Engineering / advanced
Quantitative models of service reliability
Calculate failure and repair behavior while testing independence assumptions, shared causes, and the gap between model predictions and observations.
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Module 01 advanced
Quantitative models of service reliability
Calculate failure and repair behavior while testing independence assumptions, shared causes, and the gap between model predictions and observations.
- 01
A fault tree separates failure logic from probability assumptions
Derive minimal cut sets, retain repeated-event identity, and quantify overlapping failure combinations without multiplying dependent events blindly.
25 min - 02
Series and parallel formulas need a shared mission and independence
Calculate required-path and redundant-path reliability while accounting for switching dependencies, mission duration, and the difference from repairable availability.
24 min - 03
Redundancy shares the environment unless the model says otherwise
Build a conditional common-cause mixture, distinguish marginal reliability from joint outage probability, and investigate shared failure domains and model uncertainty.
25 min - 04
Availability rates and step probabilities are different model inputs
Derive two-state repairable availability, distinguish continuous-time rates from discrete transitions, and inspect transient and degenerate behavior.
27 min - 05
Repair cycles can have memory even when their averages match
Use alternating renewal reasoning, compare exponential and nonmemoryless durations, and distinguish replacement, minimal repair, and finite-time reliability questions.
26 min - 06
Burn rate needs the same eligible-event denominator as the SLO
Calculate request-based error-budget use, distinguish traffic share from time share, and qualify exhaustion forecasts and multi-window alerts.
25 min - 07
A reachable majority is a probability event, not a correctness proof
Calculate independent quorum-availability tails, include shared failure scenarios, and separate replica count from communication, durability, and protocol safety.
26 min - 08
Retries change the load that changes their failure probability
Model bounded attempt amplification, distinguish a constant-probability baseline from overload feedback, and connect retry budgets with deadlines and safe side effects.
27 min - 09
Recovery tails include incidents that have not finished yet
Define recovery endpoints, retain right-censored observations, estimate survival carefully, and distinguish heavy-tail hypotheses from unsupported percentile forecasts.
27 min - 10
A reliability model needs held-out failures and a defensible observation process
Validate reliability predictions against exposure, censoring, changing regimes, dependence, and uncertainty instead of treating a fitted curve or green test as a guarantee.
28 min