BS-IEC-61710-2000 pdf free download – Power law model Ð Goodness-of-fit tests and estimation methods.
This International Standard specifies procedures to estimate the parameters of the power lawmodel, to provide confidence intervals for the failure intensity， to provide prediction intervalsfor the times to future failures, and to test the goodness-of-fit of the power law model to datafrom repaired items.
2Normative references
The following normative documents contain provisions which， through reference in this text,constitute provisions of this International Standard. For dated references,subsequentamendments to,or revisions of， any of these publications do not apply.However，parties toagreements based on this International Standard are encouraged to investigate the possibilityof applying the most recent editions of the normative documents indicated below.For undatedreferences,the latest edition of the normative document referred to applies. Members of lECand lsO maintain registers of currently valid lnternational Standards.
IEC60050(191):1990，International Electrotechnical Vocabulary (IEV) – Chapter 191:Dependability and quality of service
3Definitions
For the purposes of this International Standard, the terms and definitions of lEC 60050(191)apply.
4 symbols and abbreviations
For the purposes of this International Standard，the following symbols and abbreviationsapply:
shape parameter of the power law model
estimated shape parameter of the power law model
lower, upper confidence limits for p
Cramer-von-Mises goodness-of-fit test statistic
Critical value for the Cramer-von-Mises goodness-of-fit test statistic at rlevel of significance
Chi-square goodness of fit test statistic
y th fractile of the x2 distribution with v degrees of freedom
number of intervals for groups of failures
expected accumulated number of failures up to time t
expected accumulated operating time to jth failure
5Power law model
The statistical procedures for the power law model use the relevant failure and time data fromthe test or field studies.
The basic equations for the power law model are given in this clause.Background informationon the model is given in annex A and examples of its application are given in annex B.
Thus the parameters a and β both affect the failure intensity in a given time.
Methods are given in 7.2 for maximum likelihood estimation of the parameters of a and β.Subclause 7.3 gives goodness-of-fit tests for the model and 7.4 and 7.5 give confidenceinterval procedures.Subclause 7.6 gives prediction interval procedures and 7.7 gives tests forthe equality of the shape parameters.
The model is simple to evaluate.However when B<1, theoretically z(o)= o (i.e. z(t) tends toinfinity as t tends to zero) and z(xn)=0 (i.e. z(t) tends to zero as t tends to infinity); but thistheoretical limitation does not generally affect its practical use.
6 Data requirements
6.1 Case 1 – Time data for every relevant failure for one or more copies
from the same population
The normal evaluation methods assume the observed times to be exact times of failure of asingle repaired item or a set of copies of the same repaired item.The figures below illustratehow the failure times are calculated for three general cases.
6.1.1Case 1a)- One repaired item
For one repaired item observed from age 0 to age T, the relevant failure time，t,，is theelapsed operating time (that is, excluding repair and other down times)until the occurrence ofthe ith failure as shown in Figure 1.BS-IEC-61710 pdf download.