© ISO 2014Control charts —Part 5: Specialized control chartsCartes de contrôle —Partie 5: Cartes de contrôle particulièresINTERNATIONAL STANDARDISO7870-5First edition2014-01-15Reference numberISO 7870-5:2014(E)ISO 7870-5:2014(E)ii © ISO 2014 – All rights reservedCOPYRIGHT PROTECTED DOCUMENT© ISO 2014All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior written permission. Permission can be requested 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 SwitzerlandISO 7870-5:2014(E)© ISO 2014 – All rights reserved iiiContents PageForeword ivIntroduction v1 Scope . 12 Normative references 13 Terms and definitions . 14 Symbols and abbreviated terms . 44.1 Symbols . 44.2 Abbreviated terms . 55 Specialized control charts . 56 Moving average and moving range control charts . 56.1 Control limits 66.2 Interpretation 66.3 Advantages . 66.4 Limitations 66.5 Example . 67 z- chart. 97.1 Control limits 97.2 Advantages 107.3 Limitations . 107.4 Example 108 Group control chart 108.1 Control limits . 128.2 Advantages 128.3 Limitations . 138.4 Example 139 High-low control chart .169.1 Control limits . 169.2 Interpretation . 179.3 Advantages 179.4 Limitations . 179.5 Example 1710 Trend control chart .1910.1 Control limits . 2010.2 Advantages 2010.3 Limitations . 2110.4 Example 2111 Control chart for coefficient of variation .2411.1 Control limits . 2411.2 Advantage . 2411.3 Limitation . 2411.4 Example 2512 Control chart for non-normal data .2612.1 Control limits . 2712.2 Example 2813 Standardized p- chart .3213.1 Control limits . 3413.2 Advantages and limitations . 3413.3 Example 34ISO 7870-5:2014(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.The procedures used to develop this document and those intended for its further maintenance are described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the different types of ISO documents should be noted. This document was drafted in accordance with the editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).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. Details of any patent rights identified during the development of the document will be in the Introduction and/or on the ISO list of patent declarations received (see www.iso.org/patents).Any trade name used in this document is information given for the convenience of users and does not constitute an endorsement.For an explanation on the meaning of ISO specific terms and expressions related to conformity assessment, as well as information about ISO’s adherence to the WTO principles in the Technical Barriers to Trade (TBT) see the following URL: Foreword - Supplementary informationThe committee responsible for this document is ISO/TC 69, Applications of statistical methods, Subcommittee SC 4, Applications of statistical methods in process management.ISO 7870 consists of the following parts, under the general title Control charts:— Part 1: General guidelines— Part 2: Shewhart control charts— Part 3: Acceptance control charts— Part 4: Cumulative sum control charts— Part 5: Specialized control charts— Part 6: EWMA control chartsiv © ISO 2014 – All rights reservedISO 7870-5:2014(E)IntroductionThe Shewhart control charts as given in ISO 7870-2 aid in detection of unnatural patterns of variations in data from repetitive processes and provide criteria for detecting a lack of statistical control.However, there may be several special situations for variables data where Shewhart control charts may be inadequate, insufficient or less efficient in detecting the unnatural patterns of variation of the process, particularly where:a) it takes considerable time to produce an item and as such sample results are available at large intervals;b) there are several subgroup sources that have approximately the same production rate, process average and process capability;c) process average is changing systematically;d) sample size is large and sequence of production is irrelevant;e) process does not have a constant target value.In such situations, specialized control charts are to be used.Similarly, special situations may be encountered in dealing with attributes data. There may be situations when criticality of an incidence in a subgroup (nonconformity) is a matter of concern, but different nonconformities are having different criticality. As such, all types of nonconformities cannot be treated alike. Depending upon criticality, different ratings (weights) are required to be given to each class of nonconformity, and accordingly demerit scores are calculated. The control limits are calculated based on such demerit scores and accordingly control charts are plotted to exercise process control.There may be situations when inspection by attributes is preferred to that by variables, from practical considerations, for controlling both the location and the variability parameters of a measureable characteristic of a process (for example, inspection by gauging). The information is also available on the number of items less than the lower specification limits (no-go gauge) as well as the number of items above upper specification limit (go gauge) in assembly operations. In such situation, a specialized pair of control charts may be used.There may also be situations when data do not follow normal distribution. Such situations of non-normal data are quite often encountered in service industry, besides in special processes of manufacturing. In such a situation specialized control chart is to be used.This part of ISO 7870 has been prepared to provide guidance on the use of specialized control charts to address above typical, unusual situations.© ISO 2014 – All rights reserved vControl charts —Part 5: Specialized control charts1 ScopeThis part of ISO 7870 establishes a guide to the use and understanding of specialized control charts in situations where commonly used Shewhart control chart approach to the methods of statistical control of a process may either be not applicable or less efficient in detecting unnatural patterns of variation of the process.The specialized control charts included in this part of ISO 7870 for variables data are:a) moving average and moving range charts;b) z-charts;c) group control charts;d) high–low control charts;e) trend control charts;f) control charts for coefficient of variation;g) control charts for non-normal data.For attributes data, specialized control charts included in this part of ISO 7870 are:a) standardized p-charts;b) demerit control charts;c) control charts for inspection by gauging.This part of ISO 7870 also provides guidance as to when each of the above control charts should be used, their control limits, advantages and limitations. Each control chart is illustrated with an example.2 Normative referencesThe following referenced documents, in whole or in part, are normatively referenced in this document and are indispensable for its application. