1、ANSI/IEC/ASQ D61164-1997 Reliability growth-statistical test and estimation methods Approved as an American National Standard by: American Society for Quality ANSI/IEC/ASQ D61164-I997 eiiabiiity Growth- tion Approved as an American National Standard by: American Society for Quality An American Natio
2、nal Standard Approved on September 16, i 997 American National Standards: An American National Standard implies a consensus of those substantially concerned with its scope and provisions. An American National Standard is intended as a guide to aid the manufacturer, the consumer, and the general publ
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8、e use of quality principles, con- cepts, and technologies; and thereby be recognized throughout the world as the leading authority on, and champion for, quality. 10 9 8 7 65 4 3 2 1 Printed in the United States of America Printed on acid-free paper Published by: American Society for Quality Quality
9、Press 61 1 East Wisconsin Avenue Milwaukee, Wisconsin 53201 -3005 Web site http:/www.asq.org 800-248-1 946 Contents Page Introduction. Clause 1 Scope 2 Normative references . 3 Definitions 4 Symbols, . 5 The power law model . Foreword. . . . . 1 4 3 4 5 6 Use of the model in planning reliability imp
10、rovement programmes 6 7 Statistical test and estimation procedures . 6 ses . 17 Annexes A Numerical examples EB The power law reliability growth model-Background information We i i ab i I it y Statistical Test and DIS 56(CO) 1 50 1) The IEC (International Electrotechnical Commission) is a worldwide
11、organization for standardization comprising all national electrotechnical committees (IEC National Committee). The object of the IEC is to promote international cooperation on all questions concerning standardization in the electrical and electronic fields. To this end and in addition to other activ
12、ities, the IEC publishes International Standards. Their preparation is entrusted to technical committees; any IEC National Committee interested in the subject dealt with may participate in this preparatory work. International, governmental and non-gov- ernmental organizations liaising with the IEC a
13、lso participate in this preparation. The IEC collaborates closely with the International Organization for Standardization (ISO) in accordance with conditions determined by agreement between the two organizations. Report on voting 56( CO) 1 59 2) The formal decisions or agreements of the IEC on techn
14、ical matters, prepared by technical committees on which all the National Committees having a special interest therein are represented, express, as nearly as possible, an international consensus of opinion on the subjects dealt with. 3) They have the form of recommendations for international use publ
15、ished in the form of standards, tech- nical reports or guides and they are accepted by the National Committees in that sense. 4) In order to promote international unification, IEC National Committees undertake to apply IEC International Standards transparently to the maximum extent possible in their
16、 national and regional standards. Any divergence between the IEC Standard and the corresponding national or regional standard shall be clearly indicated in the latter. International Standard IEC 1164 has been prepared by IEC Technical Committee No. 56: Dependability. The text of this standard is bas
17、ed on the following documents: Full information on the voting for the approval of this standard can be found in the report on voting indi- cated in the above table. This standard shall be used in conjunction with IEC 1014. Annexes A and 8 are for information only. 1 ANSI/IEC/ASQ D61164-1997 Introduc
18、tion This International Standard describes the power law reliability growth model and related projection model and gives step-by-step directions for their use. There are several reliability growth models avail- able, the power law being one of the most widely used. This standard provides procedures
19、to estimate some or all of the quantities listed in clause 9 of IEC 1014. An input is required consisting of a data set of accumulated test times at which relevant failures occurred, or were observed, for a single system, and the time of termination of the test, if different from the time of the fin
20、al failure. It is assumed that the col- lection of data as input for the model beings after the completion of any preliminary tests, such as envi- ronmental stress screening, intended to stabilize the systems initial failure intensity. Model parameters estimated from previous results may be used to
21、plan and predict the course of fut:-ire reliability growth programmes, if the conditions are similar. Some of the procedures may require computer programs, but these are not unduly complex. This stan- dard presents algorithms for which computer programs should be easy to construct. 2 ANSI/IEC/ASQ D6
22、1164-1997 Reliability Gro Statistical Test and Estim ethods 1 Scope This International Standard gives models and numerical methods for reliability growth assessments based on failure data from a single system which were generated in a reliability improvement programme. These procedures deal with gro
23、wth, estimation, confidence intervals for system reliability and goodness-of-fit tests. 2 Normative references The following normative documents contain provisions which, through reference in this text, constitute provisions of this International Standard. At the time of publication, the editions in
24、dicated were valid. All normative documents are subject to revision, and parties to agreements based on this International Standard are encouraged to investigate the possibility of applying the most recent editions of the nor- mative documents indicated below. Members of IEC and IS0 maintain registe
25、rs of currently valid International Standards. IEC 60050( 191 ): 1990, International Electrotechnical Vocabulary (1EV)-Chapter 191: Dependability and quality of service IEC 60605-1 : 1978, Equipment reliability testing-Part 1: General requirements I EC 60605-4: 1986, Equipment reliability testing-Pa
26、rt 4: Procedures for determining point estimates and confidence limits from equipment reliability determination tests IEC 60605-6: 1986, Equipment reliability testing-Part 6: Tests for the validity of a constant failure rate assumption IEC 61 O1 4: 1989, Programmes for reliability growth 3 Definitio
27、ns For the purposes of this standard the terms and definitions of IEC 60050(191) and IEC 61014 apply, together with the following additional terms and definitions: 3.1 delayed modification: A corrective modification which is incorporated into the system at the end of a test. NOTE-A delayed modificat
