BAYESIAN ANALYSIS OF THE WEIBULL PROCESS WITH UNKNOWN SCALE AND SHAPE PARAMETERS
RESEARCH ANALYSIS CORP MCLEAN VA
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The author previously examined the Weibull process with unknown scale parameter as a model for Bayesian decision making. Here the analysis is extended by treating both the shape and scale parameters as unknown. It is not possible to find a family of continuous joint prior distributions on the two parameters that is closed under sampling, hence a family of prior distributions is used that places continuous distributions on the scale parameter and discrete distributions on the shape parameter. Prior and posterior analyses are examined and seen to be no more difficult than for the case in which only the scale parameter is treated as unknown, but preposterior analysis and determination of optimal sampling plans are considerably more complicated in this case. Two examples are presented to illustrate the use of the present model. In the first of these it is necessary to make probability statements about the mean life and reliability of a long-life component both before and after life testing. The second example involves determination of the probability distribution of the number of replacement items needed by a group of users during a specified time interval.
- Operations Research
- Manufacturing and Industrial Engineering and Control of Production Systems