# ISO 7870-1-2014

© ISO 2014Control charts —Part 1: General guidelinesCartes de contrôle —Partie 1: Lignes directrices généralesINTERNATIONAL STANDARDISO7870-1Second edition2014-02-01Reference numberISO 7870-1:2014(E)ISO 7870-1:2014(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 copyright@iso.orgWeb www.iso.orgPublished in SwitzerlandISO 7870-1:2014(E)© ISO 2014 – All rights reserved iiiContents PageForeword ivIntroduction v1 Scope . 12 Normative references 13 Terms and definitions . 14 Symbols 75 Concepts 75.1 Control chart . 75.2 Statistical control of a process . 85.3 Acceptance of a process 85.4 Management of a process with a natural drift . 85.5 Risks of decision errors . 85.6 Design of data collection . 95.7 Control charts for variables and attributes data .116 Types of control charts117 Charts for process stability .127.1 General 127.2 Partial listing of Shewhart and related control charts .128 Charts for process acceptance .148.1 General 148.2 Acceptance control charts (see ISO 7870-3) 158.3 Modified control charts (control charts with modified limits; see ISO 7870-3) .159 Process adjustment 15Bibliography .16ISO 7870-1:2014(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.This second edition of ISO 7870-1 cancels and replaces the first edition (ISO 7870-1:2007), which has been technically revised.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 charts— Part 5: Specialized control charts— Part 6: EWMA control chartsiv © ISO 2014 – All rights reservedISO 7870-1:2014(E)IntroductionEvery production, service, or administrative process contains a certain amount of variability due to the presence of a large number of causes. The observed results from a process are, as a result, not constant. Studying this variability to gain an understanding of its characteristics provides a basis for taking action on a process.Control charts are a fundamental tool of statistical process control (SPC). They provide a simple graphical method that can be used toa) indicate if the process is stable, i.e. operating within a stable system of random causes, also known as inherent variability and referred to as being in a “state of statistical control”,b) estimate the magnitude of the inherent variability of the process,c) compare information from samples representing the current state of a process against control limits reflecting this variability, with the objective of determining whether the process variability has remained stable or is reduced or increased,d) identify, investigate, and possibly reduce/eliminate the effect of special causes of variability, which can drive the process to an unacceptable level of performance,e) aid in the regulation of a process through the identification of patterns of variability such as trends, runs, cycles, etc.,f) determine if the process is behaving in a predictable and stable manner so that it will be possible to assess if the process is able to meet specifications,g) determine whether or not the process can be expected to satisfy product or service requirements and process capability for the characteristic(s) being measured,h) provide a basis for process adjustment through prediction using statistical models, andi) assist in the assessment of the performance of a measurement system.A major virtue of the control chart is its ease of construction and use. It provides the production or service operator, engineer, administrator, and manager with an online indicator about the behaviour of the process. However, in order for the control chart to be a reliable and efficient indicator of the state of the process, careful attention has to be paid at the planning stage to such matters as selecting the appropriate type of chart for the process under study and determining a proper sampling scheme.General concepts useful to a successful design of a control chart are presented in this part of ISO 7870.© ISO 2014 – All rights reserved vControl charts —Part 1: General guidelines1 ScopeThis part of ISO 7870 presents key elements and philosophy of the control chart approach, and identifies a wide variety of control charts (including those related to the Shewhart control chart, those stressing process acceptance or online process adjustment, and specialized control charts).It presents an overview of the basic principles and concepts and illustrates the relationship among various control chart approaches to aid in the selection of the most appropriate standard for given circumstances. It does not specify statistical control methods using control charts. These methods will be specified in future parts of ISO 7870.2 Normative referencesThe following 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.3.1control chartchart with control limits (3.2) on which some statistical measure of a series of samples is plotted in a particular order to steer the process with respect to that measureNote 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]3.2control limitstatistical value defining an intended level of stability for a produced characteristicNote 1 to entry: One or two control limits are represented on the control chart.Note 2 to entry: The term “stability” is not meant only for a process in control but it can also be stability against a target value.INTERNATIONAL STANDARD ISO 7870-1:2014(E)© ISO 2014 – All rights reserved 1ISO 7870-1:2014(E)3.3Shewhart control chartcontrol chart (3.1) with Shewhart control limits (3.4) 