A Neutrosophic Copula Framework for Bivariate Reliability Modelling Under Epistemic Indeterminacy

Abstract

Classical copula-based reliability models assume precisely specified marginal  distributions and dependence parameters, an assumption often violated when failure times are affected by sensor latency, interval censoring, calibration drift, or incomplete inspection records. Motivated by the copula-based reliability characterisations of Nair et al. (2018), this paper proposes the Neutrosophic Copula Framework (NCF) for bivariate reliability modelling under epistemic indeterminacy. The framework combines neutrosophic statistics (Smarandache, 1998) with copula theory to represent uncertainty through interval-valued probability bounds associated with truth (T), indeterminacy (I), and falsity (F) components, distinguishing irreducible unknowing from identifiable systematic error. The NCF extends Sklar's theorem, system reliability functions, dependence measures, copula hazard rates, and mean residual life to the neutrosophic setting. Closed-form interval-valued dependence measures are derived for Clayton, Gumbel, Frank, Gaussian, and t-copulas. A two-stage NS IFM estimation procedure is developed with boundwise consistency and asymptotic normality. Two qualitatively new states — indeterminate dependence direction and indeterminate PQD status — are identified that are not represented within standard point valued reliability frameworks. Monte Carlo simulations confirm consistent parameter recovery and reliable interval coverage. The methodology is illustrated using the Diabetic Retinopathy Study dataset (Huster et al., 1989), where the framework reveals reliability uncertainty concealed by classical point-valued analysis. Setting IL=IU=0 recovers the classical copula framework and interval statistics as special cases.

DOI: 10.5281/zenodo.22767499