Requirements — SMART (Specific, Measurable, Achievable, Relevant, Testable): Worked examples

3.6.27 · D3 · Physics › Spacecraft Structures & Systems Engineering › Requirements — SMART (Specific, Measurable, Achievable, Rele

Shuru karne se pehle, ek word jo hum baar baar use karenge: ek requirement verifiable (ya falsifiable) hoti hai agar koi concrete measurement ya calculation exist kare jiska result definitively "pass" ya "fail" bole. Ek requirement jis par tum hamesha argue kar sako woh verifiable nahi hai. Yeh picture yaad rakho: ek requirement ek locked gate hai — ya toh key fit hoti hai ya nahi hoti.

Ek term bhi baar baar aayega: FEA stands for finite-element analysis — ek computer method jo ek structure ko hazaaron chhote blocks ("elements") mein kaatta hai aur har ek par physics solve karta hai, taaki tum hardware banane se pehle stresses aur vibration frequencies predict kar sako. Jab bhi neeche FEA dekho, picture karo ki part par chhoti tiles ka ek mesh bichhaa hua hai.

Scenario matrix

Har toota hua (ya checkable) requirement jo tumhe milega, inhi cells mein se kisi ek mein aata hai. Har row ek alag failure mode ya edge case hai; aakhri column us worked example ka naam deta hai jo use cover karta hai.

#	Case class	Trap / edge	Konsa SMART letter stress hota hai	Example
1	Vague adjective	"lightweight", "robust" — koi number nahi	Specific + Measurable	Ex 1
2	Number but no conditions	value di gayi hai, lekin kab/kahan missing hai	Measurable	Ex 2
3	Physics-impossible	ek hard law violate karta hai (rocket eq.)	Achievable	Ex 3
4	Degenerate / zero input	tolerance = 0, ya "exactly" bina kisi margin ke	Measurable + Achievable	Ex 4
5	Orphan requirement	kisi cheez se trace nahi hota — bureaucracy	Relevant	Ex 5
6	Process not performance	"shall be designed to..."	Testable	Ex 6
7	Real-world word problem	ek mission goal se number derive karo	sabhon paanch	Ex 7
8	Exam twist	requirement jo theek lagti hai lekin ek limiting-value failure chhupaa ke rakhi hai	Achievable (limit)	Ex 8

Hum har cell hit karenge. Ek statement padho, fix cover karo, apna Forecast banao, phir khud ko check karo.

Worked example Ex 1 — Case 1: vague adjective

Statement (broken): "The antenna boom shall be stiff."

Forecast: Yeh kaun se do SMART letters fail karta hai, aur tum kaunsi ek quantity par number pin karoge?

Step 1 — Failure ko naam do. Yeh step kyun? Fix karne se pehle, tumhe bolna hoga kyun yeh toota hai, warna tum galat cheez fix karoge. "Stiff" ek adjective hai jisme koi number nahi → Specific fail karta hai (kitna stiff? kis load ke against?) aur Measurable fail karta hai (koi quantity nahi, koi units nahi).

Step 2 — Woh physical quantity choose karo jiska matlab "stiff" ho. Yeh step kyun? Ek boom ke liye "Stiff" ka matlab hai ki woh sag ya wobble na kare — yaani uski first natural bending frequency $f_{1}$ high ho (ek floppy boom slowly vibrate karta hai). Hum $f_{1}$ choose karte hain kyunki yeh shaker table par directly measurable hai.

Step 3 — Justification ke saath ek number choose karo. Yeh step kyun? Ek number ko ek reason chahiye, warna woh Relevant fail karta hai. Launch vehicles apni zyaadatar vibration energy $\sim 100 Hz$ se neeche daalte hain; resonance se bachne ke liye hum $f_{1} \geq 120 Hz$ demand karte hain (us band se comfortably upar).

Step 4 — Units + verification method add karo. "The antenna boom's first bending mode shall be $f_{1} \geq 120 Hz$ , verified by modal analysis (FEA) and confirmed by a sine-sweep vibration test."

