1、_. - Quality Control and Reliability HANDBOOK (Interim) H 108 SAMPLING PROCEDURES AND TABLES FOR LIFE AND .RELIABILITY TESTING ( Based on Exponential Distribution) 29 APRIL 1960 OFFICE OF THE ASSISTANT SECRETARY OF DEFENSE . (Supply and logistics) WASHINGTON 25, D.C. Provided by IHSNot for ResaleNo
2、reproduction or networking permitted without license from IHS-,-,-MIL-HDBK-HL04 QC m 7777770 0040075 4 . OFFICE OF THE ASSISTANT SECRETARY OF DEFENSE WASHINGTON PS, D.C. SUPPLY AND LOGISTICS Sampling Procedures and Tables for Life and Reliability Testing Quality Control and Reliability H-108, This h
3、andbook (interim) was developed by the Bureau of Naval Weapons, Department of the Navy on behalf of the Office of the Assistant Secretary of Defense (Supply and Logistics). It was prepared to meet a growing need for the use of standard sampling plans for life and reliability testing. Such plans may
4、be used to demonstrate the conformance of equipments, subassemblies and component parts b established reliability requirements. f Suggestions for improvements of this handbook should be addressed to the Office of the Assistant Secretary of Defense (Supply and Logistics), Washington 25, D.C. i Provid
5、ed by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-FOREWORD This handbook has been prepared to meet a growing need for the use of standard sampling proce- dures and tables for life and reliability testing in Government procurement, supply, and maintenance qua
6、lity control operations as well as in research and development activities where applicable. 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, S For example, 2A1.5 means chapter 2, section A, and paragraph 1.5.
7、Tables and graphs are numbered with the first figure representing the number of the chapter, the uppercase letter represent- ing the section, and finally the table or figure number itself. Thus, table 2C-5 means chapter 2 , section C, table 5, and fig. 2D-3 means chapter 2, section D, figure 3. When
8、ever the methodology or choice of procedures in the handbook require 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, I- 5 A characteristic feature of most life tests
9、 is that the Observations are ordered in time to failure. If, I whether the problem under consideration de.als with the life of electric bulbs, the life of electronic com- r Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I Page 1 .i 2.i 2.iii 2.1 2.
10、26. 2.42 2.56 2.66 111 . G Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-. MIL-HDBK-HL04 QC m 7977770 OOiOO78 T m CHAPTER 1 INTRODUCTION AND GENERAL DEFINITIONS OF TERMS 1 .i Provided by IHSNot for ResaleNo reproduction or networking permitted with
11、out license from IHS-,-,-MIL-HDBK-HL06 QC U 7777770 0040077 L m INTRODUCTION -=% The theory underlying the develoFment of the life test sampling plans and procedures of chapter 2 1 of this handbook assume the measurements of the length of life are drawn froman exponential distribu- tion, Statistical
12、 test procedures for determining the validity of the exponential distribution assumption have appeared in the technical statistical journals. Professor Benjamin Epstein has published a com- prehensive paper (in two parts) on this subject in the February and May 1960 issues of “Technometrics.”* Part
13、I of the paper contains descriptions of the mathematical and graphical procedures as well as an extensive bibliography for reference purposeis. Numerical examples illustrating the statistical pro- cedures are included in Part II of the paper. *B. Epatein, “Testa for the Validity of the Aaaumption th
14、at the Underlying Diatribution of Life ia Exponentid,” Technometricr, Feb. 1960 and May 1960. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-GENERAL DEFINITIONS OF LIFE AND RELIABILITY TEST TERMS 1Al SCOPE lAl.l Purpose. Chapter 1 of this handbook p
15、rovides definitions of terms required for the use of the . life test sampling plans and procedures of chapter 2. 1A1.2 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 till failure. 1A1.3 Unit of Product. Th
16、e unit of product is the entity of product which may be placed on life test. 161.4 Specifying Failure. The state that constitutes a failure must be specified in advance of the life test. 1.41.5 Life Test Sampling Plan. Alife test sampling plan is a procedure which specifies the number of units of pr
17、oduct from a lot which are to be tested, and the criterion for determining acceptability of the lot. 1A1.6 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 gi
18、ven in section 2B of this handbook. 1A1.7 Life Test Terminated at Preassigned Time. Life test sampling plans whereby testing is ter- minated when a preassigned termination time, T, is reached are given in section 2C of this handbook. 1A1.8 Sequential Life Test. Sequential life test is a life test sa
19、mpling plan whereby neither the num- ber of failures nor the time required to reach a decision are ked 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
20、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 evi- dence is insufficient for either decision (1) or (2) and the test must continue, Sequential life test sampling plans are given in sectio
