Fuzzy Reliability Estimation Within a Stress-Strength Framework Incorporating Distortion Functions
DOI:
https://doi.org/10.13052/jrss0974-8024.1913Keywords:
Stress-strength model, distortion function, membership function, fuzzy reliability estimationAbstract
The primary focus of this paper is to present an estimation of fuzzy system reliability for a stress-strength model that accounts for uncertainty in the parameters of the distribution function. A drawback of existing methods in the literature is that they do not consider data uncertainty or fuzziness when estimating system reliability. To obtain a more realistic estimation, it is necessary to incorporate the uncertainty present in real-world scenarios. In this work, we incorporate both a distortion function and data fuzziness to estimate system reliability using the stress-strength model, resulting in a more practical approach. We estimate reliability using a suitable distortion function with fuzzy parameters. Specifically, Power, Dual Power, and Piece-wise Type II distortion functions are considered in conjunction with a standard exponential lifetime distribution. Additionally, we obtain a system reliability estimate under a dynamic stress-strength model using a power distortion function with a fuzzy parameter. Several numerical examples are computed to illustrate our approach to fuzzy system reliability estimation. To demonstrate practical application, an illustrative example using simulated estimates is presented for a real-life problem, the stress-strength reliability of reinforced concrete roofs. Finally, a discussion compares the proposed method to an existing method using numerical values.
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