ASTM E2696-21

Standard Practice for Life and Reliability Testing Based on the Exponential Distribution

ABSTRACT
This practice presents standard sampling procedures and tables for life and reliability testing in procurement, supply, and maintenance quality control operations as well as in research and development activities. This practice describes general procedures and definitions of terms used in life test sampling and describes specific procedures and applications of the life test sampling plans for determining conformance to established reliability requirements.
SIGNIFICANCE AND USE
4.1 This practice was prepared to meet a growing need for the use of standard sampling procedures and tables for life and reliability testing in government procurement, supply, and maintenance quality control (QC) operations as well as in research and development activities where applicable.  
4.2 A characteristic feature of most life tests is that the observations are ordered in time to failure. If, for example, 20 radio tubes are placed on life test, and ti denotes the time when the ith tube fails, the data occur in such a way that t1 ≤ t2 ≤ ... ≤ tn. The same kind of ordered observations will occur whether the problem under consideration deals with the life of electric bulbs, the life of electronic components, the life of ball bearings, or the length of life of human beings after they are treated for a disease. The examples just given all involve ordering in time.  
4.3 In destructive testing involving such situations as the current needed to blow a fuse, the voltage needed to break down a condenser, or the force needed to rupture a physical material, the test can often be arranged in such a way that every item in the sample is subjected to precisely the same stimulus (current, voltage, or stress). If this is done, then clearly the weakest item will be observed to fail first, the second weakest next, and so forth. While the random variable considered mostly in this guide is time to failure, it should be emphasized, however, that the methodology provided herein can be adapted to the testing situations mentioned above when the random variable is current, voltage, stress, and so forth.  
4.4 Sections 6 and 7 describe general procedures and definitions of terms used in life test sampling. Sections 8, 9, and 10 describe specific procedures and applications of the life test sampling plans for determining conformance to established reliability requirements.  
4.5 Whenever the methodology or choice of procedures in the practice requires clarification, the user is adv...
SCOPE
1.1 This practice presents standard sampling procedures and tables for life and reliability testing in procurement, supply, and maintenance quality control operations as well as in research and development activities.  
1.2 This practice describes general procedures and definitions of terms used in life test sampling and describes specific procedures and applications of the life test sampling plans for determining conformance to established reliability requirements.  
1.3 This practice is an adaptation of the Quality Control and Reliability Handbook H-108, “Sampling Procedures and Tables for Life and Reliability Testing (Based on Exponential Distribution),” U.S. Government Printing Office, April 29, 1960.  
1.4 A system of units is not specified in this practice.  
1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.6 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

General Information

• Status: Published
• Publication Date: 30-Apr-2021
• ICS: 03.120.10 - Quality management and quality assurance
• ICS: 21.020 - Characteristics and design of machines, apparatus, equipment
• Technical Committee: E11 - Quality and Statistics
• Drafting Committee: E11.40 - Reliability

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E2696 − 21 An American National Standard
Standard Practice for
Life and Reliability Testing Based on the Exponential
1
Distribution
This standard is issued under the fixed designation E2696; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope butes Indexed by AQL
E2555 Practice for Factors and Procedures for Applying the
1.1 Thispracticepresentsstandardsamplingproceduresand
MIL-STD-105 Plans in Life and Reliability Inspection
tablesforlifeandreliabilitytestinginprocurement,supply,and
maintenance quality control operations as well as in research
3. Terminology
and development activities.
3.1 Definitions:
1.2 This practice describes general procedures and defini-
3.1.1 See Terminology E456 for a more extensive listing of
tions of terms used in life test sampling and describes specific
terms in ASTM Committee E11 standards.
procedures and applications of the life test sampling plans for
3.1.2 consumer’s risk, β,n—probability that a lot having
determining conformance to established reliability require-
ments. specified rejectable quality level will be accepted under a
defined sampling plan. E2555
1.3 This practice is an adaptation of the Quality Control and
3.1.2.1 Discussion—In this practice, the consumer’s risk is
Reliability Handbook H-108, “Sampling Procedures and
the probability of accepting lots with mean time to failure θ .
1
Tables for Life and Reliability Testing (Based on Exponential
3.1.2.2 Discussion—For the procedures of 9.7 and 9.8, the
Distribution),” U.S. Government Printing Office, April 29,
consumer’s risk may also be defined as the probability of
1960.
accepting lots with unacceptable proportion of lot failing
1.4 A system of units is not specified in this practice.
before specified time, p .
1
1.5 This standard does not purport to address all of the
3.1.3 life test, n—process of placing one or more units of
safety concerns, if any, associated with its use. It is the
product under a specified set of test conditions and measuring
responsibility of the user of this standard to establish appro-
the time until failure for each unit.
priate safety, health, and environmental practices and deter-
mine the applicability of regulatory limitations prior to use.
3.1.4 mean time to failure (MTTF), θ, n—in life testing, the
1.6 This international standard was developed in accor- average length of life of items in a lot.
dance with internationally recognized principles on standard-
3.1.4.1 Discussion—Also referred to as mean life.
ization established in the Decision on Principles for the
3.1.5 number of failures, n—number of failures that have
Development of International Standards, Guides and Recom-
occurred at the time the decision as to lot acceptability is
mendations issued by the World Trade Organization Technical
reached.
Barriers to Trade (TBT) Committee.
3.1.5.1 Discussion—The expected number of failures re-
quired for decision is the average of the number of failures
2. Referenced Documents
required for decision when life tests are conducted on a large
2
2.1 ASTM Standards:
number of samples drawn at random from the same exponen-
E456 Terminology Relating to Quality and Statistics
tial distribution.
E2234 Practice for Sampling a Stream of Product by Attri-
3.1.6 producer’s risk, α,n—probability that a lot having
specified acceptable quality level will be rejected under a
1
This practice is under the jurisdiction ofASTM Committee E11 on Quality and defined sampling plan.
Statistics and is the direct responsibility of Subcommittee E11.40 on Reliability.
3.1.6.1 Discussion—In this practice, the producer’s risk is
^Current edition approved May 1, 2021. Published June 2021. Originally
the probability of rejecting lots with mean time to failure θ .
approved in 2009. Last previous edition approved in 2018 as E2696 – 09 (2018). 0
DOI: 10.1520/E2696-21.
3.1.6.2 Discussion—For the procedures of 9.7 and 9.8, the
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
producer’s risk may also be defined as the probability of
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
rejecting lots with acceptable proportion of lot failing before
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. specified time, p .
0
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1

