Quality and Reliability Methods - SAS

Chapter 18 Reliability Growth 347
Statistical Details for the Reliability Growth Platform
Figure 18.24 Cumulative Events Plot with Two Models
Statistical Details for the Reliability Growth Platform
Statistical Details for the Crow-AMSAA Report
Parameter Estimates
Profilers
The estimates for λ and β are maximum likelihood estimates, computed as follows. The likelihood function
is derived using the methodology in Meeker and Escobar (1998). It is reparametrized in terms of
param = log(λ) and param 2 =log(β). This is done to enable the use of an unconstrained optimization
algorithm, namely, an algorithm that searches from - ∞ to + ∞ . The MLEs for param 1 and param 2 are
obtained. Their standard errors are obtained from the Fisher information matrix. Confidence limits for
param 1 and param 2 are calculated based on the asymptotic distribution of the MLEs, using the Wald
statistic. These estimates and their confidence limits are then transformed back to the original units using
the exponential function.
The estimates for the MTBF, Intensity, and Cumulative Events given in the profilers are obtained by
replacing the parameters λ and β in their theoretical expressions by their MLEs. Confidence limits are
obtained by applying the delta method to the log of the expression of interest.