Worked examples — FMEA — failure mode, effect, severity, detection, RPN

3.6.29 · D3 · Physics › Spacecraft Structures & Systems Engineering › FMEA — failure mode, effect, severity, detection, RPN

Neeche sab kuch sirf wahi ideas use karta hai jo parent note ne already build ki hain. Agar tumne use nahi padha, pehle woh karo — yeh practice arena hai, lecture nahi. Dekho bhi the parent topic.

The scenario matrix

Solve karne se pehle, chalte hain har us class of case ki list banaate hain jo ek FMEA problem tumhare saamne rakh sakta hai. Teeno scores mein se har ek low (1–3), middle (4–6), ya high (7–10) ho sakta hai. Jo actually matter karta hai woh exact number nahi balki answer ki shape hai jo woh produce karta hai. Yeh hain distinct shapes:

RPN scale khud, parent note se:

Shuru karne se pehle RPN space ka map neeche dekho — yeh dikhata hai ki har case class kahan land karti hai.

Example 1 — Case A: all-low (trivial risk)

Forecast: padhne se pehle andaza lagao — kya yeh 50 line ke upar ya neeche aayega?

1. Score Severity. Peeling decal spacecraft ko fly karne wali kisi cheez ko affect nahi karta. $S=1$ (parent scale se: 1 = None). Yeh step kyun? Severity hamesha pehle aata hai kyunki yeh puchta hai "agar yeh fail ho, toh outcome kitna bura hai?" — ek decal ka worst outcome ek blemish hai.
2. Score Occurrence. Adhesives flight-proven hain; peeling bahut unlikely hai. $O=2$. Yeh step kyun? Occurrence puchta hai "kitni baar?" — yeh kitna bura hai isse independent hai.
3. Score Detection. Hum ise sirf camera image se notice karte, lekin kyunki yeh matter nahi karta, detection impact ke relative mein easy hai. $D=3$. Yeh step kyun? Detection puchta hai "kya hum ise hurt karne se pehle pakad lete?" Yahan hurt karne ke liye kuch nahi hai.
4. Multiply. $\text{RPN}=1\times 2\times 3=6$. Yeh step kyun? RPN teeno ko ek comparable number mein combine karta hai.

Verify: $6<50$ → "monitor, no action" band. Ek sanity check bhi: $S=1$ ke saath, koi bhi product exceed nahi kar sakta $1\times 10\times 10=100$, aur yeh us se kaafi neeche hai. Ek decal priority nahi ho sakta — intuition se match karta hai. ✅

Example 2 — Case B: all-high (existential threat)

Forecast: yeh 1000 ke kitne paas pahunch sakta hai?

1. Severity. Koi power nahi = total mission loss. $S=10$. Yeh step kyun? Yeh catastrophic ceiling hai — array kabhi nahi khulta, spacecraft mar jaata hai.
2. Occurrence. Nayi, unproven pyro design → high failure likelihood. $O=8$. Yeh step kyun? "Known weakness / limited testing" O scale par upar baithta hai.
3. Detection. Koi confirmation sensor nahi → hum sirf tab jaante hain jab power aati hi nahi. $D=10$. Yeh step kyun? $D=10$ "catastrophe tak undetectable" ceiling hai.
4. Multiply. $\text{RPN}=10\times 8\times 10=800$.

Verify: $800\ge 500$ → unacceptable, flight se pehle fix karna zaroori. Ceiling par sanity check: absolute maximum RPN hai $10\times 10\times 10=1000$, aur $800$ uska $80\%$ hai — yeh exactly woh type ka single-point failure hai jise pakadne ke liye FMEA exist karta hai. ✅

Example 3 — Case C: high S, low O·D (survivable)

Forecast: high-S aam taur par urgent lagta hai — kya RPN agree karega?

1. Severity. Rupture propulsion feed ko destroy karta hai → mission loss. $S=9$. Yeh step kyun? Hum honestly worst case record karte hain; hum S ko shrink nahi karte sirf isliye ki yeh rare hai.
2. Occurrence. 4× margin, flight heritage → $O=2$. Yeh step kyun? Occurrence woh jagah hai jahan badi safety margin pay off karti hai.
3. Detection. Continuous pressure telemetry → $D=2$. Yeh step kyun? Early, automated detection humein rupture se pehle system ko safe karne deta hai.
4. Multiply. $\text{RPN}=9\times 2\times 2=36$.