28、ion is not incorporated during the test. 3.2 improvement effectiveness factor: The fraction by which the intensity of a systematic failure is reduced by means of corrective modification. 3 ANSI/IEC/ASQ D61164-I 997 3.3 type I test: A test which is terminated at a predetermined time or test with data
29、 available througli a time which does not correspond to a failure. NOTE-Type I test is sometimes called time terminated test. 3.4 type II test: A reliability growth test which is terminated upon the accumulation of a specified num- ber of failures, or test with data available through a time which co
30、rresponds to a failure. NOTE-Type II test is sometimes called failure terminated test. 4 Symbols For the purpose of this international standard, the following symbols apply: scale and shape parameters for the power law model critical value for hypothesis test number of intervals for grouped data ana
31、lysis mean and individual improvement effectiveness factors number of distinct types of category B failures observed general purpose indices number of category A failures number of category B failures number of i-th type category B failures observed; KB = c Ki parameter of the Cramr-von Mises test (
32、statistical) number of relevant failures number of relevant failures in i-th interval accumulated number of failures up to test time T expected accumulated number of failures up to test time T endpoints of i-th interval of test time for grouped data analysis current accumulated relevant test time ac
33、cumulated relevant test time at the i-th failure total accumulated relevant test times for type II test total accumulated relevant test times for type I test y fractile of the x2 distribution with u degrees of freedom general symbol for failure intensity y fractile of the standard normal distributio
34、n current failure intensity at time T current instantaneous mean time between failures projected mean time between failures k i=l 4 5 The power law model The statistical procedures for the power law reliability growth model use the original relevant failure and time data from the test. Except in the
35、 projection technique (see 7.6), the model is applied to the complete set of relevant failures (as in IEC 61014, figure 2, characteristic (3) without subdivision into categories. The basic questions for the power law model are given in this clause. Background information on the model is given in ann
36、ex B. The expected accumulated number of failures up to test time Tis given by: EN(T) = hT, with h O, O, T O where h is the scale parameter is the shape parameter (a function of the general effectiveness of the improvements; O 1 corresponds to negative reliability growth). The current failure intens
37、ity after T h of testing is given by: d dT z(T) = - EN(T) = hT-,With TO Thus, parameters h and both affect the failure intensity achieved in a given time. The equation rep- resents in effect the slope of a target to the N( T) vs. T characteristic at time Tas shown in IEC 61014, figure 6. The current
38、 mean time between failures after T h of testing is given by: Methods are given in 7.1 and 7.2 for maximum likelihood estimation of the parameters hand . Subclause 7.3 gives goodness-of-fit tests for the model, and 7.4 and 7.5 discuss confidence interval procedures. An extension of the model for rel
39、iability growth projections is given in 7.6. The model has the following characteristic features: -it is simple to evaluate; -when the parameters have been estimated from past programmes it is a convenient tool for planning future programmes employing similar conditions of testing and equal improvem
40、ent effec- tiveness (see clause 5, and IEC 61014, clause 6); -it gives the unrealistic indications that z(T) = 00 at T= O and that growth can be unending, that is z(T) tends to zero as T tends to infinity; however, these limitations do not generally affect its practical use; -it is relatively slow a
41、nd insensitive in indicating growth immediately after a corrective modification, and so may give a low (that is, pessimistic) estimate of the final ( T), unless projection is used (see 7.6); 5 ANSI/IEC/ASQ D61164-1997 -the normal evaluation method assumes the observed times to be exact times of fail
42、ure, but an alternative approach is possible for groups of failures within a known time period (see 7.2.2). 6 Use of the model in planning reliability improvement programmes As inputs to the procedure described in 6.3 of IEC 1014, two quantities have to be predicted by means of reliability growth mo
43、dels: -the accumulated relevant test time in hours expected to be necessary to meet the aims of the pro- gramme; -the number of relevant failures expected to occur during this time period The accumulated relevant test time is then converted to calendar time from the planned test time Iper week or mo
44、nth, making allowance for the predicted total downtime (see below) and other contingencies, and the number of relevant failures is increased by judgment to include non-relevant failures and used to predict total downtime. The inputs to the model for these calculations will be the assumed parameters
45、for the model, as already estimated from one or more previous programmes, and judged to be valid for the future application by similarity of the test items, test environment, management procedures and other significant influences. 7 Statistical test and estimation procedures 7.1 Overview The procedu
46、res in 7.2 utilize system failure data during a test programme to estimate the progress of reliability growth, and to estimate, in particular, the final system reliability at the end of the test. The relia- bility growth which is assessed in the result of corrective modifications incorporated into t
47、he system dur- ing test. The procedures discussed in 7.2.1 assume that the accumulated test time to each relevant failure is known. Subclause 7.2.2 addresses the situation where actual failure times are not known and failures are grouped in intervals of test time. Type I tests, which are concluded a
48、t T: which is not a failure time, and type II tests, which are concluded at failure time TN, use slightly different formulae, as indicated in 7.2.1. An appropriate goodness-of-fit test, as described in 73, shall be performed after the growth test proce- dures of 7.2.1 and 7.2.2. Subclause 7.6 addres
49、ses the situation where the corrective modifications are incorporated into :he system at the end of the test as delayed modifications. The projection technique estimates the system reliability resulting from these corrective modifications. 7.2 Growth tests and parameter estimation 7.2.1 Case l-Time data for every relevant failure This method applies only where the time of failure has been logged for every failure. 6 I/ EWAS Q D6d 1 64 -1 9 Step 1: exclude non-relevant failures by reference to 7.1 of IEC 61014, and/or other appropriate docu- mentation. Step 2: assemble i
