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Official Data Lab

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STATLABAcademyStatistics through data and R practice

All STATLAB Academy lessons, quizzes, datasets, and notes are original or properly licensed. Textbooks may be used only as curriculum references.

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STATLAB Academy | Learn Statistics with R and Real-World Data

Lesson 9 of 16

System Reliability and Redundancy

Home/Modules/Module 5/System Reliability and Redundancy

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

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44 minutes56% path

Learning objectivesBy the end of this lesson, students will be able to:

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.

Explanation 1

All fail: Every required backup component is unavailable.

Explanation 2

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

Explanation 3

Common cause: One condition affects several components together.

Terminology

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.

Notation and formulas

Independent redundancy

Key relationship

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

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

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

Interactive Mission

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.

Worked example

Regional service backups

Scenario

A platform considers three nominally independent failover components.

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

R connection

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.

Reflection

Pause and write

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.

Assistant

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.

Exit check

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%.

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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.

Resource

Recommended reading

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

Resource

Module 5 learning material

Download an original worksheet or guide for this lesson.

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