Verify: $36<50$ → sirf monitor karo, $S=9$ ke bawajood. Yahi multiply karne ka poora point hai: ek high severity jo rare bhi hai aur visible bhi hai, chhhote $O\times D=4$ factor se damp ho jaati hai. Compare karo Ex 2 se jahan $O\times D=80$ tha. ✅ Yeh directly Redundancy and Fault Tolerance aur Reliability Engineering se link karta hai — margins aur monitoring woh tarike hain jisse tum severity ko touch kiye bina risk buy down karte ho.

Example 4 — Case D: low S, high O·D (death by a thousand cuts)

Forecast: har event trivial hai — kya RPN phir bhi action demand kar sakta hai?

1. Severity. Ek rejected sample = negligible. $S=2$. Yeh step kyun? Per-event impact genuinely chhota hai.
2. Occurrence. Belts mein frequent. $O=9$. Yeh step kyun? Frequency high hai even though har event minor hai.
3. Detection. Koi corruption flag nahi → glitches unseen accumulate ho sakte hain. $D=8$. Yeh step kyun? Detection problem ki invisibility capture karta hai, size nahi.
4. Multiply. $\text{RPN}=2\times 9\times 8=144$.

Verify: $144$ $50$–$150$ design-review band mein aata hai — action chahiye even though $S=2$ hai! Lesson: ek chhota severity free pass nahi hai; $O\times D=72$ term ise upar khich leta hai. Contrast karo Ex 3 se ($S=9$ lekin RPN $36$). ✅

Example 5 — Case E: degenerate floor, $D=1$

Forecast: sabse chhota possible $D$ kisi product ke saath kya karta hai?

1. Severity. Propellant loss mission ko risk mein daalta hai. $S=7$.
2. Occurrence. Valves reliable hain lekin perfect nahi. $O=3$.
3. Detection. "Almost certain, automated, pre-failure" $D=1$ hai — scale ka floor. Yeh step kyun? $D=1$ ideal hai: hum ise hamesha jaldi pakad lete hain.
4. Multiply. $\text{RPN}=7\times 3\times 1=21$.

Verify: $21<50$ → monitor karo. Degenerate insight: 1 se multiply karna baaki factors ko unchanged chhod deta hai — perfect detection RPN ko sirf $S\times O$ tak collapse kar deta hai. Isliye $D$ kabhi $0$ nahi ho sakta: zero saara risk erase kar deta, jo dishonest hoga — even perfect sensors ko floor value $1$ milta hai, $0$ kabhi nahi. ✅

Example 6 — Case F: degenerate ceiling, $S=10$

Forecast: numbers chhote lagte hain… kya woh settle ho jaata hai?

1. Severity. Loss of crew → $S=10$ by definition. Yeh step kyun? $S=10$ loss of life ya flagship mission ke liye reserved hai — non-negotiable ceiling.
2. Occurrence. Mature design → $O=2$.
3. Detection. Triple-redundant sensors → $D=1$.
4. Multiply. $\text{RPN}=10\times 2\times 1=20$.

Verify — aur twist: Raw scale se $20<50$ hai, lekin koi bhi $S=10$ item RPN ke bawajoood review hota hai. Real programs ek severity override apply karte hain: catastrophic hazards ko special scrutiny milti hai even jab product low ho, kyunki RPN akela ek chhote number ke peechhe single-point loss-of-crew chhupa sakta hai. Toh checkable arithmetic $20$ hai, lekin decision escalate hota hai. Yeh override policy Mission Assurance aur Risk Management in Spacecraft Design ka core hai. ✅

Example 7 — Case G: the mitigation loop (before → after)

Forecast: kaun sa factor RPN ko sabse zyada move karega — S, ya D?

