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

3.6.27 · D1 · Physics › Spacecraft Structures & Systems Engineering › Requirements — SMART (Specific, Measurable, Achievable, Rele

Isse pehle ki tum judge karo ki koi requirement "Specific" hai ya "Measurable", tumhe us chhoti si alphabet ke symbols mein fluent hona padega jo parent note quietly use karta hai. Yeh page unhe ek-ek karke zero se build karta hai. Ise upar se neeche padho — har symbol use hone se pehle samjhaya gaya hai.

1. Comparison operators: $<$ , $\leq$ , $\geq$ , $=$

Picture. Ek number line socho — ek ruler jo left (chhota) se right (bada) tak jaata hai. Ek requirement us ruler par ek region paint karta hai jahan real spacecraft land kar sakta hai.

Topic ko yeh kyun chahiye. Parent note likhta hai "mass $\leq 150$ kg". Yeh koi wish nahi hai — yeh ruler par ek line drawn hai. Koi bhi bana hua satellite jiska mass green region mein aata hai (line ke left) pass karta hai; kuch bhi right mein fail karta hai. Falsifiability poori tarah is picture mein rehti hai: ek requirement tab acchi hoti hai jab woh ek clear line draw kare taaki tum point karke keh sako "hum pass side par hain."

2. Units, aur kyun ek akela number meaningless hai

Pehle, teen base units jinse baaki sab bana hai:

Is chapter mein baaki har unit inhe multiply aur divide karke bani hai — isliye kisi number ko kuch matlab hone ke liye unit chahiye.

Picture. " $150$ " akela 150 grams (ek phone) bhi ho sakta hai ya 150 tonnes (ek truck). Sirf unit hi fix karti hai ki hum ruler par kaun se tick-marks count kar rahe hain.

Symbol	Padha jaata hai	Base-unit composition	Measure karta hai
$kg$	kilogram	(base)	mass (kitna stuff)
$m/s$	metres per second	$m \cdot s^{- 1}$	speed / velocity change
$N$	newton	$kg \cdot m \cdot s^{- 2}$	force (ek push ya pull)
$J$	joule	$kg \cdot m^{2} \cdot s^{- 2}$	energy
$W$	watt	$kg \cdot m^{2} \cdot s^{- 3}$	power (energy per second)
$N\cdotm$	newton-metre	$kg \cdot m^{2} \cdot s^{- 2}$	torque (ek twist)
$N\cdotm\cdots$	newton-metre-second	$kg \cdot m^{2} \cdot s^{- 1}$	angular momentum (stored spin)

(Note: chhote raised numbers jaise $s^{- 2}$ exponents hain — "kitni baar multiply kiya" wali notation jo Section 5 mein define ki gayi hai. $s^{- 2}$ ka matlab hai "seconds se do baar divide kiya".)

Topic ko yeh kyun chahiye. SMART mein M — Measurable — literally yeh hai ki "requirement mein ek unit hai." Units ke bina, "generate $\geq 2.5$ " falsifiable nahi hai: 2.5 kya? Watts, kilowatts, horsepower? Dekho Mass Budget aur Interface Control Document (ICD), jahan har line ek number-plus-unit hai exactly isi liye.

3. Tolerance: $\pm$ aur $%$

Picture. Koi bhi factory kuch bhi exactly nahi banati. Toh ek razor-thin line ki jagah, tolerance ruler par ek band draw karta hai.

2.5 kW \pm 5% ⟺ allowed range [2.375, 2.625] kW

Topic ko yeh kyun chahiye. Real hardware degrade aur vary karta hai. Tolerance ke bina ek requirement secretly perfection maangti hai, jo koi test kabhi pass nahi kar sakta. Tolerance hi hai jo ek measurable requirement ko ek hi saath achievable aur testable banati hai.

4. Statistical symbol $σ$ (aur " $3 σ$ ")

Gaussian assumption. " $68%$ / $99.7%$ " rules universal nahi hain — yeh tab hold karte hain jab scatter bell-shaped normal (Gaussian) distribution follow kare, jo measurement noise aksar karta hai. Us specific curve ke under, mean ke $\pm k σ$ ke andar aane wale measurements ka fraction ek fixed number hota hai:

\pm 1 σ \approx 68.3%, \pm 2 σ \approx 95.4%, \pm 3 σ \approx 99.7%.

Yeh percentages sirf un limits ke beech bell curve ke neeche ka area hain — picture ise concrete banati hai.

Topic ko yeh kyun chahiye. Parent ki traceability example altitude knowledge " $\pm 5$ m $(3 σ)$ " ki maang karti hai. $3 σ$ attach karna (Gaussian assumption ke under) ek vague "accurate" ko ek statistical promise mein badal deta hai: roughly 1000 mein 3 se zyada baar fail mat karo. Yahi ek accuracy requirement ko genuinely testable banata hai — dekho Verification and Validation.

