ANSI IEEE 101-1987 Guide for the Statistical Analysis of Thermal Life Test Data.pdf

1、ANSI/IEEE Std 101-1987(R2010)(Revision of IEEE Std 101-1972)An American National Standard IEEE Guide for the Statistical Analysis of Thermal Life Test Data Sponsor Statistics Technical Committee of the IEEE Dielectrics and Electrical Insulation Society Approved September 10, 1987 Reaffirmed December

2、 8, 2010 IEEE Standards Board Approved January 12, 1996 Reaffirmed June 28, 2011 American National Standards Institute Copyright 1988 by The Institute of Electrical and Electronics Engineers, Inc 345 East 47th Street, New York, NY 10017, USA No part of this publication may be reproduced in any form,

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21、use can also be obtained through the Copyright Clearance Center. iiiForeword(This Foreword is not a part of ANSI/IEEE Std 101-1987, IEEE Guide for the Statistical Analysis of Thermal Life Test Data.)ANSI/IEEE Std 101-1987 is substantially revised from IEEE Std 101-1972. Extensive revision was deemed

22、 necessaryto reect the widespread access of users of this document to advanced calculators and computers. Thus the tediousworkbook approach used in previous versions was no longer necessary. However, Annex 3 of this document doescontain a detailed worked example to provide guidance to those individu

23、als without advanced calculators orcomputers.This document was prepared by the Statistics Technical Committee of the IEEE Dielectrics and Electrical InsulationSociety. The members of the working group were as follows:G. C. Stone, Chair T. W. Dakin,Past ChairP. E. AlexanderA. BulinskiT. ClaussenE. M.

24、 FortJ. FothergillH. N. GalpernJ. F. LawlessW. B. NelsonH. RosenG. A. VincentB. E. WardThe members of the balloting committee that approved this document for submission to the IEEE Standards Boardwere as follows:P. E. AlexanderA. BulinskiT. ClaussenT. W. DakinE. M. FortJ. FothergillH. N. GalpernJ. F

25、. LawlessW. B. NelsonH. RosenG. C. StoneG. A. VincentB. E. WardWhen the IEEE Standards Board approved this standard on September 10, 1987, it had the following membership:Donald C. Fleckenstein, Chair Marco W. Migliaro, Vice Chair Andrew G. Salem, Secretary James H. BeallDennis BodsonMarshall L. Cai

26、nJames M. DalyStephen R. DillonEugene P. FogartyJay ForsterKenneth D. HendrixIrvin N. HowellLeslie R. KerrJack KinnIrving KolodnyJoseph L. Koepfinger*Edward LohseJohn MayLawrence V. McCallL. Bruce McClungDonald T. Michael*L. John RankineJohn P. RiganatiGary S. RobinsonFrank L. RoseRobert E. Rountree

27、William R. TackaberryWilliam B. WilkensHelen M. Wood* Member emeritusivCLAUSE PAGE1. Introduction.11.1 General Background 11.2 The Arrhenius Model . 11.3 Test Data Recommendations . 32. Data Analysis 32.1 Graphical Analysis of Data for Individual Temperatures 32.2 Calculation of the Mean and Standar

28、d Deviation of Data at a Temperature . 52.3 Analysis of Incomplete Test Data 73. Estimation of the Relationship Between Life and Temperature .73.1 Estimation by Plotting 73.2 Estimation by Numerical Methods 73.3 Calculation Outline 154. Comparison of Two Sets of Data174.1 Comparison of Two Means at

29、a Temperature 174.2 Comparison of Two Arrhenius Lines at a Temperature. 185. Bibliography19Annex 1 (Informative) 20Annex 2 (Informative) 22Annex 3 (Informative) 28Copyright 1998 IEEE All Rights Reserved1An American National StandardIEEE Guide for the Statistical Analysis of Thermal Life Test Data1.

30、IntroductionThis revision of IEEE Std 101-1972 describes statistical analyses for data from thermally accelerated aging tests. Itexplains the basis and use of statistical calculations for an engineer or scientist. Statistical methods discussed in 2 1through 6 provide more information. Life test data

31、 analysis is dealt with more specically in 7 through 13. Thesubject of this guide is treated extensively in 11 and 12.1.1 General BackgroundANSI/IEEE Std 1-1986 (see Annex 1) discusses the principles for temperature rating of electrical insulation. Theseprinciples are carried forward in ANSI/IEEE St

32、d 98-1972 and ANSI/IEEE Std 99-1980 (see Annex 1) whichrespectively outline test procedures for the experimental estimation of the life of insulating materials and systems. Lifetest procedures for specic insulating materials and systems are outlined in other IEEE publications (see Annex 1).Insulatio