1. Before — Severity. Total downlink loss → $S=9$.
2. Before — Occurrence. $O=5$.
3. Before — Detection. Sirf tab notice hota jab link die ho → $D=7$.
4. Before — RPN. ${\text{RPN}}_{\text{before}}=9\times 5\times 7=315$ → redesign band. Yeh step kyun? $150\le 315<500$ redundancy add karne ya redesign karne ki demand karta hai.
5. After — re-score. Redundancy severity cut karta hai: $S=4$. BIT detection cut karta hai: $D=3$. Occurrence unchanged hai — ek spare primary ko fail hone ki likelihood kam nahi karta: $O=5$. Yeh step kyun? Har mitigation ek specific factor ko target karti hai; honestly note karo ki woh kaun sa touch karti hai.
6. After — RPN. ${\text{RPN}}_{\text{after}}=4\times 5\times 3=60$.
7. Reduction. Drop $=315-60=255$. Percent $=\frac{255}{315}\times 100\approx 81\%$.

Verify: $60$ design-review band mein baithta hai (redesign se neeche) — ek genuine, defensible improvement. Sanity check: $S$ ek factor $9/4=2.25$ se gira aur $D$ $7/3\approx 2.33$ se, toh RPN $\approx 2.25\times 2.33\approx 5.25\times$ se girna chahiye; aur wakai $315/60=5.25$. ✅ Yeh FMEA ek living document ki tarah hai — har design change loop mein re-enter karta hai. Dekho Redundancy and Fault Tolerance.

Example 8 — Case H: real-world word problem

Forecast: story mein kaun se phrases kaun se score se map karte hain?

1. Severity find karo. "mission ends" → mission loss, lekin electronics ek limit tak survive karte hain → $S=8$ (major, mission success at risk). Yeh step kyun? Worst outcome wording dhundho.
2. Occurrence find karo. "seen on most long missions after several years" → common aging effect → $O=6$. Yeh step kyun? How often / how likely wording dhundho.
3. Detection find karo. "trend upward for months before any limit is exceeded" → excellent early warning → $D=2$. Yeh step kyun? How early we'd notice wording dhundho.
4. Multiply. $\text{RPN}=8\times 6\times 2=96$.

Verify: $96$ $50$–$150$ design-review band mein hai. Mapping par sanity check: high-O (common) lekin low-D se rescue hua (mahino ki warning) — exactly Case C wala pattern, sirf ek story ki tarah sunaya gaya. Agar tumne "months of warning" ko galti se $D=8$ padha, toh tumhe $384$ milta aur tum galat panic karte — toh detection phrase real kaam kar raha hai. ✅

Example 9 — Case I: the exam twist (equal RPN, unequal priority)

Forecast: numbers identical hain — kya risk bhi hai?

1. Dono compute karo. $3\times 5\times 8=120$ aur $8\times 5\times 3=120$. Equal. Yeh step kyun? Multiplication commutative hai — yeh $S$ ko $D$ se alag nahi bata sakta.
2. Severities padho. Item Y ka $S=8$ hai (major, mission lose ho sakti hai). Item X ka $S=3$ hai (minor). Yeh step kyun? Severity woh ek factor hai jise tum kabhi "manage around" nahi kar sakte — ek low-detection annoyance ek lost mission nahi hai.
3. Decide karo. Item Y pehle fix karo. Ek high-severity item jinke paas low detection bhi hai ($D=3$) phir bhi mission risk karta hai agar woh fire kare; Item X ka high $D=8$ sirf ek minor consequence expose karta hai. Yeh step kyun? Yeh standard severity tie-break hai: equal RPN → higher $S$ wale ko prioritise karo.

Verify: Dono products $120$ ke barabar hain (checkable). Lesson, jo har FMEA course test karta hai: RPN ek screening tool hai, final word nahi. Kyunki $S\times O\times D$ individual factors chhupata hai, tables hamesha raw $S$, $O$, $D$ columns rakhte hain aur $S$ par ties break karte hain. Yeh RPN ki ek known criticism hai Quality Assurance and Testing aur Reliability Engineering mein, aur yeh exactly woh class of oversight hai jo Mars Climate Orbiter loss ke peechhe thi — woh dangerous mode table mein tha hi nahi. ✅

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