5. Exponents, natural logarithm $ln$ , aur Euler's number $e$

Pehle woh notation jo rocket equation mein likhi jaati hai — exponentiation.

Parent ka Achievable example Tsiolkovsky Rocket Equation par lean karta hai, jo ek special base ko power par raise karta hai. Ise zero se banao.

Picture. $e^{x}$ ek curve hai jo tezi se upar rocket karti hai. $ln (x)$ wahi curve hai diagonal line ke across reflect ki gayi — pehle tezi se chadhti hai, phir crawl karti hai, aur sirf $x = 0$ ke right mein exist karti hai. Yeh mirror images hain kyunki ek doosre ko undo karta hai.

Yeh tool kyun, simple division kyun nahi? Rocket jo velocity gain karta hai woh fuel add karne ke proportional nahi badhti — fuel ka har extra kilo bhi carry aur accelerate karna padta hai. Woh "diminishing return" exactly wahi hai jo $ln$ capture karta hai. Rocket equation mein,

$Δ v = I_{s p} g_{0} ln (\frac{m _{0}}{m _{f}})$

$Δ v$ ko double karne ke liye mass ratio $m_{0} / m_{f}$ ko square karna padta hai, double nahi — woh brutal maths jo "chemistry par $Δ v = 50$ km/s" ko absurd banata hai.

6. TRL — Technology Readiness Level

Picture. Ek staircase socho "napkin sketch" (bottom) se "flight-proven" (top) tak. Parent ka Achievable test — "kya yeh kam se kam TRL 6 par hai?" — puch raha hai ki technology real mission par trust kiye jaane ke liye kaafi upar chadh chuki hai. Full ladder: Technology Readiness Levels (TRL).

Prerequisite map

Neeche diya diagram dikhata hai ki har foundation agla kaisa feed karta hai. Ise ek flow ki tarah padho: comparison operators aur base units (top) raw grammar hain; tolerance aur $σ$ (units se bane) ek stated number ko honest banate hain; exponents/ $ln$ TRL ke saath milke Achievable check feed karte hain; aur yeh sab ek single SMART requirement par converge karta hai, jo phir verification mein flow karta hai.

Shabdon mein, chain padha jaata hai: operators + units ek number ko kuch matlab dete hain → tolerance aur $σ$ us number ko honest banate hain → exponents, $ln$ aur TRL check karne dete hain ki yeh possible hai → milke yeh requirement ko testable banate hain.

Equipment checklist

Right side cover karo aur reveal karne se pehle jawab do.

<

aur

\leq

mein kya fark hai?

<

boundary value ko exclude karta hai;

\leq

include karta hai — exactly limit par ek part

\leq

pass karta hai lekin

<

fail karta hai.

\leq 150 kg

number line par kya draw karta hai?

Ek ceiling: zero se lekar 150 kg tak (inclusive) har value pass karti hai.

Teen base units kya hain, aur unke terms mein newton kya hai?

metre (m), second (s), kilogram (kg);

N = kg \cdot m / s^{2}

Base units mein watt kya hai?

W = J/s = kg \cdot m^{2} / s^{3}

2.5

" jaisa akela number valid requirement kyun nahi hai?

Iske paas koi unit nahi, toh yeh measurable nahi hai — 2.5 kya ka?

2.5 kW \pm 5%

kaun sa band allow karta hai?

[2.375, 2.625] kW

Standard deviation

σ

ka formula likho.

σ = \frac{1}{N} \sum_{i} (x_{i} - μ)^{2}

— mean se mean squared distance ka root.

68 percent / 99.7 percent rules ko assumption kyun chahiye?

Yeh Gaussian (normal) bell curve ke neeche areas hain aur sirf tab hold karte hain jab scatter normally distributed ho.

b^{- 2}

ka matlab kya hai?

1/ b^{2}

— negative exponent ka matlab divide karo.

ln (x)

kaun sa sawaal ka jawab deta hai, aur kis

x

ke liye?

e

ko kaunsi power par raise karein toh

x

milega?" — sirf

x > 0

ke liye defined;

ln (0)

aur negatives ka

ln

undefined hai.

Rocket equation mein

ln

safe kyun hai?

Iska input mass ratio

m_{0} / m_{f} > 1

hai, hamesha positive.

Rocket equation mein division ki jagah

ln

kyun use karte hain?

Zyada fuel add karne se diminishing returns milte hain —

Δ v

mass ratio ke logarithm ke saath badhta hai, linearly nahi.

"Achievable" count karne ke liye technology roughly kaunse TRL tak pahunchni chahiye?

Kam se kam TRL 6 — ek relevant environment mein demonstrate kiya gaya system.