Fuzzy Smart FMEA with DEA (FSFMEA) - Fuzzy FMEA + CCR Data Envelopment Analysis for corrective action prioritization

Overview

Efficient FMs (DEA θ*=1) should be prioritized for corrective actions first, as they have lower cost and time requirements. Among efficient FMs, rank by RPN descending. Then handle inefficient FMs by RPN. Note: DEA efficiency here means the FM's corrective action is cost-time efficient - NOT that the FM itself is less risky (higher RPN = higher risk, lower C+T = easier to fix efficiently).

Output

priority rank, lower is better

Data

Fuzzy (TFN), linguistic expert ratings

Weights

Needs a weight source

Size

6+ alternatives, 3 criteria works best

Used for

FMEA risk assessment, Safety engineering, Reliability analysis, Corrective action prioritization

How it works

1. 1

   Her uzman k her FM_i için S, O, D dilsel etiket verir (Very low/Low/Medium/High/Very high). Tables 7.1-7.3 ile TFN veya TrFN'e çevir. Severity: Very high=(0.8,0.9,1), High=(0.5,0.6,0.7,0.8) TrFN, Medium=(0.4,0.5,0.6), Low=(0.2,0.3,0.4,0.5) TrFN, Very low=(0,0.1,0.2). Detectability İNVERTED: Non-detection=(0,0.1,0.2) en kötü.

2. 2

   Uzmanların yaş/deneyim/eğitim üzerinde pairwise TFN matrisi kur, Buckley 1985 geometrik ortalama yöntemi uygula. Çıktı w_k uzman ağırlıkları, Σw_k=1 (paper §7.2.2.1).

3. 3

   Her FM_i ve risk faktörü j için Z_i^(j) = Σ_k w_k ⊗ f_ij^(k). TFN/TrFN fuzzy toplama (element-wise). FM8 örneği p.164: (M,M,M,H) uzmanlardan → (0.14+0.18+0.33)·(0.4,0.5,0.5,0.6) + 0.35·(0.7,0.8,0.9) = (0.505,0.505,0.605,0.705).

4. 4

   TFN için X*=(a1+a2+a3)/3 (Eq.7.5). TrFN için X*=⅓·[(a4+a3)²−a4·a3−(a1+a2)²+a1·a2]/(a4+a3−a1−a2) (Eq.7.6). 1-10 ölçeğine çevir: X_scaled=X*·10. FM8_O örneği: X*=0.587 ≈ 0.6 → scaled 5.87.

5. 5

   RPN_i = S_i · O_i · D_i (1-10 ölçeğinde crisp). Yüksek RPN = yüksek risk.

6. 6

   Her FM_i bir DMU. Inputs x_io = (S_i, O_i, D_i, 1/RPN_i) [4 input]; outputs y_ro = (1/C_i, 1/T_i) [2 output]. Dual LP: min θ s.t. Σ_j λ_j·x_ij ≤ θ·x_io, Σ_j λ_j·y_rj ≥ y_ro, λ_j≥0. θ*=1 efficient, θ*<1 inefficient.

7. 7

   Efficient FMs (θ*=1) ÖNCE - RPN azalan sırada. Sonra inefficient FMs (θ*<1) - RPN azalan sırada. Paper §7.3: efficient={FM3,FM4,FM7,FM9,FM10}, inefficient={FM1,FM2,FM5,FM6,FM8}; final FM9>FM10>FM7>FM4>FM3>FM1>FM8>FM2>FM5>FM6.

Fits when / Look elsewhere when

Assumptions to verify

• Corrective action cost C and time T are measurable and provided per FM
• DEA CCR assumes constant returns to scale - appropriate for FM efficiency
• Expert group must be heterogeneous for reliable Buckley FAHP weighting

Edge cases and pitfalls

• •TFN ve TrFN aynı FM agregasyonunda karışık → Eq.7.5 ve Eq.7.6 ayrı uygula (paper FM8 örneği p.164 her ikisini de gösterir)
• •DEA CCR DMU sayısı < 6 (inputs+outputs) → ayrımcılık güç kaybı; rapor edilebilir ama güvenilmez (K.common_pitfalls)
• •Tüm FMs efficient (θ*=1) → DEA discriminative değil, RPN-only ranking'e geri dön
• •RPN=0 → 1/RPN tanımsız, büyük M ile değiştir veya 'no risk' flag
• •TFN'i degenerate TrFN olarak işle (a3=a4): mixed Eq.7.3 toplamı için TFN (l,m,u) → (l,m,m,u) broadcast (FM8 p.164 örtük yapıyor)
• •Aynı RPN ama farklı C/T → DEA kırar (FM9 vs FM10 cost=10.525 same, FM9 time=2.14 vs FM10 time=1.84; combined FM9>FM10 RPN-dominant)

• Confusing DEA efficiency (corrective action efficiency) with FM risk level - an efficient FM may still have high RPN.

• DEA requires at least as many DMUs (FMs) as the sum of inputs + outputs (4+2=6 minimum FMs for reliable results).

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