Reliability distribution upper and lower parameter estimate

AlexVishay

• I measure 6 events of failure and calculate, with JMP reliability function, the Kaplan-Meier survival function and Weibull fit (red curves).
• I plot also lower 95% and upper 95% function (pink curves).
• I repeat the analysis adding 6 measurements (total of 12) and I get the blue curves and upper, lower 95% (light blue).
• Questions:

1.How lower 95% and upper 95% are calculated? Maximum likelihood estimator ratio???

2.I have only plotted the lower 95% alpha lower 95% beta and upper 95% alpha upper 95% beta curves, but I can also plot the lower 95% alpha upper 95% beta and upper 95% alpha lower 95% beta curves, do these combinations of parameters also have a meaning in defining the uncertainty interval of my distribution?

 

Thanks in advance for answers

Mark_Bailey

1. JMP Help says:

 

"The Life Distribution platform offers two methods for calculating confidence intervals for the distribution parameters. These methods are labeled as Wald or Likelihood and can be selected in the launch window for the Life Distribution platform. Wald confidence intervals are used as the default setting. The computations for the confidence intervals for the cumulative distribution function (cdf) start with Wald confidence intervals on the standardized variable. Next, the intervals are transformed to the cdf scale (Nelson 1982, pp. 332–333 and pp. 346-347). The confidence intervals given in the other graphs and profilers are transformed Wald intervals (Meeker and Escobar 1998, ch. 7). Joint confidence intervals for the parameters of a two-parameter distribution are shown in the log-likelihood contour plots. They are based on approximate likelihood ratios for the parameters (Meeker and Escobar 1998, ch. 8)."

 

See Help > Books > Reliability and Survival.