RELIABILITY ESTIMATION OF STRESS-STRENGTH MODEL USING FUZZY DISTORTION FUNCTION UNDER UNCERTAINTY IN ENVIRONMENTAL FACTORS.

In the reliability estimation of stress-strength models, external factors such as temperature, humidity, etc. may influence the distribution of stress and strength random variables. In traditional reliability analysis, these external factors are accounted for by introducing a real-valued distortion function, which replaces the original distribution with a distorted one. However, it's important to note that the effect of these external factors is not always adequately represented by a single real-valued function. To address this issue, we propose the use of fuzzy numbers within the distortion function. In this paper, we introduce the concept of a "fuzzy distortion function" to incorporate the uncertainty stemming from external factors when estimating the reliability of stress-strength relationships. We present a methodology for estimating fuzzy reliability by employing this fuzzy distortion function. Through an illustrative example, we demonstrate how this approach to estimating fuzzy reliability offers a wider range of possibilities for system reliability and provides more comprehensive insights into the system's behaviour. Throughout our exploration, we have delved into the diverse properties inherent in fuzzy distortion functions. These properties highlight the versatility and adaptability of such functions in capturing uncertainty within data sets. Moreover, we have scrutinized several methods for constructing fuzzy distortion functions from pre-existing ones. By examining these methods, we gain valuable insights into how fuzzy distortion functions can be tailored to specific contexts and applications, thereby enhancing the accuracy and robustness of reliability analysis in complex systems. Additionally, in the conventional stress-strength model, reliability is determined without considering the uncertainty in the parameters of the distribution function. The drawback of existing methods in the literature is that they do not consider the uncertainty or fuzziness in the parameters of the distribution. Therefore, we estimate the system reliability in the presence of fuzzy parameters in the distribution function of corresponding random variables. The method we discuss in this paper provides a reliability estimate of the given system under realistic situations. A sensitivity analysis study is carried out to examine the behaviour of mean square errors (MSE) of estimated system reliability under various scenarios. It is observed that MSE can be significantly reduced by a suitable choice of parameters in the membership function of fuzzy parameters. [ABSTRACT FROM AUTHOR]