Safety-critical standards — DO-178C (airborne software), IEC 61508, ISO 26262: Foundations

5.5.18 · D1 · Coding › Embedded Systems & Real-Time Software › Safety-critical standards — DO-178C (airborne software), IEC

Is page par kuch bhi assume nahi kiya gaya. Parent note padhne se pehle, tumhe usmein aane wale har symbol ko bina rukke padhna aana chahiye. Chalte hain — ek-ek karke build karte hain, har ek pichle ke upar.

1. Shuru ka picture: hazard, harm, aur rigor

Koi bhi letter ya number se pehle, yeh image apne dimaag mein rakh lo.

Figure — Safety-critical standards — DO-178C (airborne software), IEC 61508, ISO 26262

Figure s01 — Ek see-saw: left side par ek bhaari pan jispe likha hai HAZARD (possible harm) neeche jhuk raha hai; right side par ek pan jispe likha hai RIGOR (safe prove karne ki koshish) upar uth raha hai. Ek arrow pivot par "must balance" likhke mark kiya gaya hai. Yeh poore topic ka ek hi rule dikhata hai — jitna zyada possible harm, utna zyada engineering rigor chahiye.

Neeche har symbol us see-saw ka ek side measure karne ka tool hai — ya to danger kitna bada hai ya humne kitna thoroughly check kiya.

2. Failure, fault, aur error — teen words jo log mix up karte hain

Picture: fault ek landmine hai jo field mein dabi hui hai. Error hai uske upar paon rakhna. Failure hai woh explosion jo sab dekhte hain.

Topic ko yeh kyun chahiye: har standard dangerous failures se obsessed hai — woh explosions jo kisi insaan tak pahunch ke harm kar sakti hain. Jo faults kabhi failure nahi bante woh kisi ko hurt nahi karte. Dekho Fault Tolerance & Redundancy — kaise systems errors ko failures banne se pehle pakad lete hain.

3. Probability — 0 aur 1 ke beech ka number

Picture: 0 se 1 tak ka ek ruler. Ek marker slide karo; 0 ke paas matlab "basically kabhi nahi," 1 ke paas matlab "basically hamesha."

Parent note mein $1 0^{- 3}$ jaisi numbers likhte hain. Yeh koi mistake nahi hai ya koi weird unit — yeh sirf bahut chhoti probability hai. Chalte hain yeh notation kamate hain.

4. Powers of ten aur $1 0^{- n}$ — chhote numbers likhna

Picture: exponent mein har minus-one decimal point ko ek step left shift karta hai, number ko das guna chhota kar deta hai.

Figure s02 — Ek horizontal number line of dots jispe $1 0^{0}, 1 0^{- 1}, \dots, 1 0^{- 6}$ label hain aur neeche unki decimal values (1, 0.1, ..., 0.000001) hain, aur ek arrow note karta hai "har step: 10x smaller (safer)." Yeh define karta hai ki SIL bands mein use hone wali tiny probabilities kaise padhni hain.

Topic ko yeh kyun chahiye: failure probabilities naturally tiny hoti hain (har ghante mein $1$ million mein ek). Unhe $0.000001$ likhna error-prone hai; $1 0^{- 6}$ clean hai. Har safety band inhi ki ek range hai.

5. Rate: $λ$ (lambda), time $t$ , aur "per hour"

Picture: imagine karo ek wall par tally marks aa rahe hain, har baar kuch fail hone par ek. $λ$ hai kitni tezi se marks aa rahe hain. Ek dripping tap jo har ghante ek baar drip karta hai uski "drip rate" $λ = 1/ hr$ hai.

Subscript $λ_{D U}$ kyun? Parent ise tag karta hai: Dangerous, Undetected. Har fault dangerous nahi hota, aur kuch dangerous ones diagnostics se pakad liye jaate hain. $λ_{D U}$ sirf woh count karta hai jo dono hain — dangerous bhi aur silent bhi — woh truly scary wale. Dekho Failure Rate & Reliability.

6. Constant $e$ aur kyun exponential $e^{- λ t}$ aata hai

Parent $1 - e^{- λ t} \approx λ t$ use karta hai bina explain kiye. Pehle hume letter $e$ kama lena hoga.

Exponential kyun, straight line kyun nahi? Straight line eventually zero hit karke negative ho jaati — impossible hai fraction ke liye. Exponential decay zero ki taraf smoothly jaata hai aur kabhi cross nahi karta, aur yeh wahi ek curve hai jahan shrink rate proportional hai kitna bacha hai ke. Woh "proportional to what remains" exactly wahi hai jo constant-rate, memoryless failure ka matlab hai.

Figure s03 — Time ke against do curves: lavender "still working" survival curve $e^{- λ t}$ 1 se girta hai, aur coral "already failed" curve $1 - e^{- λ t}$ 0 se utha hai, ek dashed straight line $λ t$ origin ke paas failed curve ke saath chipki hui hai (shaded butter region). Yeh dikhata hai kyun exact risk ko straight line $λ t$ se sirf chhote $t$ ke liye replace kiya ja sakta hai.

Picture: girte curve ka bilkul shuru mein zoom karo — woh straight dikhta hai. Woh straight bit hai $λ t$ . Isliye parent scary exponential ko simple product $λ_{D U} t$ se replace kar sakta hai — lekin sirf isliye kyunki real safety systems mein $λ_{D U} T_{1}$ ek se bahut neeche hai.

7. Integral $\int$ , aur average failure probability $P F D_{a v g}$

Parent compute karta hai $P F D_{a v g} = \frac{1}{T _{1}} \int_{0}^{T_{1}} λ_{D U} t d t$ . Teen cheezein nayi hain: $P F D$ , $\int$ , aur $T_{1}$ .

