NIST/SEMATECH e-Handbook of Statistical Methods: Chapter 8, Assessing Product Reliability

Overview

The chapter gives four core formulas. For independent components that must all survive, system reliability is the product of the component reliabilities. For independent parallel components where one survivor suffices, system failure probability is the product of the component failure probabilities. For n identical independent components needing at least r survivors, reliability is the sum of the binomial probabilities for r through n survivors.

With a constant failure rate lambda, lifetime reliability is exp(-lambda x time) and mean time to failure (MTTF) is 1/lambda. For instance, two independent components of reliability 0.9 give 0.81 in series and 1 - 0.1 x 0.1 = 0.99 in parallel; these numbers are a simple application of the formulas, not an example from the document. Exponential life means no ageing is modelled.

The limit matters: the chapter supplies no failure data for a particular facility and does not model common-cause failures. The formulas hold only if components are independent; two 'redundant' units fed by the same generator line violate that assumption. Results are therefore an assumption-dependent calculation, not proof of achieved service availability. In short, the formulas are a calculator, not a data source; the failure rates must come from the user and their source.

Key points

1. For independent components that must all survive, system reliability is the product of individual reliabilities.
2. For independent parallel components where one survivor suffices, system failure probability is the product of component failure probabilities.
3. For n identical independent components needing at least r survivors, reliability is the sum of binomial probabilities from r through n.
4. With constant failure rate lambda, reliability is exp(-lambda x time) and MTTF is 1/lambda.
5. The chapter gives no facility-specific failure data and does not model common-cause failures.

Using it in design

• Make independence and capacity assumptions required inputs of every reliability calculation and keep input provenance.
• Use series, parallel and r-out-of-n blocks as a numeric check of N, N+1 and 2N redundancy schemes.
• Do not present the output as achieved service availability; add a separate note on common-cause failure.

Who should read it

Designers calculating the reliability of redundancy schemes and engineers auditing a calculation's assumptions.

Publication details

Authors

NIST/SEMATECH

Publisher

NIST / SEMATECH

Year

2012

Document number

Chapter 8, Assessing Product Reliability

Document language

English

Source type

Government / public

Access

Free to read

DOI

10.18434/M32189

Licence

Copyright retained; citation only — the publisher’s terms apply to the original document

Citation