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]3.4Shewhart control limitcontrol limit (3.2) determined statistically from the variation of the process due to the random causes alone3.5acceptance control chartcontrol chart (3.1) intended primarily to evaluate whether or not the plotted measure can be expected to satisfy specified tolerances[SOURCE: ISO 3534-2:2006, 2.3.3]3.6process adjustment control chartcontrol chart (3.1) which uses a prediction model of the process to estimate and plot the future course of the process if no change is made, and to quantify the change to be made to keep the process deviations within acceptable limits[SOURCE: ISO 3534-2:2006, 2.3.4]3.7variables control chartcontrol chart (3.1) in which the plotted measure represents data on a continuous scale[SOURCE: ISO 3534-2:2006, 2.3.6]3.8attributes control chartcontrol chart (3.1) in which the plotted measure represents countable or categorized data[SOURCE: ISO 3534-2:2006, 2.3.7]3.9c chartcount control chartattributes control chart (3.8) for the number of incidences where the opportunity for occurrence is fixedNote 1 to entry: Incidences of a particular type, for example, number of absentees and number of sales leads, form the count. In the quality field, incidences are often expressed as nonconformities and the fixed opportunity relates to samples of constant size or fixed amount of material. Examples are “flaws in each 100 m2of fabric” and “errors in each 100 invoices”.[SOURCE: ISO 3534-2:2006, 2.3.8]3.10u chartcount per unit control chartattributes control chart (3.8) for the number of incidences per unit where the opportunity is variableNote 1 to entry: Incidences of a particular type, for example, number of absentees and number of sales leads, form the count. In the quality field, incidences are often expressed as nonconformities and the variable opportunity relates to subgroups of variable size or variable amounts of material.[SOURCE: ISO 3534-2:2006, 2.3.9]2 © ISO 2014 – All rights reservedISO 7870-1:2014(E)3.11np chartnumber of categorized units control chartattributes control chart (3.8) for number of units of a given classification where the subgroup size is constantNote 1 to entry: In the quality field, the classification usually takes the form of “nonconforming units”.[SOURCE: ISO 3534-2:2006, 2.3.10]3.12p chartproportion categorized units control chartpercent categorized units control chartattributes control chart (3.8) 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 subgroup 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]3.13standardized p chartattributes control chart (3.8)where proportion of given classification are expressed as standardized normal variates3.14X bar control chartaverage control chartvariables control chart (3.7) for evaluating the process level in terms of subgroup averages[SOURCE: ISO 3534-2:2006, 2.3.12]3.15median control chartvariables control chart (3.7) for evaluating the process level in terms of subgroup medians[SOURCE: ISO 3534-2:2006, 2.3.13]3.16moving average control chartcontrol chart (3.1) 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]© ISO 2014 – All rights reserved 3ISO 7870-1:2014(E)3.17individuals control chartX control chartvariables control chart (3.7) for evaluating the process level in terms of the individual observations in the sampleNote 1 to entry: This chart is usually accompanied by a moving range chart, frequently with n = 2.Note 2 to entry: It sacrifices the advantages of averaging in terms of minimizing random variation and the normal distribution central limit theorem assumptions.Note 3 to entry: Individual values are expressed by the symbols x1, x2, x3,…Note 4 to entry: In the case of charts for individuals, the symbol R represents the value of the moving range, which is the absolute value of the difference between two successive values, thus, xxxx1223−−, , etc.[SOURCE: ISO 3534-2:2006, 2.3.15, modified]3.18cumulative sum control chartCUSUM chartcontrol chart (3.1) where the cumulative sum of deviations of successive sample values from a reference value is plotted to detect shifts in the level of the measure plottedNote 1 to entry: The ordinate of each plotted point represents the algebraic sum of the previous ordinate and the most recent deviation from the reference, target, or control value.Note 2 to entry: The best discrimination of changes in level is achieved when reference value is equal to the overall average value.Note 3 to entry: The chart can be used in control, diagnostic, or predictive mode.Note 4 to entry: When used in control mode, it can be interpreted graphically by a mask (e.g. V-mask) superimposed on the graph. A signal occurs if the path of the CUSUM intersects or touches the boundary of the mask.[SOURCE: ISO 3534-2:2006, 2.3.5]3.19EWMA control chartexponentially weighted moving average control chartcontrol chart (3.1) for evaluating the process level in terms of an exponentially smoothed moving average[SOURCE: ISO 3534-2:2006, 2.3.16]3.20Z chartvariables control chart (3.7) for evaluating the process in terms of subgroup standardized normal variates3.21group control chart for averagesvariables control chart (3.7) for evaluating the process level in terms of subgroup (with several sources) highest and lowest averages with corresponding source identification3.22group control chart for rangesvariables control chart (3.7) for evaluating the process variation in terms

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