1、raising standards worldwideNO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAWBSI Standards PublicationBS ISO 14802:2012Corrosion of metals andalloys Guidelines forapplying statistics to analysisof corrosion dataBS ISO 14802:2012 BRITISH STANDARDNational forewordThis British Stand
2、ard is the UK implementation of ISO 14802:2012.The UK participation in its preparation was entrusted to TechnicalCommittee ISE/NFE/8, Corrosion of metals and alloys.A list of organizations represented on this committee can beobtained on request to its secretary.This publication does not purport to i
3、nclude all the necessaryprovisions of a contract. Users are responsible for its correctapplication. The British Standards Institution 2012. Published by BSI StandardsLimited 2012ISBN 978 0 580 70254 9ICS 77.060Compliance with a British Standard cannot confer immunity fromlegal obligations.This Briti
4、sh Standard was published under the authority of theStandards Policy and Strategy Committee on 31 July 2012.Amendments issued since publicationDate Text affectedBS ISO 14802:2012 ISO 2012Corrosion of metals and alloys Guidelines for applying statistics to analysis of corrosion dataCorrosion des mtau
5、x et alliages Lignes directrices pour lapplication des statistiques lanalyse des donnes de corrosionINTERNATIONAL STANDARDISO14802First edition2012-07-15Reference numberISO 14802:2012(E)BS ISO 14802:2012ISO 14802:2012(E)ii ISO 2012 All rights reservedCOPYRIGHT PROTECTED DOCUMENT ISO 2012All rights r
6、eserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or ISOs member body in the country of the req
7、uester.ISO copyright officeCase postale 56 CH-1211 Geneva 20Tel. + 41 22 749 01 11Fax + 41 22 749 09 47E-mail copyrightiso.orgWeb www.iso.orgPublished in SwitzerlandBS ISO 14802:2012ISO 14802:2012(E) ISO 2012 All rights reserved iiiContents PageForeword iv1 Scope 12 Significance and use 13 Scatter o
8、f data 13.1 Distributions . 13.2 Histograms 13.3 Normal distribution . 23.4 Normal probability paper . 23.5 Other probability paper 23.6 Unknown distribution . 33.7 Extreme value analysis 33.8 Significant digits 33.9 Propagation of variance 33.10 Mistakes . 34 Central measures 34.1 Average 34.2 Medi
9、an 44.3 Which to use . 45 Variability measures . 45.1 General . 45.2 Variance . 45.3 Standard deviation 55.4 Coefficient of variation . 55.5 Range 55.6 Precision 65.7 Bias . 66 Statistical tests . 66.1 Null hypothesis 66.2 Degrees of freedom 76.3 t-Test 76.4 F-test . 86.5 Correlation coefficient . 8
10、6.6 Sign test . 96.7 Outside count . 97 Curve fitting Method of least squares 97.1 Minimizing variance 97.2 Linear regression 2 variables . 97.3 Polynomial regression .107.4 Multiple regression .108 Analysis of variance . 118.1 Comparison of effects 118.2 The two-level factorial design 119 Extreme v
11、alue statistics 119.1 Scope of this clause . 119.2 Gumbel distribution and its probability paper 129.3 Estimation of distribution parameters .139.4 Report .159.5 Other topics 15Annex A (informative) Sample calculations .46Bibliography .60BS ISO 14802:2012ISO 14802:2012(E)ForewordISO (the Internation
12、al Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee has been e
13、stablished has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standard
14、ization.International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.The main task of technical committees is to prepare International Standards. Draft International Standards adopted by the technical committees are circulated to the member bodies for voti
15、ng. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote.Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such
16、patent rights.ISO 14802 was prepared by Technical Committee ISO/TC 156, Corrosion of metals and alloys.iv ISO 2012 All rights reservedBS ISO 14802:2012INTERNATIONAL STANDARD ISO 14802:2012(E)Corrosion of metals and alloys Guidelines for applying statistics to analysis of corrosion data1 ScopeThis In
17、ternational Standard gives guidance on some generally accepted methods of statistical analysis which are useful in the interpretation of corrosion test results. This International Standard does not cover detailed calculations and methods, but rather considers a range of approaches which have applica
18、tions in corrosion testing. Only those statistical methods that have wide acceptance in corrosion testing have been considered in this International Standard.2 Significance and useCorrosion test results often show more scatter than many other types of tests because of a variety of factors, including
19、 the fact that minor impurities often play a decisive role in controlling corrosion rates. Statistical analysis can be very helpful in allowing investigators to interpret such results, especially in determining when test results differ from one another significantly. This can be a difficult task whe
