ASTM E2696-09(2018)
(Practice)Standard Practice for Life and Reliability Testing Based on the Exponential Distribution
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.
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.
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...
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Designation: E2696 − 09 (Reapproved 2018) An American National Standard
Standard Practice for
Life and Reliability Testing Based on the Exponential
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 .
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 .
1.5 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, θ, n—in life testing, the average
1.6 This international standard was developed in accor- length of life of items in a lot.
dance with internationally recognized principles on standard-
3.1.4.1 Discussion—Also known 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
2.1 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
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 Dec. 1, 2018. Published December 2018. Originally
the probability of rejecting lots with mean time to failure θ .
approved in 2009. Last previous edition approved in 2013 as E2696 – 09 (2013). 0
DOI: 10.1520/E2696-09R18.
3.1.6.2 Discussion—For the procedures of 9.7 and 9.8, the
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 service@astm.org. 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 .
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2696 − 09 (2018)
3.1.7 sequential life test, n—life test sampling plan whereby 5. Introduction
neither the number of failures nor the time required to reach a
5.1 The theory underlying the development of the life test
decision are fixed in advance but instead decisions depend on
sampling plans of this section, including the operating charac-
the accumulated results of the life test.
teristic curves, assumes that the measurements of the length of
life are drawn from an exponential distribution. Statistical test
3.1.8 unit of product, n—that which is inspected to deter-
procedures for determining the validity of the exponential
mine its classification as defective or nondefective or to count
distribution assumption have appeared in the technical statis-
the number of defects. E2234
tical journals. Professor Benjamin Epstein published a com-
3.1.9 waiting time, n—in life testing, the time elapsed from
prehensive paper (in two parts) on this subject in the February
the start of testing until a decision is reached as to lot
and May 1960 issues of Technometrics. Part I of the paper
acceptability.
contains descriptions of the mathematical and graphical pro-
3.1.9.1 Discussion—The expected waiting time required for
cedures as well as an extensive bibliography for reference
decision is the average of the waiting times required for purposes. Numerical examples illustrating the statistical pro-
decision when life tests are conducted on a large number of cedures are included in Part II of the paper.
samples drawn at random from the same exponential distribu-
5.2 It is important to note that the life test sampling plans of
tion.
this practice are not to be used indiscriminately simply because
it is possible to obtain life test data. Only after the exponential
4. Significance and Use
assumption is deemed reasonable should the sampling plans be
used.
4.1 This practice was prepared to meet a growing need for
the use of standard sampling procedures and tables for life and 5.3 Sections 6 and 7 describe general procedures and
reliability testing in government procurement, supply, and description of life test sampling plans. Section 8 describes
specific procedures and applications of sampling plans when
maintenance quality control (QC) operations as well as in
life tests are terminated upon the occurrence of a preassigned
research and development activities where applicable.
number of failures, and Section 9 provides sampling plans
4.2 A characteristic feature of most life tests is that the
when life tests are terminated at a preassigned time. Section 10
observations are ordered in time to failure. If, for example, 20
describes sequential life test sampling plans. Section 8 covers:
radio tubes are placed on life test, and t denotes the time when
i
(1) acceptance procedures; (2) expected duration of life tests
the ith tube fails, the data occur in such a way that t ≤ t ≤ .
1 2
andcostconsiderationsinselectionofsamplesizes;and(3)life
≤ t .The same kind of ordered observations will occur whether
n
test plans for certain specified values of α, β, and θ /θ . Section
1 0
the problem under consideration deals with the life of electric
9 covers: (1) acceptance procedures; (2) life test plans for
bulbs, the life of electronic components, the life of ball
certain specified values of α, β, θ /θ , and T/θ ; and (3) life test
1 0 0
bearings, or the length of life of human beings after they are
plans based on proportion of lot failing before specified time.
treated for a disease. The examples just given all involve
Section 10 covers: (1) acceptance procedures; (2) graphical
ordering in time.
acceptance procedures; and (3) expected number and waiting
time required for decision.
