IEC 61710:2000 pdf download

IEC 61710:2000 pdf download.Power law model – Goodness-of-fit tests and estimation methods
1 Scope
This International Standard specifies procedures to estimate the parameters of the power law model, to provide confidence intervals for the failure intensity, to provide prediction intervals for the times to future failures, and to test the goodness-of-fit of the power law model to data from repaired items.
2 Normative references
The following normative documents contain provisions which, through reference in this text, constitute provisions of this International Standard. For dated references， subsequent amendments to, or revisions of, any of these publications do not apply. However, parties to agreements based on this International Standard are encouraged to investigate the possibility of applying the most recent editions of the normative documents indicated below. For undated references, the latest edition of the normative document referred to applies. Members of IEC and ISO maintain registers of currently valid International Standards. IEC 60050(191):1990， ， International Electrotechnical Vocabulary (IEV) 一Chapter 191: Dependability and quality of service
3 Definitions
For the purposes of this International Standard, the terms and definitions of IEC 60050(191) apply.
Time terminated data are observed to T , which is not a failure time, and failure terminated data are observed to tN， which is the time of the Nth failure. Time terminated and failure terminated data use slightly different formulae. 6.1.2 Case 1b)一Multiple copies of repaired item observed for same length of time It is assumed there are k items, which all represent the same population. That is, they are nominally identical copies operating under the same conditions (e.g. environment and load). When all copies are observed to time T，which is not a failure time (i.e. time terminated data), then the failure time data are combined by superimposing failure times (t;i= .,2… for all k systems on the same time line as shown in Figure 2.
6.2 Case 2- Time data for groups of relevant failures for one or more copies from the same population
This alternative method is used when there is at least one copy of an item and the data consists of known time intervals, each containing a known number of failures. The observation period is over the interval (0,T) and is partitioned into d intervals at times 0<+(1)<+(2)<…<t(d). The ith interval is the time period between t(i-1) and t(i), i= .,2…..= 0,r(d)=T. It is important to note that the interval lengths and the numbers of failures per interval need not be the same. 6.3 Case 3 – Time data for every relevant failure for more than one repaired item from different populations It is assumed there are k items which do not represent the same population and are to be compared. It should be noted that if each item is to be considered individually then it is appropriate to use case 1a) in 6.1.1.
7 Statistical estimation and test procedures
7.1 Overview In case 1 – time data for every relevant failure – the formulae given for failure terminated data assume one repaired item, that is k=1. All output results correspond to that item. The formulae given for time terminated data assume k copies of the item observed for the same length of time. |f there is only one repaired item then k =1. The point estimation procedures for all the aforementioned cases are given in 7.2.1. The appropriate procedures for the case when all copies are observed for different lengths of time are given in 7.2.2. Procedures for the case of time data for groups of relevant failures are given in 7.2.3. An appropriate goodness-of-fit test, as described in 7.3 shall be performed after the parameter estimation procedures of 7.2. Note that these tests, and the procedures given in 7.4 to 7.7 for constructing interval estimates and carrying out statistical tests, distinguish only between the cases of time data for every relevant failure (i.e. all instances of case 1 data – 1a), 1b) and 1c)) and time data for groups of relevant failures (i.e. case 2). NOTE The inference procedures that follow provide approximate estimates in some circumstances and so caution is required if they are to be applied to very small samples of data.