20、n a variety of materials are under test, but statistical methods provide a rational approach to this problem.Modern data reduction programs in combination with computers have allowed sophisticated statistical analyses to be made on data sets with relative ease. This capability permits investigators
21、to determine whether associations exist between different variables and, if so, to develop quantitative expressions relating the variables.Statistical evaluation is a necessary step in the analysis of results from any procedure which provides quantitative information. This analysis allows confidence
22、 intervals to be estimated from the measured results.3 Scatter of data3.1 DistributionsWhen measuring values associated with the corrosion of metals, a variety of factors act to produce measured values that deviate from expected values for the conditions that are present. Usually the factors which c
23、ontribute to the scatter of measured values act in a more or less random way so that the average of several values approximates the expected value better than a single measurement. The pattern in which data are scattered is called its distribution, and a variety of distributions such as the normal,
24、lognormal, bi-nominal, Poisson distribution, and extreme-value distribution (including the Gumbel and Weibull distribution) are observed in corrosion work.3.2 HistogramsA bar graph, called a histogram, may be used to display the scatter of data. A histogram is constructed by dividing the range of da
25、ta values into equal intervals on the abscissa and then placing a bar over each interval of a height equal to the number of data points within that interval.The number of intervals, k, can be calculated using the following equation:kn=+()1332,log (1)wheren is the total number of data. ISO 2012 All r
26、ights reserved 1BS ISO 14802:2012ISO 14802:2012(E)3.3 Normal distributionMany statistical techniques are based on the normal distribution. This distribution is bell-shaped and symmetrical. Use of analysis techniques developed for the normal distribution on data distributed in another manner can lead
27、 to grossly erroneous conclusions. Thus, before attempting data analysis, the data should either be verified as being scattered like a normal distribution or a transformation should be used to obtain a data set which is approximately normally distributed. Transformed data may be analysed statistical
28、ly and the results transformed back to give the desired results, although the process of transforming the data back can create problems in terms of not having symmetrical confidence intervals.3.4 Normal probability paper3.4.1 If the histogram is not confirmatory in terms of the shape of the distribu
29、tion, the data may be examined further to see if it is normally distributed by constructing a normal probability plot as follows (see Reference 2).3.4.2 It is easiest to construct a normal probability plot if normal probability paper is available. This paper has one linear axis and one axis which is
30、 arranged to reflect the shape of the cumulative area under the normal distribution. In practice, the “probability” axis has 0,5 or 50 % at the centre, a number approaching 0 % at one end, and a number approaching 1,0 or 100 % at the other end. The scale divisions are spaced close in the centre and
31、wider at both ends. A normal probability plot may be constructed as follows with normal probability paper.NOTE Data that plot approximately on a straight line on the probability plot may be considered to be normally distributed. Deviations from a normal distribution may be recognized by the presence
32、 of deviations from a straight line, usually most noticeable at the extreme ends of the data.3.4.2.1 Rearrange the data in order of magnitude from the smallest to the largest and number them as 1,2, i, n, which are called the rank of the points.3.4.2.2 In order to plot the ith ranked data on the nor
33、mal probability paper, calculate the ”midpoint” plotting position, F(xi), defined by the following equation:Fxini()=()100 (2)3.4.2.3 The data points xi, F(xi) can be plotted on the normal probability paper.NOTE Occasionally, two or more identical values are obtained in a set of results. In this case
34、, each point may be plotted, or a composite point may be located at the average of the plotting positions for all identical values.It is recommended that probability plotting be used because it is a powerful tool for providing a better understanding of the population than traditional statements made