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This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E2696 − 09 (Reapproved 2018) E2696 − 21 An American National Standard
Standard Practice for
Life and Reliability Testing Based on the Exponential
1
Distribution
This standard is issued under the fixed designation E2696; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 This practice presents standard sampling procedures and tables for life and reliability testing in procurement, supply, and
maintenance quality control operations as well as in research and development activities.
1.2 This practice describes general procedures and definitions of terms used in life test sampling and describes specific procedures
and applications of the life test sampling plans for determining conformance to established reliability requirements.
1.3 This practice is an adaptation of the Quality Control and Reliability Handbook H-108, “Sampling Procedures and Tables for
Life and Reliability Testing (Based on Exponential Distribution),” U.S. Government Printing Office, April 29, 1960.
1.4 A system of units is not specified in this practice.
1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of
regulatory limitations prior to use.
1.6 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2
2.1 ASTM Standards:
E456 Terminology Relating to Quality and Statistics
E2234 Practice for Sampling a Stream of Product by Attributes Indexed by AQL
E2555 Practice for Factors and Procedures for Applying the MIL-STD-105 Plans in Life and Reliability Inspection
3. Terminology
3.1 Definitions:
3.1.1 See Terminology E456 for a more extensive listing of terms in ASTM Committee E11 standards.
1
This practice is under the jurisdiction of ASTM Committee E11 on Quality and Statistics and is the direct responsibility of Subcommittee E11.40 on Reliability.
^Current edition approved Dec. 1, 2018May 1, 2021. Published December 2018June 2021. Originally approved in 2009. Last previous edition approved in 20132018 as
E2696 – 09 (2013).(2018). DOI: 10.1520/E2696-09R18.10.1520/E2696-21.
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1

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E2696 − 21
3.1.2 consumer’s risk, β, n—probability that a lot having specified rejectable quality level will be accepted under a defined
sampling plan. E2555
3.1.2.1 Discussion—
In this practice, the consumer’s risk is the probability of accepting lots with mean time to failure θ .
1
3.1.2.2 Discussion—
For the procedures of 9.7 and 9.8, the consumer’s risk may also be defined as the probability of accepting lots with unacceptable
proportion of lot failing before specified time, p .
1
3.1.3 life test, n—process of placing one or more units of product under a specified set of test conditions and measuring the time
until failure for each unit.
3.1.4 mean time to failure, failure (MTTF), θ, n—in life testing, the average length of life of items in a lot.
3.1.4.1 Discussion—
Also known referred to as mean life.
3.1.5 number of failures, n—number of failures that have occurred at the time the decision as to lot acceptability is reached.
3.1.5.1 Discussion—
The expected number of failures required for decision is the average of the number of failures required for decision when life tests
are conducted on a large number of samples drawn at random from the same exponential distribution.
3.1.6 producer’s risk, α, n—probability that a lot having specified acceptable quality level will be rejected under a defined
sampling plan.
3.1.6.1 Discussion—
In this practice, the producer’s risk is th
...