An Analytical Interval Fuzzy Inference System for Risk Evaluation and Prioritization in Failure Mode and Effect Analysis

The fuzzy inference system (FIS) is useful for developing an improved Risk Priority Number (RPN) model for risk evaluation in failure mode and effect analysis (FMEA). A general FIS_RPN model considers three risk factors, i.e., severity, occurrence, and detection, as the inputs and produces an FIS_RPN score as the output. At present, there are two issues pertaining to practical implementation of classical FIS_RPN models as follows: 1) the fulfillment of the monotonicity property between the FIS_RPN score (output) and the risk factors (inputs); and 2) difficulty in obtaining a complete and monotone fuzzy rule base. The aim of this paper is to propose a new analytical interval FIS_RPN model to solve the aforementioned issues. Specifically, the incomplete and potentially nonmonotone fuzzy rules provided by FMEA users are transformed into a set of interval-valued fuzzy rules in order to produce an interval FIS_RPN model. The interval FIS_RPN model aggregates a set of risk ratings and produces a risk interval, which is useful for risk evaluation and prioritization. Properties of the proposed interval FIS_RPN model are analyzed mathematically. An FMEA procedure that incorporates the proposed interval FIS_RPN model is devised. A case study with real information from a semiconductor company is conducted to evaluate the usefulness of the proposed model. The experimental results indicate that the interval FIS_RPN model is able to appropriately rank the failure modes, even when the fuzzy rules provided by FMEA users are incomplete and nonmonotone.