raising standards worldwide™NO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAWBSI Standards PublicationBS ISO 14802:2012Corrosion of metals andalloys — Guidelines forapplying statistics to analysisof corrosion dataLicensed copy: University of Auckland Library, University of Auckland Library, Version correct as of 15/08/2012 03:52, (c) The British Standards Institution 2012BS ISO 14802:2012 BRITISH STANDARDNational forewordThis British Standard 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 include 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 British Standard was published under the authority of theStandards Policy and Strategy Committee on 31 July 2012.Amendments issued since publicationDate Text affectedLicensed copy: University of Auckland Library, University of Auckland Library, Version correct as of 15/08/2012 03:52, (c) The British Standards Institution 2012BS ISO 14802:2012© ISO 2012Corrosion of metals and alloys — Guidelines for applying statistics to analysis of corrosion dataCorrosion des métaux et alliages — Lignes directrices pour l’application des statistiques à l’analyse des données de corrosionINTERNATIONAL STANDARDISO14802First edition2012-07-15Reference numberISO 14802:2012(E)Licensed copy: University of Auckland Library, University of Auckland Library, Version correct as of 15/08/2012 03:52, (c) The British Standards Institution 2012BS ISO 14802:2012ISO 14802:2012(E)ii © ISO 2012 – All rights reservedCOPYRIGHT PROTECTED DOCUMENT© ISO 2012All rights reserved. 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 ISO’s member body in the country of the requester.ISO copyright officeCase postale 56 • CH-1211 Geneva 20Tel. + 41 22 749 01 11Fax + 41 22 749 09 47E-mail

[email protected] www.iso.orgPublished in SwitzerlandLicensed copy: University of Auckland Library, University of Auckland Library, Version correct as of 15/08/2012 03:52, (c) The British Standards Institution 2012BS ISO 14802:2012ISO 14802:2012(E)© ISO 2012 – All rights reserved iiiContents PageForeword iv1 Scope 12 Significance and use 13 Scatter of 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 Median 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 . 86.6 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 value 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 .60Licensed copy: University of Auckland Library, University of Auckland Library, Version correct as of 15/08/2012 03:52, (c) The British Standards Institution 2012BS ISO 14802:2012ISO 14802:2012(E)ForewordISO (the International 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 established 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 standardization.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 voting. 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 patent rights.ISO 14802 was prepared by Technical Committee ISO/TC 156, Corrosion of metals and alloys.iv © ISO 2012 – All rights reservedLicensed copy: University of Auckland Library, University of Auckland Library, Version correct as of 15/08/2012 03:52, (c) The British Standards Institution 2012BS ISO 14802:2012INTERNATIONAL STANDARD ISO 14802:2012(E)Corrosion of metals and alloys — Guidelines for applying statistics to analysis of corrosion data1 ScopeThis International 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 applications 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 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 when 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 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 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 contribute 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, log–normal, 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 data 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 rights reserved 1Licensed copy: University of Auckland Library, University of Auckland Library, Version correct as of 15/08/2012 03:52, (c) The British Standards Institution 2012BS 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 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 statistically 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 distribution, 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 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 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 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 normal probability paper, calculate the ”midpoint” plotting position, F(xi), defined by the following equation:Fxini()=−()100 ½(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, 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 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 possible 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 transformations 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 = sin−1(x/n)0,52 © ISO 2012 – All rights reservedLicensed copy: University of Auckland Library, University of Auckland Library, Version correct as of 15/08/2012 03:52, (c) The British Standards Institution 2012BS ISO 14802:2012ISO 14802:2012(E)wherey is the transformed datum;x is the original datum;n is the number of data points.Time to failure in stress corrosion cracking is often fitted with a log x transformation (see References [3][4]).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 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 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 suggestions. 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 analysisIf 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 digits 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 References [6][7] 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 statistical 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 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 3Lic