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.ISO 3534-2, Statistics — Vocabulary and symbols — Part 2: Applied statistics3 Terms and definitionsFor the purposes of this document, the terms and definitions given in ISO 3534-2 and the following apply.INTERNATIONAL STANDARD ISO 7870-5:2014(E)© ISO 2014 – All rights reserved 1ISO 7870-5:2014(E)3.1control chartchart on which some statistical measure of a series of samples is plotted in a particular order to steer the process with respect to that measure and to control and reduce variationNote 1 to entry: The particular order is usually based on time or sample number order.Note 2 to entry: The control chart operates most effectively when the measure is a process variable which is correlated with an ultimate product or service characteristic.[SOURCE: ISO 3534-2:2006, 2.3.1]3.2Shewhart control chartcontrol chart with Shewhart control limits intended primarily to distinguish between the variation in the plotted measure due to random causes and that due to special causes[SOURCE: ISO 3534-2:2006, 2.3.2]3.3variables control chartShewhart control chart in which the measure plotted represents data on a continuous scale[SOURCE: ISO 3534-2:2006, 2.3.6]3.4attributes control chartShewhart control chart in which the measure plotted represents countable or categorized data[SOURCE: ISO 3534-2:2006, 2.3.7]3.5Xbar control chartaverage control chartvariables control chart for evaluating the process level in terms of subgroup averages[SOURCE: ISO 3534-2:2006, 2.3.12]3.6R chartrange control chartvariables control chart for evaluating variation in terms of subgroup rangesNote 1 to entry: The value of the subgroup range, given by the symbol R, is the difference between the largest and smallest observation of a subgroup.Note 2 to entry: The average of the range values for all subgroups is denoted by the symbol R.[SOURCE: ISO 3534-2:2006, 2.3.18]3.7moving average control chartcontrol chart for evaluating the process level in terms of the arithmetic average of each successive n observationsNote 1 to entry: This chart is particularly useful when only one observation per subgroup is available. Examples are process characteristics such as temperature, pressure and time.Note 2 to entry: The current observation replaces the oldest of the latest n + 1 observations.Note 3 to entry: It has the disadvantage of an unweighted carry-over effect lasting n points.[SOURCE: ISO 3534-2:2006, 2.3.14]2 © ISO 2014 – All rights reservedISO 7870-5:2014(E)3.8moving range control chartvariables control chart for evaluating variation in terms of the range of each successive n observationsNote 1 to entry: The current observation replaces the oldest of the latest n +1 observations.[SOURCE: ISO 3534-2:2006, 2.3.20]3.9z-chartvariables control chart for evaluating the process in terms of subgroup standardized normal variates3.10group control chart for averagesvariables control chart for evaluating the process level in terms of subgroup (with several sources) highest and lowest averages with corresponding source identification3.11group control chart for rangesvariables control chart for evaluating the process variation in terms of subgroup (with several sources) highest ranges with corresponding source identification3.12high – low control chartvariables control chart for evaluating the process level in terms of subgroup largest and smallest values3.13trend control chartcontrol chart for evaluating the process level with respect to the deviation of the subgroup averages from an expected change in the process levelNote 1 to entry: The trend may be determined empirically or by regression techniques.Note 2 to entry: A trend is an upward or downward tendency, after exclusion of the random variation and cyclical effects, when observed values are plotted in the time order of the observations.[SOURCE: ISO 3534-2:2006, 2.3.17]3.14control chart for coefficient of variationvariables control chart for evaluating variation in terms of subgroup coefficient of variation3.15p chartproportion or percent categorized units control chartattributes control chart for number of units of a given classification per total number of units in the sample expressed either as a proportion or percentNote 1 to entry: In the quality field, the classification usually takes the form of “nonconforming unit”.Note 2 to entry: The “p” chart is applied particularly when the sample size is variable.Note 3 to entry: The plotted measure can be expressed as a proportion or as a percentage.[SOURCE: ISO 3534-2:2006, 2.3.11]3.16standardized p-chartattributes control chart where proportions of given classification are expressed as standardized normal variatesNote 1 to entry: In this chart, the centre line is zero, upper control limit is +3 and lower control limit is −3.© ISO 2014 – All rights reserved 3ISO 7870-5:2014(E)3.17demerit control chartquality score chartmultiple characteristic control chart for evaluating the process level where different weights are apportioned to events depending on their perceived significance[SOURCE: ISO 3534-2:2006, 2.3.23]3.18control chart for inspection by gaugingattributes control chart when the inspection is done by gauging and the information is available on the number of units above upper gauge limit and below lower gauge limit4 Symbols and abbreviated terms4.1 Symbolsn subgroup sample sizek number of subgroupsxindividual measured valuexiaverage value of i-th subgroupxaverage of the subgroup average valuesµtrue process mean valueσtrue process standard deviation valueR rangeRaverage rangessample standard deviations average of subgroup sample standard deviationspproportion or fraction of unitsp average value of the proportion or fraction of unitsCLcentre lineUCLupper control limitLCLlower control limitXaverage value of the variable X plotted on a control chartxHlargest observation in a subgroupxLsmallest observation in a subgroup4 © ISO 2014 – All rights reservedISO 7870-5:2014(E)xHaverage of largest observations for all subgroupsxLaverage of smallest observations for all subgroupszvariable that has a normal distribution with zero mean and unit standard deviationvcoefficient of variationv average of coefficient of variation values4.2 Abbreviated termsBPO business process outsourcingCV coefficient of variationLGLlower gauge limitUGLupper gauge limit5 Specialized control chartsThe following specialized control charts for variables have been included:a) moving average and moving range control charts;b) z-charts;c) group control charts;d) high–low control charts;e) trend control charts;f) control charts for coefficient of variation;g) control charts for non-normal data.The following specialized control charts for attributes have been included:a) standardized p-chart;b) demerit control chart;c) control chart for inspection by gauging.6 M