Verify: Ise wapas padho — kya koi aisi measurement hai jo pass/fail return kare? Shaker sweep karo, pehla resonance peak padho, 120 se compare karo. Haan. Units Hz mein hain. Gate ab lock hota hai. ✅

Verification and Validation step yahan do methods use karta hai (analysis + test) — structural requirements ke liye yeh normal hai.

Worked example Ex 2 — Case 2: ek number, lekin koi conditions nahi

Statement (broken): "The solar array shall generate 3 kW."

Forecast: Isme ek number aur units hain. Toh phir bhi kya missing hai — aur kya ek panel jo ground par 3 kW output karta hai woh orbit mein isi exact wording ke hisaab se fail ho sakta hai?

Step 1 — Unbounded condition spot karo. Yeh step kyun? Power depend karta hai kab par (beginning vs end of life), kahan par (Sun se distance), kaise oriented hai (sunlight se angle), aur kitna hot hai (ek cell ka voltage, isliye power, garam hone par girta hai). Inke bina "3 kW" unverifiable hai — tum koi test nahi bana sakte jo kuch bhi mean kare.

Step 2 — Har condition ko bound karo. Yeh step kyun? Har missing condition ek tarika hai jisse number silently badal sakta hai:

Time: radiation se panels degrade hoti hain → end-of-life (EOL) specify karo, yahi worst case hai.
Distance: solar flux $1/ d^{2}$ ki tarah girta hai → 1 AU par fix karo (flux $S = 1367 W/m^{2}$ ).
Orientation: power $\propto cos θ$ jahan $θ$ normal se angle hai → normal ( $θ = 0$ ) specify karo.
Temperature: silicon-cell output roughly $0.4%$ per $^{\circ} C$ heating se girta hai, isliye wahi panel garam hone par kam power produce karta hai thande ki tulna mein → hume woh thermal range bound karni hogi jis par requirement hold kare, jaise $- 100^{\circ} C$ se $+ 120^{\circ} C$ tak (panel ka cold eclipse exit le kar hot full-sun soak tak).

Step 3 — Tolerance add karo. Yeh step kyun? Koi real cell exact number nahi hit karta; manufacturing spread aur measurement error ko ek band chahiye. $\pm 5%$ use karo.

Step 4 — Assemble karo. "The solar array shall generate $\geq 3 kW \pm 5%$ electrical power at EOL, oriented normal to sunlight at 1 AU, over $- 100^{\circ} C$ to $+ 120^{\circ} C$ ."

Verify — physics self-consistent hai ya nahi, sanity-check karo. Agar array $θ = 6 0^{\circ}$ par tilted ho, power $cos 6 0^{\circ} = 0.5$ se girkar, yaani $1.5 kW$ ho jaayegi. Toh "normal" condition cosmetic nahi hai — yeh answer ko 2 ke factor se badal deta hai. Condition apni jagah earn karta hai. ✅

Figure — Requirements — SMART (Specific, Measurable, Achievable, Relevant, Testable)

Upar ki figure dikhati hai kyun har condition maayane rakhti hai: orange curve off-normal angle $θ$ ke versus power hai ( $cos θ$ law — $6 0^{\circ}$ par half ho jaata hai), aur teal curve cell temperature ke versus power hai (gentle downward slope). "3 kW" bina conditions ke kisi bhi curve par kahin bhi land ho sakta hai.

Worked example Ex 3 — Case 3: physics-impossible (Achievability ki wall)

Statement (broken): "The propulsion system shall provide $Δ v = 20 km/s$ using chemical propulsion with dry mass $\leq 200 kg$ ."

Forecast: Required mass ratio $m_{0} / m_{f}$ guess karo. 10 se zyaada? 100 se zyaada?

Step 1 — Tool choose karo: Tsiolkovsky Rocket Equation. Yeh tool kyun, koi aur kyun nahi? $Δ v$ , exhaust speed aur mass exactly ek hi law se link hain: $Δ v = v_{e} ln (\frac{m _{0}}{m _{f}})$ jahan $m_{0}$ = wet (full) mass, $m_{f}$ = dry (empty) mass, aur $v_{e} = I_{s p} g_{0}$ exhaust speed hai. Yeh wahi ek equation hai jo answer deta hai "kya yeh $Δ v$ is propellant ke saath possible hai?" — isliye yeh Achievable decide karta hai.

