(α₁, α₂)-Cut Sets of Reliability Measures in Moore and Bilikam Lifetime Family Using the Generalized Intuitionistic Fuzzy Numbers

Abstract

The parameters of lifetime distribution are frequently measured with some imprecision. However, classical lifetime analyses are based on precise measurement assumptions and cannot handle parameter imprecision. Accordingly, to accommodate the imprecision, the generalized intuitionistic fuzzy reliability analysis is preferred over classical reliability analysis. In reliability analysis, generalized intuitionistic fuzzy parameters provide a flexible model and elucidate the uncertainty and vagueness demanded in the reliability analysis. This study generalizes the parameters and reliability characteristics of the Moore and Bilikam family to cover the fuzziness of the lifetime parameters based on the generalized intuitionistic fuzzy numbers. The Moore and Bilikam family includes several lifetime distributions, such that the resulting reliability measures are more comprehensive than other lifetime distributions. The generalized intuitionistic fuzzy reliability functions and their α 1 -cut and α 2 -cut sets are provided, such as the reliability, conditional reliability, and hazard rate functions with generalized intuitionistic fuzzy parameters. We also evaluate the bands with upper and lower bounds in reliability measures than the curve. Based on a numerical example, the generalized intuitionistic fuzzy reliability measures are provided based on the Weibull distribution of the Moore and Bilikam family.