural log of alpha, and delta is equal to the reciprocal of beta. Therefore, the delta parameter determines how the hazard rate changes over time. If delta > 1, the hazard rate decreases over time; if delta < 1, the hazard rate increases over time; and if delta = 1, the hazard rate is constant over time. A Weibull distribution with a constant hazard function is equivalent to an exponential distribution.
alpha=alpha
beta=beta
eta=alpha
beta=beta
c = alpha
m = beta
eta=alpha
beta=beta
beta=alpha
alpha=beta
p = beta
mu=log(alpha)
Figure 12.6 Confidence Contour Plot

Help created on 7/12/2018