21、n 2D of this handbook and have the advantage over the lif test sampling plans mentioned in paragraphs 1A1.6 and 1A1.7 in that, for the same operating characteristic curve, the but, for the sampling plans mentioned in paragraphs 1A1.7 and 1A1.8, this number cannot be pre- determined. The expected num
22、ber 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 ran- dom from the same exponential distribution. The expected number of failures can be predetermined for the sampling plans mentio
23、ned in paragraphs 1A1.6, 1A1.7, knd 1A1.8. 1A1.10 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 s
24、ampling plans mentioned in paragraph 1A1.6, 1A1.7, or 1A1.8, The expected waiting time required for decision is the average of the waiting timesrequired for -. decision when life tests are conducted. on a large number of samples drawn at random from the same . 1.1 Provided by IHSNot for ResaleNo rep
25、roduction or networking permitted without license from IHS-,-,-exponential distribution. The expected waiting time can be predetermined for the sampling plans men- tioned in paragraphs lAl.6, lA1.7, and.lA1.8. 1A2 LENGTH OF LIFE 1A2.1 Length of Life. The terms “length of life” and “time to fai1ure”m
26、ay be used interchangeably and shall denote the length of time it takes for a unit.of product to fail after being placed on life test. The length of time may be expressed in any convenient time scale such as seconds, hours, days, etc. 1A2.2 Mean Time to Failure. The terms “mean timetofai1ure”and “me
27、an 1ife”may be used interchange- ably and shall denote the mean (or equivalently, the average) length of life of items in the lot, Mean life is denoted by B. IA2.3 Acceptable Mean Life. The acceptable mean life, Bo, is the minimum mean time to failure which is considered satisfactory. 1A2.4 Unaccept
28、able Mean Life. The unacceptable mean life, BI, (Blpo), is the minimum fraction of the lot that may fail before time T and results in the lot being considered unsatisfactory. The interval between po and pl is a zone of indifference in which there is a progressively greater degree of dissatisfaction
29、as the fraction of the lot failing before time T increases from po topl. 1A3.6 Acceptable Failure Rate During Period of Time. The “acceptable failure rate during period of time,” G, is the maximum failure rate during period of time that can be considered satisfactory. IA3.7 Unacceptable Failure Rate
30、 During Period of Time. The dunacceptable failure rate during period of time,” GI, (G1Go), is tho minimum failure rate during period of time that results in the lot being considered unsatisfactory. The interval between Go and Cl is 8 zone of indifference in which there is a progressively greater deg
31、ree of*dissatisfaction as the failure rate increases from Go to GI. 1A3.8 Life Test Sampling Plans Based on Failure Rates. Life test sampling plans which are based on failure rates are given in section 2C, part III. 1A4 OPERATING CHARACTERISTIC CURVES AND SAMPLING RISKS 1A4.1 Operating Characteristi
32、c Curves, The operating characteristic (OC) curve of a life test sampling plan is the curve which shows the probability that a submitted lot with given mean lite would meet the acceptability criterion on the basis of that sampling plan. 1 1% Provided by IHSNot for ResaleNo reproduction or networking
33、 permitted without license from IHS-,-,-. n. e 1A4.2 Producers Risk. The producers risk, a, is the probability of rejecting lots with mean life eo. For the procedures of section 2C, part III, the producer”s risk may also be defined as the probability of rejecting lots with acceptable proportion of l
34、ot failing before specified time, P,. lA4.3 Consumers Risk. The consumers risk, 8, is the probability of accepting lots with mean life el. For the procedures of section 2C, part III, the consumers risk may also be defined as the probability of accepting lots with unacceptable proportion of lot faili
35、ng before specified time, pl. 1A5 SUBMITTAL OF PRODUCT lA5.1 Lot. The term “lot” shall mean either an “inspection lot”, Le., a collection of units of product, manufactured under essentially the same conditions, from which a sample is drawn and tested to deter- mine compliance with the acceptability
36、criterion; or, a “preproduction lot”, i.e., one or more units of product submitted prior to initiation of production for test to determine compliance with the acceptability criterion. 1.46 SAMPLE SELECTION 1lhS.l Drawing of Samples. A sample is one or more units ot product drawn at random from a lot
37、. 1A6.2 Testing Without Replacement. Life tsst sampling without replacement is a life test procedure whereby failed units are not replaced. 1A6.3 Testing With Replacement Life test sampling with replacement is a life test procedure whereby the life test is continued with each failed unit of product
38、replaced by a new one, drawn at random from the same lot, es soon as the failure occurred. In the case of complex unit of product, this may be in- terpreted to mean replacement of the component which caused the failure by a new component drawn at random from the same lot of components. When the “sam
39、ple sizes” are the same in both instances, the expected waieing time required for decision when testing with replacement is less than when testing without replacement. 1A6.4 Sample Size. The sample size, n, for a life test is the number of units of product placed on test at the start of a life test.