35、 only about the mean and standard deviation.3.5 Other probability paperIf the histogram is not symmetrical and bell-shaped, or if the probability plot shows non-linearity, a transformation may be used to obtain a new, transformed data set that may be normally distributed. Although it is sometimes po
36、ssible to guess the type of distribution by looking at the histogram, and thus determine the exact transformation to be used, it is usually just as easy to use a computer to calculate a number of different transformations and to check each for the normality of the transformed data. Some transformati
37、ons based on known non-normal distributions, or that have been found to work in some situations, are listed as follows:y = log x y = exp xy = x0,5y = x2y = 1/x y = sin1(x/n)0,52 ISO 2012 All rights reservedBS ISO 14802:2012ISO 14802:2012(E)wherey is the transformed datum;x is the original datum;n is
38、 the number of data points.Time to failure in stress corrosion cracking is often fitted with a log x transformation (see References 34).Once a set of transformed data is found that yields an approximately straight line on a probability plot, the statistical procedures of interest can be carried out
39、on the transformed data. It is essential that results, such as predicted data values or confidence intervals, be transformed back using the reverse transformation.3.6 Unknown distribution3.6.1 GeneralIf there are insufficient data points or if, for any other reason, the distribution type of the data
40、 cannot be determined, then two possibilities exist for analysis.3.6.1.1 A distribution type may be hypothesized, based on the behaviour of similar types of data. If this distribution is not normal, a transformation may be sought which will normalize that particular distribution. See 3.5 for suggest
41、ions. Analysis may then be conducted on the transformed data.3.6.1.2 Statistical analysis procedures that do not require any specific data distribution type, known as non-parametric methods, may be used to analyse the data. Non-parametric tests do not use the data as efficiently.3.7 Extreme value an
42、alysisIf determining the probability of perforation by a pitting or cracking mechanism, the usual descriptive statistics for the normal distribution are not the most useful. Extreme value statistics should be used instead (see Reference 5).3.8 Significant digitsThe proper number of significant digit
43、s should be used when reporting numerical results.3.9 Propagation of varianceIf a calculated value is a function of several independent variables and those variables have errors associated with them, the error of the calculated value can be estimated by a propagation of variance technique. See Refer
44、ences 67 for details.3.10 MistakesMistakes when carrying out an experiment or in the calculations are not a characteristic of the population and can preclude statistical treatment of data or lead to erroneous conclusions if included in the analysis. Sometimes mistakes can be identified by statistica
45、l methods by recognizing that the probability of obtaining a particular result is very low. In this way, outlying observations can be identified and dealt with.4 Central measures4.1 AverageIt is accepted practice to employ several independent (replicate) measurements of any experimental quantity to
46、improve the estimate of precision and to reduce the variance of the average value. If it is assumed that the ISO 2012 All rights reserved 3BS ISO 14802:2012ISO 14802:2012(E)processes operating to create error in the measurement are random in nature and are as likely to overestimate the true unknown
47、value as to underestimate it, then the average value is the best estimate of the unknown value in question. The average value is usually indicated by placing a bar over the symbol representing the measured variable and calculated byxxni=(3)NOTE In this International Standard, the term “mean” is rese
48、rved to describe a central measure of a population, while “average” refers to a sample.4.2 MedianIf processes operate to exaggerate the magnitude of the error, either in overestimating or underestimating the correct measurement, then the median value is usually a better estimate. The median value, x
49、m, is defined as the value in the middle of all data and can be determined from the m-th ranked data.xxnxmnn=+/()/212for an even number, , of data pointsfor an odd number, , of data pointsn(4)4.3 Which to useIf the processes operating to create error affect both the probability and magnitude of the error, then other approaches are required to find the best estimation procedure. A qualified statistician should be consulted in this case.In corrosion testing, it is generally observed that average values are useful in char
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