Fuzzy Truncated Life Test Plans for the Type-II Exponentiated Log-Logistic Distribution with Application to Cardiac Stent Reliability

Abstract

Classical truncated life test acceptance sampling plans assume exact knowledge of lifetime distribution parameters - an assumption rarely satisfied in high-stakes reliability applications such as drug-eluting cardiac stent qualification, where scale parameter estimates carry inherent epistemic uncertainty from limited pilot data or expert judgment. This paper addresses that gap by developing a fuzzy acceptance sampling plan for the Type-II Exponentiated Log-Logistic (TII-ELL) distribution under truncated life testing, generalizing the classical crisp framework to a fuzzy environment. The scale parameter corresponding to the specified minimal mean life is modeled as a triangular fuzzy number. Using the λ-cut representation and Zadeh's extension principle, closed-form interval expressions are derived for the fuzzy failure probability and fuzzy operating characteristic (OC) function. A key theoretical result, proved as Theorem 5.1, establishes that the TII-ELL failure probability is strictly monotone decreasing in the scale parameter, enabling efficient endpoint-based λ-cut propagation without exhaustive search. Fuzzy interval formulations of consumer's and producer's risk are derived, and a systematic iterative algorithm determines the jointly optimal fuzzy sample size and acceptance number satisfying dual risk constraints across all λ-cut levels. Applied to drug-eluting cardiac stent reliability data with truncation time t= 36 months and plan (n=22, c=2 & n=23, c=2), the fuzzy OC band confirms lot acceptance probability below 0.11% even under optimistic parameter assumptions - demonstrating that the proposed framework provides stronger, more transparent consumer protection than its crisp counterpart under realistic parameter uncertainty. The framework is theoretically consistent and reduces to the classical crisp plan as fuzziness vanishes, confirming its validity as a mathematically sound and practically robust alternative to deterministic reliability-based quality control.