ASTM E2696-09e1
(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
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 and health practices and determine the applicability of regulatory limitations prior to use.
General Information
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Standards Content (Sample)
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Designation: E2696 − 09 AnAmerican National Standard
Standard Practice for
Life and Reliability Testing Based on the Exponential
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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.
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ε NOTE—Corrected 6.7.1.1 and 6.7.2.1 editorially in February 2013.
1. Scope 3. Terminology
3.1 Definitions:
1.1 Thispracticepresentsstandardsamplingproceduresand
tablesforlifeandreliabilitytestinginprocurement,supply,and 3.1.1 See Terminology E456 for a more extensive listing of
maintenance quality control operations as well as in research
terms in ASTM Committee E11 standards.
and development activities.
3.1.2 consumer’s risk, β,n—probability that a lot having
specified rejectable quality level will be accepted under a
1.2 This practice describes general procedures and defini-
defined sampling plan. E2555
tions of terms used in life test sampling and describes specific
3.1.2.1 Discussion—In this practice, the consumer’s risk is
procedures and applications of the life test sampling plans for
the probability of accepting lots with mean time to failure θ .
determining conformance to established reliability require- 1
ments. 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
1.3 This practice is an adaptation of the Quality Control and
accepting lots with unacceptable proportion of lot failing
Reliability Handbook H-108, “Sampling Procedures and
before specified time, p .
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Tables for Life and Reliability Testing (Based on Exponential
3.1.3 life test, n—process of placing one or more units of
Distribution),” U.S. Government Printing Office, April 29,
product under a specified set of test conditions and measuring
1960.
the time until failure for each unit.
1.4 A system of units is not specified in this practice.
3.1.4 mean time to failure, θ, n— in life testing, the average
1.5 This standard does not purport to address all of the
length of life of items in a lot.
safety concerns, if any, associated with its use. It is the
3.1.4.1 Discussion—Also known as mean life.
responsibility of the user of this standard to establish appro-
3.1.5 number of failures, n—number of failures that have
priate safety and health practices and determine the applica-
bility of regulatory limitations prior to use. occurred at the time the decision as to lot acceptability is
reached.
2. Referenced Documents
3.1.5.1 Discussion—The expected number of failures re-
2 quired for decision is the average of the number of failures
2.1 ASTM Standards:
required for decision when life tests are conducted on a large
E456 Terminology Relating to Quality and Statistics
number of samples drawn at random from the same exponen-
E2234 Practice for Sampling a Stream of Product by Attri-
tial distribution.
butes Indexed by AQL
E2555 Practice for Factors and Procedures for Applying the 3.1.6 producer’s risk, α,n—probability that a lot having
MIL-STD-105 Plans in Life and Reliability Inspection 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
the probability of rejecting lots with mean time to failure θ .
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This practice is under the jurisdiction ofASTM Committee E11 on Quality and 0
Statistics and is the direct responsibility of Subcommittee E11.30 on Statistical
3.1.6.2 Discussion—For the procedures of 9.7 and 9.8, the
Quality Control.
producer’s risk may also be defined as the probability of
Current edition approved May 1, 2009. Published June 2009. DOI: 10.1520/
rejecting lots with acceptable proportion of lot failing before
E2696-09E01.
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For referenced ASTM standards, visit the ASTM website, www.astm.org, or specified time, p .
0
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
3.1.7 sequential life test, n—life test sampling plan whereby
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. neither the number of failures nor the time required to reach a
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E2696 − 09
decision are fixed in advance but instead decisions depend on life are drawn from an exponential distribution. Statistical test
the accumulated results of the life test. procedures for determining the validity of the exponential
distribution assumption have appeared in the technical statis-
3.1.8 unit of product, n—that which is inspected to det
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