40、 When testing wit1 replacement, the total number of units of product placed on test will, in general, be greater than the original sample size. The sample sizes, for the life test plans of chapter 2, depend on the relative cost of placing,large numbers of units of product on test and on the expected
41、 length of time the life testa must continue in order to determine acceptability of the lots. In- creasing the sample size will, on one hand, cut the average time required to determine acceptability but on the other hand will increme the cost due to placing more units of product on test. 1A7 EXPONEN
42、TIAL DISTRIBUTION 1A7.1 Exponential Distribution With One Parameter. The density function for the exponentid distribution with one parameter is given by- f(t;e)=l/eezp(-t/e) t20, eo =O t 2A1.3 Specifying Unacceptable Mean Life. The particular value of the unacceptable mean life, e, shall be specifie
43、d in advance of the life test when. using the life test procedures of section 2B, part III, and section 2C, part II. 2A1.4 Specifying Acceptable Proportion of Lot Failing Before Specified Time. The particular value, P, of the acceptable proportion of lot failing before specified time to be used in t
44、he life test shall be specified in advance for the procedures of section 2C, part III. 2A1.5 Specifying Unacceptable Proportion of Lot Failing Before Specified Time. The particular value, pl, of the unacceptable proportion of latfailing before specified time shall be specified in advance of the life
45、 test when using the procedures of section 20, part III. 2A2 SAMPLING RISKS 2A2.1 Producers Risk. The producers risk,. a, is the probability of rejecting lots with mean life eo. For the procedures of section 2C, part III, the producers- risk may also be defined as the probability of rejecting lots w
46、ith po as the acceptable proportion of lot failing before specified time. Summarized below are the various numerical values of a and the master sampling tables in which they are given. Section 2B, part I _-_-_-_ 0.01, 0.05, 0.10,0.25, 0.50 _ _ 28-1 Section 2B, part III- _ _ - .01, .05, .lo, .25“- _
47、- - - - - - _ _ _ - _ 2B-5 Section 2C, part 1“ _ _ - - _ - _ - _ - - - - - - - - - - _ - - _ - - .01, .05, .lo, .25, .50- - - - - - - - - - - - - - - - - 2C-1, 2C-2 Section 2c, part II-= -_-_ _ _ - _ _-_ .01, .05, .lo, .25 _ _ _ _ - _ - - - - 2C-3, 2C-4 Bection 2C, part III- _ _ _ _ - - _ - _ .01, .
48、05, .10 _ _ - _ _ _ - - 2C-5 Section 2D _-_- .01, .05, .lo, .25, .50 _ _ 21)-1 2A2.2 Specifying Producers Risk. The particularvalue of a to be used in the life test shall be selected from among those given in paragraph 2A2.1 and specified in advance of the life test. Rocainrw /m- Prducerr rirk Table The smaller the value of 6, the greater is the protection against acceptance of lots with low mean life or high failure rate. I 81 Provided by IHSNot for ResaleNo reproduction or networking
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