Step 2 — Best chemical propellant ke liye $v_{e}$ nikalo. Yeh step kyun? Achievability ek best-case test hai: agar best chemistry nahi kar sakti, toh koi nahi kar sakta. Best chemical specific impulse $I_{s p} \approx 450 s$ , aur $g_{0} = 9.81 m/s^{2}$ , toh $v_{e} = 450 \times 9.81 = 4414.5 m/s .$

Step 3 — Mass ratio ke liye rocket equation invert karo. Yeh step kyun? Hum woh demand chahte hain jo requirement design par daalta hai: $\frac{m _{0}}{m _{f}} = exp (\frac{Δ v}{v _{e}}) = exp (\frac{20000}{4414.5}) = e^{4.530} \approx 92.8.$

Step 4 — Propellant mass mein translate karo. Yeh step kyun? Ek ratio abstract hota hai; kilograms nahi. $m_{f} = 200 kg$ ke saath: $m_{0} = 92.8 \times 200 \approx 18560 kg, m_{prop} = m_{0} - m_{f} \approx 18360 kg .$ 200 kg spacecraft move karne ke liye 18 tonnes se zyaada propellant — physically legal, lekin ek giant stage ke alawa kisi bhi cheez ke liye absurd. Achievable fail karta hai ek small satellite ke liye.

Step 5 — Kuch feasible likhne ke liye rewrite karo. "The propulsion system shall provide $Δ v \geq 500 m/s$ using monopropellant hydrazine ( $I_{s p} \approx 230 s$ ), propellant mass $\leq 50 kg$ , dry mass $\leq 10 kg$ ."

Verify karo ki fix deliver karta hai. $v_{e} = 230 \times 9.81 = 2256.3 m/s$ , mass ratio $= (50 + 10) /10 = 6$ : $Δ v = 2256.3 \times ln 6 = 2256.3 \times 1.7918 \approx 4043 m/s \geq 500. ✓$ Comfortable margin. ✅

Plot ko dhyan se padho. Horizontal axis mass ratio $m_{0} / m_{f}$ hai aur vertical axis $Δ v$ km/s mein hai. Orange curve rocket equation hi hai: yeh bend over karta hai kyunki $ln$ kabhi dheemare dheemare badhta hai — ratio ko double karna ek fixed chunk of $Δ v$ add karta hai, kabhi proportional nahi. Teal dashed line impossible $20 km/s$ demand mark karti hai; seedha neeche drop karo aur tum ratio $93$ ke paas land karte ho, jahan curve almost flat hai, yaani jahan har further km/s ke liye propellant ki ek diwar laagti hai. Plum dot feasible fix (ratio 6) hai. Yahi poori reason hai ki Case 3 kyun fail hota hai: log high $Δ v$ ko exponentially expensive banata hai.

Worked example Ex 4 — Case 4: degenerate / zero-tolerance input

Statement (broken): "The optical bench alignment shall be exactly $0.000 000 rad$ (perfectly parallel)."

Forecast: Kisi bhi physics se pehle, bilkul zero tolerance mein mathematically kya galat hai?

Step 1 — Boundary case test karo: tolerance $\to 0$ . Yeh step kyun? Ek requirement measure karke verify hoti hai, aur har measurement ki finite precision $δ > 0$ hoti hai. Pass condition hai: $∣ measured - target ∣ \leq tolerance .$ Agar tolerance $= 0$ , toh yeh tabhi satisfy ho sakti hai jab tumhara instrument perfect zero read kare — lekin koi bhi instrument apne khud ke noise floor se neeche resolve nahi kar sakta. Toh pass ki probability effectively $0$ hai. Ek zero-tolerance requirement unverifiable hai → limit mein Measurable fail karta hai.

Step 2 — Zero ko sabse chhote meaningful tolerance se replace karo. Yeh step kyun? Sahi tolerance (a) mission ko actually kya chahiye aur (b) tum kya measure kar sakte ho, inse set hoti hai. Maano ki science ko $50 μ rad$ ke andar parallelism chahiye, aur tumhara autocollimator $5 μ rad$ resolve karta hai (yaani sabse chhota angle change jo woh read kar sakta hai $5 μ rad$ hai). Science value ( $50 μ rad$ ) choose karo, kyunki yeh looser, driving number hai aur instrument jo dekh sakta hai usse comfortably coarser hai.

