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دوره‌ها ماژول‌ها مجموعه‌داده‌ها منابع مدرس

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دوره‌ها ماژول‌ها مجموعه‌داده‌ها منابع مدرس

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دوره‌ها ماژول‌ها مجموعه‌داده‌ها منابع مدرس

آزمایشگاه داده‌های رسمی

منابع داده عمومی برای مثال‌ها، نمودارها و تمرین‌های R

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درس 9 از 16

System Reliability and Redundancy

خانه/ماژول‌ها/ماژول 5/System Reliability and Redundancy

Calculate redundant uptime and downtime while accounting for shared failure risks.

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هدف‌های یادگیریتا پایان این درس، دانشجویان می‌توانند:

1Define the events and probability quantities used in system reliability and redundancy.
2Select and calculate an appropriate probability rule with a visible denominator or assumption.
3Interpret the result for a business decision without overstating certainty or causation.

Theory

Core probability reasoning

Calculate redundant uptime and downtime while accounting for shared failure risks.

توضیح 1

All fail: Every required backup component is unavailable.

توضیح 2

At least one works: The complement of all components failing.

توضیح 3

Common cause: One condition affects several components together.

اصطلاحات

Concept map

All fail

Every required backup component is unavailable.

Product of independent failure probabilities.

At least one works

The complement of all components failing.

1 - P(all fail).

Common cause

One condition affects several components together.

Shared power or network.

نمادگذاری و فرمول‌ها

Independent redundancy

رابطه اصلی

P(at least one works) = 1 - (1 - r)^n

Define every event before substituting values, then validate the result and denominator.

گام 1Convert reliability r to failure probability.
گام 2Raise failure probability to n.
گام 3Use the complement and state independence.

فعالیت تعاملی

system reliability builder

Component reliabilityComponent countShared infrastructure is present

All fail

0.0004

At least one works

0.9996

Expected downtime

3.504 h/year

This calculation assumes independent failures. Check power, software, network, and location dependencies.

مثال حل‌شده

Regional service backups

سناریو

A platform considers three nominally independent failover components.

Five-nines language should be translated into expected downtime and operational consequences.

ارتباط با R

R note: Reliability and Redundancy

Run and edit the code, inspect intermediate output, and use the movable R Code Guide while practising.

Live R Lab

Reliability and Redundancy

Calculate redundant-system uptime and expected downtime while challenging independence assumptions.

Editable R code

Results

Ready to run

Ready to run

Ready to run. Results, errors, tables, plots, and fallback messages will appear here.

Calculate all-fail probability.

Use the complement.

Name common-cause risks.

Dataset provenance

Original synthetic data generated for STATLAB Academy. No textbook data used.

Interpretation safeguard

Redundant components sharing power, software, location, or networks may not fail independently.

بازاندیشی

مکث و یادداشت

Where could an unclear event definition or assumption change the conclusion in system reliability and redundancy?

Name the event, denominator, probability interpretation, and one operational limitation.

دستیار

Ask your probability coach

Help me reason through System Reliability and Redundancy by asking questions about my event definitions, denominator, formula choice, assumptions, and interpretation. Do not give a quiz answer before I submit.

ارزیابی پایانی

Lesson checkpoint

Use a hint before submitting if needed. Full calculations and interpretations appear after submission.

Checkpoint

Module 5 Lesson 9 Checkpoint

Question 1 of 2. Answered 0/2. Passing score: 70%.

برای دریافت بازخورد امتیازدهی‌شده و ذخیره پیشرفت، وارد شوید.ورود ساخت حساب

Question 1: Numeric answer

mediumCalculate and responsibly interpret probability for a defined event.

Two independent backup components each fail with probability 0.02. Find the probability both fail.

منبع

Recommended reading

Explore additional probability explanations and exercises from properly licensed or publisher resources.

منبع

Module 5 learning material

Download an original worksheet or guide for this lesson.

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