Quality and Reliability Methods - SAS

Chapter 18 Reliability Growth 331
Fit Model Options
Figure 18.8 MTBF Plot
To see why the MTBF plot is linear when logarithmic scaling is used, consider the following. The mean
time between failures is the reciprocal of the intensity function. For the Weibull intensity function, the
MTBF is 1 ⁄ ( λβt β – 1 ), where t represents the time since testing initiation. It follows that the logarithm of
the MTBF is a linear function of log(t), with slope 1 - β. The estimated MTBF is defined by replacing the
parameters λ and β by their estimates. So the log of the estimated MTBF is a linear function of log(t).
Estimates
Maximum likelihood estimates for lambda (λ), beta (β), and the Reliability Growth Slope (1 - β), appear in
the Estimates report below the plot. (See Figure 18.8.) Standard errors and 95% confidence intervals for λ,
β, and 1 - β are given. For details about calculations, see “Parameter Estimates” on page 347.
Show Intensity Plot
This plot shows the estimated intensity function (Figure 18.9). The Weibull intensity function is given by
ρ() t = λβt β – 1 , so it follows that log(Intensity) is a linear function of log(t). If Time to Event Format is
used, both axes are scaled logarithmically.