Step 3 — Rewrite karo. "The optical bench alignment shall be $0 \pm 50 μ rad$ about each axis, verified by autocollimator inspection (resolution $\leq 5 μ rad$ )."

Verify — kya instrument kaafi accha hai? Rule of thumb: tolerance instrument resolution se kaafi zyaada baar honi chahiye, warna tum pass aur noise mein farq nahi kar sakte. Yahan $50/5 = 10 \times$ headroom hai — kaafi zyaada. Agar hum usi $5 μ rad$ instrument ke saath $0 \pm 2 μ rad$ demand karte, toh ratio $2/5 = 0.4 < 1$ hota → tolerance instrument se bhi fine hai jo read kar sake, isliye yeh unmeasurable hai — ek aur degenerate failure. Yehi reason hai ki Step 2 ne tolerance ( $50$ ) resolution ( $5$ ) se kaafi upar rakha. ✅

Worked example Ex 5 — Case 5: orphan (Relevant fail karta hai)

Statement (suspicious): "The onboard computer shall log every CPU temperature reading to permanent storage at 100 Hz for the full mission."

Forecast: Yahan kuch bhi vague ya impossible nahi hai. Toh phir ek reviewer ise delete kyun kar sakta hai?

Step 1 — Pucho "yeh kaunse mission objective se trace hota hai?" Yeh step kyun? Relevant ka matlab hai ki har requirement ek Requirements Traceability Matrix ke zariye upar ek mission need se link ho. Agar iske upar kuch bhi ise nahi chahiye, toh yeh dead weight hai — cost aur mass bina kisi payoff ke.

Step 2 — Woh burden compute karo jo yeh impose karta hai. Yeh step kyun? Cost dikhao taaki "ise kaat do" defensible ho. Ek temperature word $2$ bytes hota hai. $100 Hz$ par $2$ -year mission mein: $N = 100 \times (2 \times 365 \times 24 \times 3600) = 100 \times 63072000 = 6.307 \times 1 0^{9} samples,$ $storage = 2 bytes \times 6.307 \times 1 0^{9} = 1.261 \times 1 0^{10} bytes \approx 12.6 GB (decimal, 1 0^{9} bytes) .$ Lagbhag $12.6 GB$ non-volatile memory — real mass, power, aur downlink cost.

Step 3 — Decide karo: retie karo ya kaat do. Yeh step kyun? Agar thermal engineers ko sirf trend data chahiye, toh $1 Hz$ ke saath ek rolling buffer kaafi hai. Ise ek real objective se retie karo aur rate kaat do: "The computer shall record CPU temperature at $1 Hz$ into a $24$ -hour rolling buffer, to support in-flight thermal-anomaly diagnosis (traces to Mission Obj. Maintain safe thermal state)."

Verify — burden recompute karo. $1 Hz \times 86400 s \times 2 bytes = 172800 bytes \approx 0.17 MB$ . $12.6 GB$ se gir kar $\sim 0.17$ MB — ek $\sim 73000 \times$ reduction, aur ab yeh trace karta hai. ✅

Worked example Ex 6 — Case 6: process, performance nahi (Testable fail karta hai)

Statement (broken): "The bracket shall be designed to withstand launch vibration."

Forecast: Tum kaise test karoge ki kuch cheez kisi kaam ke liye "designed to" hai? (Trick: tum nahi kar sakte.)

Step 1 — Process words ko performance words se alag karo. Yeh step kyun? "Designed to", "intended to", "shall consider" describe karte hain ki engineers kya karte hain, na ki hardware kya achieve karta hai. Tum ek hardware outcome inspect kar sakte ho; tum ek intention test nahi kar sakte. Isliye yeh Testable fail karta hai.

