Fuzzy FMEA DEA (Adesina, Yazdi, Zarei and Pouyakian, 2022)

Cells. In classical DEA the input and output columns are direct crisp numbers. Here the three input-side measures, severity (S), occurrence (O) and detectability (D), are collected from experts as triangular fuzzy numbers; each expert scores these three measures on a verbal scale declared in advance, from "very low" to "very high", and the scale converts every term into a triangle. The corrective action's cost and duration, by contrast, are entered directly as crisp numbers; they are not fuzzified.

Scale equalisation and defuzzification. When more than one expert is involved, the scores are first pooled by a weighted sum, using each expert's own reliability weight; DecisionMind takes these weights as an external input. This pooled triangle is then reduced to a single crisp number by the centre-of-area (CoA) method and carried onto FMEA's standard 1-10 scale. This defuzzification happens before the DEA step, in the middle of the calculation, not right at the start as in Fuzzy DEMATEL, but immediately before the RPN is calculated.

Distance, score and combination. The classical FMEA product gives the risk priority number (RPN = S×O×D) from the defuzzified S, O and D values. Each failure mode then counts as a DEA unit (DMU): the inputs are S, O, D and the inverse of RPN; the outputs are the inverses of the corrective action's cost and duration. Classical input-oriented DEA (CCR) here answers the question of how efficiently this failure mode's corrective action uses its resources, cost and duration, relative to the other failure modes.

Result and defuzzification. The output is not a single number but two separate pieces of information: the RPN, the risk magnitude from the defuzzified S, O, D, and the DEA efficiency score theta (the corrective action's resource efficiency). DecisionMind reports the two side by side; a failure mode with theta=1 is efficient in terms of its corrective action, but this does not mean it is risk-free.

RPN is read as on the classical FMEA card: a high RPN means high risk, but it is not, on its own, a ranking tool. DEA's theta value is read as on the DEA card: a value of 1 shows that this failure mode's corrective action sits at the frontier of resource use.

The difference is this: these two numbers answer different questions and do not substitute for one another. A failure mode with a high RPN can still come out DEA-efficient (theta=1); this means "high risk, but the corrective action is cheap and fast." A failure mode with a low RPN may also be DEA-inefficient; this means "low risk, but the corrective action is expensive and slow."

For this reason, instead of writing:

"This failure mode came out DEA-efficient, so it is not a priority"

the report should read:

"This failure mode's corrective action is efficient in resource use (θ=1), but if its RPN is high the risk priority is still high; the two pieces of information should be read together"

Use this extension when the severity, occurrence and detectability scores for failure modes are collected from experts verbally or approximately, and the cost-time efficiency of corrective actions also needs to be compared at the same time. If S, O and D are already given as crisp numbers, for example ratios calculated from historical failure records, fuzzifying them is unnecessary; classical FMEA's RPN can be fed directly into crisp DEA. DEA's exit condition applies here too: the number of failure modes must be sufficient relative to the sum of inputs (four: S, O, D, 1/RPN) and outputs (two: 1/cost, 1/duration); DecisionMind recommends at least six failure modes.

Confusing DEA efficiency with risk level. As the manifest itself points out, a failure mode that is efficient in terms of its corrective action (θ=1) can still carry a high RPN; the priority decision requires both together.

Having too few failure modes relative to the sum of inputs and outputs. With four inputs and two outputs, a reliable distinction needs at least six failure modes; if this condition is not met, almost every failure mode comes out DEA-efficient and the discriminating power is lost.

Failing to declare the verbal scale, or letting it vary from expert to expert. The meaning of a term such as "high" is fixed before the analysis, written into the report, and applied identically to every expert.

Ranking efficient failure modes by theta alone, without looking at RPN at all. DecisionMind's current engine lists failure modes with equal theta values in input order; this order does not automatically reflect the size of RPN. The illustrative example below shows this distinction clearly, and the RPN column must be read separately when the final priority decision is made.

The governing principle is this:

RPN measures the risk magnitude, DEA's theta measures the corrective action's resource efficiency; the two need not be high together or low together, and the priority decision is made by looking at both at once.