33、n life test procedures are also described in ASTM (American Society for Testing and Materials), NEMA(National Electrical Manufacturers Association), and IEC (International Electrotechnical Commission) standards (seeAnnex 1). Also, proposed life test procedures continue to appear in the literature. A

34、ll such publications assume that thelife of insulation with organic materials is a decreasing function of temperature.Accelerated test procedures usually call for a number of specimens to be aged at each of several temperaturesappreciably above normal operating temperatures. High temperatures are ch

35、osen to produce specimen failures(according to specied failure criteria) in typically one week to one year. The test objective is to determine thedependence of median life on temperature from the data and to estimate, by extrapolation, the median life to beexpected at service temperature. This guide

36、 presents methods for analyzing such data and for comparing test data ondifferent materials.1.2 The Arrhenius ModelThe Arrhenius equation gives the rate of a chemical reaction as a function of temperature. It has been adapted 1 toapproximate the relationship between insulation life and temperature a

37、s follows.1The numbers in brackets refer to those of the bibliographic entries listed in Section 52Copyright 1998 IEEE All Rights ReservedANSI/IEEE Std 101-1987 IEEE GUIDE FOR THE STATISTICAL ANALYSISThe Arrhenius equation for a chemical reaction rate is(1)wherek= specic reaction rateE= activation e

38、nergy of the reaction (assumed to be constant), in calories/mol, or J/mol or electron voltsR= Boltzmann gas constant = 1.987 calories/mol/K or 8.314 J/mol/K, or electron volts/KT= absolute temperature in degrees Kelvin (273 + temperature in C)D= frequency factor, a quantity that is assumed to be con

39、stant; it depends on the number of collisions of themolecules reacting to produce chemical deterioration of the insulation.The median life Lof insulation specimens is assumed to be inversely proportional to the chemical reaction rate k. Thisyields(2)where log is the base 10 logarithm throughout.This

40、 Arrhenius equation has the algebraic form(3)in whichM(X) = log(L) = the mean log lifeX= 1/TA= a constant characteristic of the insulation population, test specimen, test method, and failure modeB= E/(2.303R), another constant characteristic of the insulation population, test specimen, test method,

41、andfailure modeThe coefcients Aand Bare estimated by tting the above equation to experimental data. This tting can be donegraphically or, more precisely, by the method of least squares. These methods are presented in sections 2 and 3.Section 3 gives condence limits that indicate the uncertainty in e

42、stimates from data. Throughout, population valuesare denoted by capital letters (A, B, M(X), etc), and their sample estimates based on experimental data by lower-caseletters (a, b, m(X), etc) to distinguish them.Theoretically, Eq 3 is valid only if a single chemical reaction and failure mode control

43、 the insulation failuremechanism. Other reactions may occur, but if they are not dominant, application of the Arrhenius equation may still bevalid. The Arrhenius equation application is often valid in practice. Sometimes one reaction and failure modedominates over a temperature range, but another re

44、action with a different temperature coefcient and/or failure modedominates at lower or higher temperatures. Deviations from the simple Arrhenius relation may be caused by differentfailure modes dominant at different temperatures or by variations in mechanical stress, with temperature, that affectthe

45、 life. Therefore, while the Arrhenius relation will often t insulation life-temperature data, it will not always apply.Presented in 8 are valid analyses of such data with two or more failure modes identied by examination of failedspecimens.With these reservations, this guide assumes the Arrhenius eq

46、uation applies and outlines statistical calculations to tthis equation to test data.kD ERT()exp=L()log constant + ERT()2.303=MX() ABX+=Copyright 1998 IEEE All Rights Reserved3OF THERMAL LIFE TEST DATA ANSI/IEEE Std 101-19871.3 Test Data RecommendationsStatistical analysis will not compensate for inv

47、alid test data. The following recommendations on test procedures ensurecorrect test data. Some test conditions needed for validity of the Arrhenius relation were mentioned in section 1.2.Periodic proof tests are often used to measure an insulation property that deteriorates. Failure to withstand the

48、specied proof test level is then only detected after a cycle of aging. It is more rigorous to treat the failure as if itoccurred at the midpoint of the cycle. If there are different modes of failure, the data require special data analysismethods 8.In planning and carrying out life tests, one should

49、aim toward valid failure time data. One obtains more accurate lifeestimates at design temperatures from a test with a larger number of specimens at the low end of the test temperaturerange and fewer at the high end and the middle of this range 11. It is also best to select the lowest accelerated testtemperature as close to the anticipated service use temperature as is possibleconsistent with a reasonable estimatedtest time and enough failures in the allotted test time. Further comments on planning the aging test are given in ANSI/IEEE