Analysis of equivalent dynamic reliability with repairs under partial information

Abstract For repairable system it is usual to evaluate the effectiveness of repair by considering the life extended between failures. Traditional definition of dynamic reliability is not suitable for the evaluation due to that the population diminishes gradually as failed events may induce non-repairable situations. More often the failure record presents sometimes only the sequence of failure number, it does not specify the system in a repairable or non-repairable condition as it fails. This kind of information is dim in describing the whole picture of failures after repair that should be accounted for estimating the repaired system dynamic reliability. In this paper the cumulative failure data set with repairs, which depicts the failure number in the successive operating ranges, is constructed from such incomplete information. It is developed by fuzzy consideration which (1) distinguishes repairable vs. non-repairable cases in the failure sequence data, and (2) identifies the system failed again after repair in the next time failure sequence data. The membership values in the fuzzy treatment about the data are incorporated with physical sense of cumulative damage. Thus, an equivalent dynamic reliability with repairs (EDRWR) is obtained in comparison with that by jumps representation at the time taking repairs. Finally, an example with different times of repairs for about 191 bus motors is used to demonstrate the suggested methodology. The fittings of EDRWR are quite well accepted in Weibull distribution.