4.3 In destructive testing involving such situations as the
5.4 Operating characteristic (OC) curves for the life test
current needed to blow a fuse, the voltage needed to break
sampling plans of 8.1 – 8.5, 9.1 – 9.5, and Section 10 are
down a condenser, or the force needed to rupture a physical
shown in Fig. A1.1 for the corresponding sampling plans in
material,thetestcanoftenbearrangedinsuchawaythatevery
these sections were matched with respect to their OC curves.
item in the sample is subjected to precisely the same stimulus
The OC curves in Fig. A1.1 have been computed for the life
(current, voltage, or stress). If this is done, then clearly the
test sampling plans of 8.1 – 8.5 but are equally applicable for
weakest item will be observed to fail first, the second weakest
the sampling plans of 9.1 – 9.5 and Section 10.
next, and so forth. While the random variable considered
mostly in this guide is time to failure, it should be emphasized,
5.5 The procedures of this section are based on the premise
however, that the methodology provided herein can be adapted
that the life tests are monitored continuously. If the tests are
to the testing situations mentioned above when the random
monitored only periodically, the values obtained from the
variable is current, voltage, stress, and so forth.
tables and curves are only approximations.
4.4 Sections 6 and 7 describe general procedures and
6. General Definitions of Life and Reliability Test Terms
definitions of terms used in life test sampling. Sections 8, 9,
6.1 Discussion of Terms and Procedures:
and 10 describe specific procedures and applications of the life
6.1.1 Purpose—This section provides definitions of terms
testsamplingplansfordeterminingconformancetoestablished
required for the life test sampling plans and procedures of
reliability requirements.
Sections 7 through 10.
4.5 Whenever the methodology or choice of procedures in
the practice requires clarification, the user is advised to consult
a qualified mathematical statistician, and reference should be
Epstein, B., “Tests for the Validity of the Assumption that the Underlying
made to appropriate technical reports and other publications in
Distribution of Life is Exponential,” Technometrics, Vol 2, February and May 1960,
the field. pp. 83–101 and 167–183.
E2696 − 09 (2018)
6.1.2 Life Test—Life test is the process of placing the “unit exponential distribution. The expected waiting time can be
of product” under a specified set of test conditions and predetermined for the sampling plans mentioned in 6.1.6 –
6.1.8.
measuring the time it takes until failure.
6.1.3 Unit of Product—The unit of product is the entity of
6.2 Length of Life:
product that may be placed on life test.
6.2.1 LengthofLife—Theterms“lengthoflife”and“timeto
failure” may be used interchangeably and shall denote the
6.1.4 Specifying Failure—The state that constitutes a failure
length of time it takes for a unit of product to fail after being
shall be specified in advance of the life test.
placed on life test. The length of time may be expressed in any
6.1.5 Life Test Sampling Plan—A life test sampling plan is
convenient time scale such as seconds, hours, days, and so
a procedure that specifies the number of units of product from
forth.
a lot that are to be tested and the criterion for determining
6.2.2 Mean Time to Failure—The terms “mean time to
acceptability of the lot.
failure”and“meanlife”maybeusedinterchangeablyandshall
6.1.6 Life Test Terminated upon Occurrence of Preassigned
denote the mean (or equivalently, the average) length of life of
Number of Failures—Life test sampling plans whereby testing
items in the lot. Mean life is denoted by θ.
is terminated when a preassigned termination number of
6.2.3 Acceptable Mean Life—The acceptable mean life, θ ,
failures, r, occur are given in Section 8 of this practice.
is the minimum mean time to failure that is considered
6.1.7 Life Test Terminated at Preassigned Time—Life test
satisfactory.
sampling plans whereby testing is terminated when a preas-
6.2.4 Unacceptable Mean Life—The unacceptable mean
signed termination time, T, is reached are given in Section 9 of
life, θ (θ < θ ), is the mean time to failure such that lots
1 1 0
this practice.
having a mean life less than or equal to θ are considered
6.1.8 Sequential Life Test—Sequential life test is a life test
unsatisfactory. The interval between θ and θ is a zone of
0 1
sampling plan whereby neither the number of failures nor the indifference in which there is a progressively greater degree of
time required to reach a decision are fixed in advance but, dissatisfaction as the mean life decreases from θ to θ .