Step 2 — Woh performance state karo jo hardware ko reach karni chahiye, aur number kahan se aaya yeh bhi batao. Yeh step kyun? Intent ko ek measurable survival condition se replace karo — lekin number invent nahi ho sakta, ise launch environment se aana chahiye. Launch-vehicle user manuals ek quasi-static design limit load publish karte hain: woh steady acceleration jo ek payload peak thrust aur transients ke dauran feel karta hai. Ek typical small-launcher value $8 g$ axial (thrust axis ke along) hai. Hum manual ka $8 g$ adopt karte hain kyunki yeh woh load hai jo hardware actually dekhega; phir qualification testing $1.25 \times$ tak jaati hai (ek standard margin factor, $10 g$ ) flight case se pare margin prove karne ke liye.

Step 3 — Verification method ke saath rewrite karo. "The bracket shall survive $\geq 8 g$ axial quasi-static load without yielding, verified by FEA and by vibration qualification testing to $1.25 \times$ limit load ( $10 g$ )."

Verify — kya pass/fail concrete hai? Qualification level compute karo: $1.25 \times 8 g = 10 g$ . Shaker par $10 g$ test karo, yield/crack ke liye inspect karo — ek binary result. Process version se compare karo: koi bhi test nahi hai jo pass/fail return kare. Rewrite testable hai, original nahi. ✅

Yeh Systems Engineering V-Model ko mirror karta hai: left descending arm par har requirement ka right ascending arm par ek matching verification hona chahiye. Ek process requirement ka koi partner nahi hota jo wapas upar climb kare.

Worked example Ex 7 — Case 7: real-world word problem (sabhon paanch letters)

Statement (goal, abhi tak requirement nahi): "Humare Earth-observation mission ko har image pixel ko ground par $\pm 30 m$ ke andar geolocate karna hai. Camera $500 km$ altitude par fly karta hai. Ise attitude control system ke liye ek SMART pointing requirement mein badlo."

Forecast: Guess karo — kya allowed pointing error $60 μ rad$ ke aas paas hogi, ya $600 μ rad$ ?

Step 1 — Geometry tool choose karo. Yeh tool kyun? Ek pointing error ek angle $θ$ hai; ground miss $Δ x$ jo yeh slant range $h$ par cause karta hai, small angles ke liye, $Δ x \approx h \cdot θ .$ Hum small-angle form use karte hain kyunki $θ$ yahan microradians mein hai — ek microradian ka $tan$ 12 decimal places tak microradian ke barabar hai, isliye linear form kaafi accurate hai.

Step 2 — Allowed angle ke liye solve karo. Yeh step kyun? Invert karo woh constraint paane ke liye jo ACS ko meet karni chahiye: $θ \leq \frac{Δ x}{h} = \frac{30 m}{500 000 m} = 6.0 \times 1 0^{- 5} rad = 60 μ rad .$ (Toh Forecast ka pehla guess sahi nikla.)

Step 3 — Arcseconds mein convert karo (attitude-control specs aksar inhi mein likhi jaati hain). Yeh step kyun? $1 rad = 206265 arcsec$ , isliye $θ = 6.0 \times 1 0^{- 5} \times 206265 \approx 12.4 arcsec .$

Step 4 — SMART likhao. "The attitude control system shall control line-of-sight pointing to $\leq 60 μ rad$ ( $\leq 12.4 arcsec$ , $3 σ$ ) per axis during imaging, verified by star-tracker telemetry analysis and closed-loop simulation."

Specific: line-of-sight, per axis, imaging ke dauran.
Measurable: $60 μ rad$ , $3 σ$ .
Achievable: modern star trackers kuch arcsec tak pahunchte hain — $12.4$ se comfortably neeche.
Relevant: directly $\pm 30 m$ geolocation objective se trace karta hai.
Testable: telemetry + simulation.

Verify — number ko round-trip karo. $θ = 60 μ rad$ plug karo: $Δ x = 500000 \times 6.0 \times 1 0^{- 5} = 30 m$ . Exactly objective — isliye koi margin na kho jaata hai na waste hota hai. ✅

Figure dikhata hai ki small-angle tool yahan kyun legitimate hai: true miss $h tan θ$ (teal dashed) aur linear $h θ$ (orange) poore microradian range mein visually ek hi line hain, aur plum dot $60 μ rad \to 30 m$ mark karta hai.