Picture: failure probability $0$ se (abhi test kiya, perfect) roughly $λ_{D U} T_{1}$ tak (agle test se thoda pehle) ek almost straight ramp ke along badhti hai. Integral woh ramp ke neeche area hai. $T_{1}$ se divide karne par "total area" "average height" ban jaata hai, jo hai $P F D_{a v g}$ .

Figure s04 — Ek coral ramp "just tested" par 0 se "just before next test" par $λ_{D U} T_{1}$ tak uthta hai, uske neeche triangular area shaded hai, aur ek dashed mint line half-height par average $λ_{D U} T_{1} /2$ mark karti hai. Yeh geometrically dikhata hai kyun straight risk ramp average karne par one-half ka factor aata hai.

Integral kyun: yeh honest tarika hai "risk jo tests ke beech badhti rehti hai" ko ek average number ( $P F D_{a v g}$ ) mein convert karne ka jise safety band se compare kar sako. (Approximation $λ_{D U} t$ us integral ko curve ki jagah triangle banata hai — theek hai kyunki $λ_{D U} T_{1} ≪ 1$ .)

8. Level letters aur numbers — aur kyun yeh alag directions mein point karte hain

Picture: teen staircases. DAL staircase par, sabse upar ki step A label hai. SIL staircase par, top 4 hai. ASIL staircase par, top D hai. Same height (max rigor) — top par alag label.

Topic ko levels kyun chahiye: rigor expensive hota hai aur strictness ke saath roughly exponentially badhta hai. Levels woh tarika hai jisse tum effort wahan spend karte ho jahan lives depend karti hain — see-saw ek dial mein badal gaya. Dekho Functional Safety aur FMEA & Hazard Analysis — hazard side kaise measure hoti hai.

9. Coverage words: statement, decision, MC/DC

Picture: program ka ek road map socho. Statement coverage = "kya humne har road drive kiya?" Decision coverage = "kya humne har fork dono taraf liya?" MC/DC = "kya humne prove kiya ki har individual signpost actually matter karta hai kahan pahunche ke liye?"

Topic ko teen kyun chahiye: stricter coverage subtler bugs pakadti hai lekin zyada tests cost karte hain — isliye parent sabse deadly level (DAL A) ko strictest coverage (MC/DC) se jodta hai. Poori detail dekho Code Coverage Metrics mein.

10. Prerequisite map

Neeche node names section concepts se match karte hain; (see …) mark kiye boxes related vault topics ki taraf point karte hain jo text mein link hain, is page ke sections ki taraf nahi.

Equipment checklist

Right side cover karo; reveal karne se pehle answer de sakte ho?

1 0^{- 4}

decimal mein kya hoga?

0.0001

— das hazaar mein ek.

Hazard aur harm mein kya difference hai?

Hazard danger ki possibility hai; harm woh actual injury ya loss hai jo result mein hoti hai.

Fault aur failure mein kya difference hai?

Fault ek hidden flaw hai; failure woh flaw hai jo actually bahar galat behaviour cause karta hai (visible explosion).

λ

kya measure karta hai, aur kis unit mein?

Failure rate — per unit time kitne failures, usually per hour (

1/ hr

Symbol

t

yahan kya represent karta hai?

Elapsed time ki duration, hours mein.

λ_{D U}

mein D aur U letters kyun hain?

Dangerous aur Undetected — woh failures jo matter bhi karte hain aur silent bhi rehte hain.

Survival function

P (t)

kya represent karta hai?

Woh probability ki component last test ke baad time

t

par abhi bhi kaam kar raha hai;

P (0) = 1

, 0 ki taraf girta hai.

e

kya number hai, aur iska special kya hai?

e \approx 2.71828

;

e^{- λ t}

woh ek curve hai jiska rate of change

- λ

times khud ke barabar hai (

d P / d t = - λ P

Kaun si modeling assumption

e^{- λ t}

ko survival ke liye use karne deti hai?

Constant-rate, memoryless (Poisson) failure process — agle moment fail hone ka chance age par depend nahi karta.

1 - e^{- λ t} \approx λ t

chhote

t

ke liye kyun, aur kab valid hai?

Origin ke paas rising "already failed" curve slope

λ

se shuru hoti hai, isliye straight line

λ t

ke saath chipki rehti hai; approximation valid hai sirf jab

λ t ≪ 1

ho (abhi tak bahut kam failures).

P F D

ka matlab kya hai, aur

P F D_{a v g}

kya hai?

Probability of Failure on Demand — woh chance ki safety function already toot chuka hai jab zaroorat ho;

P F D_{a v g}

woh test interval par average ki gayi hai.

\int_{0}^{T_{1}}

yahan geometrically kya compute karta hai?

Ek test aur agle ke beech risk-vs-time ramp ke neeche area.

P F D_{a v g} = λ_{D U} T_{1} /2

mein

\frac{1}{2}

kahan se aata hai?

Straight ramp ki average height uska midpoint hota hai — peak ka aadha.

DO-178C mein, DAL A sabse safe hai ya sabse critical?

Sabse critical (worst-case failure) — isme sabse zyada rigor chahiye, including MC/DC.

ISO 26262 mein, kaun sa letter sabse demanding hai?

D (QM matlab "koi safety requirement nahi").

MC/DC decision coverage se zyada kya require karta hai?

Har individual condition ko yeh dikhana hoga ki woh independently outcome flip kar sakti hai.

Back to parent topic par wapas.