Subjective Modification of Aging Stochastic Systems

The overall uncertainty of an aging stochastic system is analyzed through the consideration of both objective uncertainty and subjective imprecision. The updated probability distribution of a normal variate is determined through the constructions of global and local entropy equations. A subjective pairwise comparison method is applied in transforming subjective information concerning the overall uncertainty of the stochastic system to fuzzy support. A comparison of two fuzzy entropy functions is made. Since the fuzzy entropy function is not unique, calibration on the actual probability distribution is needed in order to justify the use of the proposed expressions. However, in many practical situations it is possible to make sensible pairwise comparisons without being able to make sensible parameter estimates. In such circumstances the proposed scheme will be of value.