0 1
instead, decisions depend on the accumulated results of the life
6.3 Failure Rate:
test. Information on the observed time to failure are accumu-
6.3.1 Proportion of Lot Failing Before Specified Time—The
lated over time and the results at any time determine the choice
term “proportion of lot failing before specified time,” p,
of one among three possible decisions: (1) the lot meets the
denotes the fraction of the lot that fails before some specified
acceptability criterion, (2) the lot does not meet the acceptabil-
time, T, that is:
ity criterion, or (3) the evidence is insufficient for either
p 5 1 2 exp 2T/θ (1)
~ !
decision (1) or (2) and the test must continue. Sequential life
test sampling plans are given in Section 10 of this practice and
6.3.2 Failure Rate during Period of Time—The “failure rate
have the advantage over the life test sampling plans mentioned
during period of time T,” G, is given by:
in 6.1.6 and 6.1.7 in that, for the same OC curve, the expected
G 5 1 2 exp T/θ 5 p/T (2)
waiting time and the expected number of failures required to $ ~ !%
T
reach a decision as to lot acceptability are less for the
6.3.3 Instantaneous Failure Rate—The “instantaneous fail-
sequential life tests.
ure rate” or “hazard rate” is given by:
6.1.9 Expected Number of Failures—Thenumberoffailures
required for decision is the number of failures that have Z 51/θ (3)
occurred at the time the decision as to lot acceptability is
6.3.4 Acceptable Proportion of Lot Failing Before Specified
reached. For the life test sampling plans mentioned in 6.1.6,
Time—The “acceptable proportion of lot failing before speci-
this number of failures is known in advance of the life test;
...
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 2013) E2696 − 09 (Reapproved 2018)An American National Standard
Standard Practice for
Life and Reliability Testing Based on the Exponential
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 safety, health, and healthenvironmental 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
2.1 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.
3.1.2 consumer’sconsumer’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’sconsumer’s risk is the probability of accepting lots with mean time to failure θ .
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 .
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^Current edition approved April 1, 2013Dec. 1, 2018. Published April 2013December 2018. Originally approved in 2009. Last previous edition approved in
ε1
20092013 as E2696 – 09 . (2013). DOI: 10.1520/E2696-09R13.10.1520/E2696-09R18.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’sstandard’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
E2696 − 09 (2018)
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, θ, n—in life testing, the average length of life of items in a lot.
3.1.4.1 Discussion—
Also known 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’sproducer’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’sproducer’s risk is the probability of rejecting lots with mean time to failure θ .
3.1.6.2 Discussion—
For the procedures of 9.7 and 9.8, the producer’s risk may also be defined as the probability of rejecting lots with acceptable
proportion of lot failing before specified time, p .
3.1.7 sequential life test, n—life test sampling plan whereby neither the number of failures nor the time required to reach a
decision are fixed in advance but instead decisions depend on the accumulated results of the life test.
3.1.8 unit of product, n—that which is inspected to determine its classification as defective or nondefective or to count the
number of defects. E2234
3.1.9 waiting time, n—in life testing, the time elapsed from the start of testing until a decision is reached as to lot acceptability.
3.1.9.1 Discussion—
The expected waiting time required for decision is the average of the waiting times required for decision when life tests are
conducted on a large number of samples drawn at random from the same exponential distribution.
4. 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 t denotes the time when the ith tube fails, the data occur in such a way that t ≤ t ≤ . ≤ t . The same
i 1 2 n
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.
E2696 − 09 (2018)
4.5 Whenever the methodology or choice of procedures in the practice requires clarification, the user is advised to consult a
qualified mathematical statistician, and reference should be made to appropriate technical reports and other publications in the
field.
5. Introduction
5.1 The theory underlying the development of the life test sampling plans of this section, including the operating characteristic
curves, assumes that the measurements of the length of life are drawn from an exponential distribution. Statistical test procedures
for determining the validity of the exponential distribution assumption have appeared in the technical statistical journals. Professor
Benjamin Epstein published a comprehensive paper (in two parts) on this subject in the February and May 1960 issues of
Technometrics. Part I of the paper contains descriptions of the mathematical and graphical procedures as well as an extensive
bibliography for reference purposes. Numerical examples illustrating the statistical procedures are included in Part II of the paper.
5.2 It is important to note that the life test sampling plans of this practice are not to be used indiscriminately simply because
it is possible to obtain life test data. Only after the exponential assumption is deemed reasonable should the sampling plans be used.