Worked example Ex 8 — Case 8: exam twist (ek hidden limiting-value failure)

Statement (theek lagta hai): "The reaction wheel shall store angular momentum $\geq 10 N\cdotm\cdots$ and be sized so that saturation is reached no sooner than once per orbit under a disturbance torque of $2 \times 1 0^{- 4} N\cdotm$ ."

Forecast: Har word quantitative aur testable hai — isliye yeh SMART lagta hai. Lekin kya yeh Achievable hai? Compute karo ki $10 N\cdotm\cdots$ us torque ke against actually kitne time tak chalta hai.

Step 1 — Accumulation tool choose karo. Yeh tool kyun? Ek constant torque $τ$ stored momentum linearly build karta hai: $H = τ t$ . Isliye saturate hone ka time hai $t_{sat} = \frac{H _{m a x}}{τ} .$ Yeh wahi ek relation hai jo stated capacity, stated torque, aur "once per orbit" claim ko link karta hai — isliye yahi trap expose karta hai.

Step 2 — Saturation time compute karo. $t_{sat} = \frac{10 N\cdotm\cdots}{2 \times 1 0 ^{- 4} N\cdotm} = 5 \times 1 0^{4} s .$

Step 3 — Ek orbit se compare karo. Yeh step kyun? Requirement demand karti hai $t_{sat} \geq$ ek orbit. Ek low-Earth orbit lagbhag $90 min = 5400 s$ ka hota hai. Toh: $5 \times 1 0^{4} s = 50000 s ≫ 5400 s .$ Wheel lagbhag $50 000/5400 \approx 9.3$ orbits chalta hai — required se kaafi zyaada. "Twist" yeh hai ki requirement impossible nahi hai; yeh loosely over-specified hai: $10 N\cdotm\cdots$ ka momentum floor once-per-orbit condition ko jo chahiye usse $\sim 9 \times$ bada hai.

Step 4 — Matched number nikalo. Yeh step kyun? Exactly ek orbit ke liye just-sufficient capacity hai $H_{need} = τ \cdot t_{orbit} = 2 \times 1 0^{- 4} \times 5400 = 1.08 N\cdotm\cdots .$ Toh ek tighter, phir bhi safe requirement (maano $2 \times$ margin ke saath) $H \geq 2.2 N\cdotm\cdots$ hogi — ek halka, sasta wheel jo phir bhi intent meet karta hai.

Verify — margin ratio dono taraf check karo. Original: $10/1.08 \approx 9.3 \times$ margin (wasteful). Proposed: $2.2/1.08 \approx 2.0 \times$ margin (healthy). Dono Achievable hain; exam point yeh hai ki SMART ke letters pass karna zaroori hai lekin kaafi nahi — phir bhi silent over-design ke liye audit karo. ✅

Recall Self-test: har requirement kis cell mein hai?

"The panel shall be robust." ::: Case 1 — vague adjective (Specific + Measurable fail karta hai). "The thruster gives $Δ v = 20 km/s$ on hydrazine, dry mass $\leq 200 kg$ ." ::: Case 3 — physics-impossible (rocket equation ke zariye Achievable fail karta hai). "Alignment shall be exactly $0 rad$ ." ::: Case 4 — zero tolerance unverifiable hai. "The bracket shall be designed to survive launch." ::: Case 6 — process na ki performance (Testable fail karta hai). $Δ v$ mass ratio ke saath sirf logarithmically kyun badhta hai? ::: Kyunki $Δ v = v_{e} ln (m_{0} / m_{f})$ — log flat ho jaata hai, isliye extra speed ke liye exponentially zyaada propellant lagta hai. Ex 7 mein, small-angle ( $Δ x = h θ$ ) valid kyun hai? ::: Kyunki $θ \approx 60 μ rad$ hai, aur us size par $tan θ = θ$ ~12 decimals tak. FEA ka kya matlab hai? ::: Finite-element analysis — ek part ko tiny elements mein divide karna taaki computer se stress aur vibration predict kiya ja sake.

Dekho bhi: Mass Budget (mass requirements ki Achievability), Technology Readiness Levels (TRL) (Achievable ke liye TRL-6 gate), Interface Control Document (ICD) (jahan interface requirements rehti hain), Failure Modes and Effects Analysis (FMEA) (konsi failures ek requirement ki Relevance ko justify karti hain).