Developing an Approach to Calculate Fuzzy Reliability Based on Fuzzy Failure Rate

The aim of this paper is to propose a new method to deal with uncertainty in computing the reliability of components through expressing the failure rate as a fuzzy triangular number and using fuzzy calculations to convert it to a fuzzy reliability number. Firstly, considering its uncertainty the failure rate is expressed as a triangular fuzzy number. Then, assuming the exponential life-time function for the target component, based on the fuzzy failure rate, the fuzzy reliability is calculated in two different ways and the results are compared with each other. In the first method, the extension principle is used and the fuzzy reliability number is calculated, accurately. In this case, the fuzzy number of reliability has a nearly triangular shape. In the second method, using linear regression, two linear functions are fitted for the right and left edges of the reliability fuzzy number, and thus a triangular fuzzy number is obtained. When the exponential density function is used for lifetime of a component, the fuzzy reliability calculation error, using the regression method is very small, compared to the original extension method. The approximation of the fuzzy reliability function, applying the regression method, provides sufficient accuracy and can be used instead of the extension principle method.