5.3 Sections 6 and 7 describe general procedures and description of life test sampling plans. Section 8 describes specific
procedures and applications of sampling plans when life tests are terminated upon the occurrence of a preassigned number of
failures, and Section 9 provides sampling plans when life tests are terminated at a preassigned time. Section 10 describes sequential
life test sampling plans. Section 8 covers: (1) acceptance procedures; (2) expected duration of life tests and cost considerations in
selection of sample sizes; and (3) life test plans for certain specified values of α, β, and θ /θ . Section 9 covers: (1) acceptance
1 0
procedures; (2) life test plans for certain specified values of α, β, θ /θ , and T/θ ; and (3) life test plans based on proportion of lot
1 0 0
failing before specified time. Section 10 covers: (1) acceptance procedures; (2) graphical acceptance procedures; and (3) expected
number and waiting time required for decision.
5.4 Operating characteristic (OC) curves for the life test sampling plans of 8.1 – 8.5, 9.1 – 9.5, and Section 10 are shown in
Fig. A1.1 for the corresponding sampling plans in these sections were matched with respect to their OC curves. The OC curves
in Fig. A1.1 have been computed for the life test sampling plans of 8.1 – 8.5 but are equally applicable for the sampling plans of
9.1 – 9.5 and Section 10.
5.5 The procedures of this section are based on the premise that the life tests are monitored continuously. If the tests are
monitored only periodically, the values obtained from the tables and curves are only approximations.
6. General Definitions of Life and Reliability Test Terms
6.1 Discussion of Terms and Procedures:
6.1.1 Purpose—This section provides definitions of terms required for the life test sampling plans and procedures of Sections
7 through 10.
6.1.2 Life Test—Life test is the process of placing the “unit of product” under a specified set of test conditions and measuring
the time it takes until failure.
6.1.3 Unit of Product—The unit of product is the entity of product that may be placed on life test.
6.1.4 Specifying Failure—The state that constitutes a failure shall be specified in advance of the life test.
6.1.5 Life Test Sampling Plan—A life test sampling plan is a procedure that specifies the number of units of product from a lot
that are to be tested and the criterion for determining acceptability of the lot.
6.1.6 Life Test Terminated upon Occurrence of Preassigned Number of Failures—Life test sampling plans whereby testing is
terminated when a preassigned termination number of failures, r, occur are given in Section 8 of this practice.
6.1.7 Life Test Terminated at Preassigned Time—Life test sampling plans whereby testing is terminated when a preassigned
termination time, T, is reached are given in Section 9 of this practice.
6.1.8 Sequential Life Test—Sequential life test is a life test sampling plan whereby neither the number of failures nor the time
required to reach a decision are fixed in advance but, instead, decisions depend on the accumulated results of the life test.
Information on the observed time to failure are accumulated over time and the results at any time determine the choice of one
among three possible decisions: (1) the lot meets the acceptability criterion, (2) the lot does not meet the acceptability criterion,
or (3) the evidence is insufficient for either decision (1) or (2) and the test must continue. Sequential life test sampling plans are
given in Section 10 of this practice and have the advantage over the life test sampling plans mentioned in 6.1.6 and 6.1.7 in that,
for the same OC curve, the expected waiting time and the expected number of failures required to reach a decision as to lot
acceptability are less for the sequential life tests.
6.1.9 Expected Number of Failures—The number of failures required for decision is the number of failures that have occurred
at the time the decision as to lot acceptability is reached. For the life test sampling plans mentioned in 6.1.6, this number of failures
is known in advance of the life test; but, for the sampling plans mentioned in 6.1.7 and 6.1.8, this number cannot be predetermined.
The expected number of failures required for decision is the average of the number of failures required for decision when life tests
Epstein, B., “Tests for the Validity of the Assumption that the Underlying Distribution of Life is Exponential,” Technometrics, Vol 2, February and May 1960, pp. 83–101
and 167–183.
E2696 − 09 (2018)
are conducted on a large number of samples drawn at random from the same exponential distribution. The expected number of
failures can be predetermined for the sampling plans mentioned in 6.1.6 – 6.1.8.
6.1.10 Expected Waiting Time—The waiting time required for decision is the time elapsed from the start of the life test to the
time decision is reached as to lot acceptability. The waiting time required for decision cannot be predetermined for any of the
sampling plans mentioned in 6.1.6 – 6.1.8. The expected waiting time required for decision is the average of the waiting times
required for decision when life tests are conducted on a large number of samples drawn at random from the same exponential
distribution. The expected waiting time can be predetermined for the sampling plans mentioned in 6.1.6 – 6.1.8.
6.2 Length of Life:
6.2.1 Length of Life—The terms “length of life” and “time to failure” may be used interchangeably and shall denote the length
of time it takes for a unit of product to fail
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