1、raising standards worldwideNO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAWBSI Standards PublicationBS ISO 7870-2:2013Control chartsPart 2: Shewhart control chartsBS ISO 7870-2:2013 BRITISH STANDARDNational forewordThis British Standard is the UK implementation of ISO 7870-2:20
2、13. It supersedes BS 7785:1994, which is withdrawn.The UK participation in its preparation was entrusted to T e c h n i c a l C o m m i t t e e S S / 4 , S t a t i s t i c a l P r o c e s s M a n a g e m e n t .A list of organizations represented on this committee can be obtained on request to its s
3、ecretary.This publication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application. The British Standards Institution 2013. Published by BSI Standards Limited 2013.ISBN 978 0 580 68960 4 ICS 03.120.30 Compliance with a British Standard
4、 cannot confer immunityfrom legal obligations.This British Standard was published under the authority of the Standards Policy and Strategy Committee on 30 April 2013.Amendments issued since publicationDate T e x t a f f e c t e dBS ISO 7870-2:2013 ISO 2013Control charts Part 2: Shewhart control char
5、tsCartes de contrle Partie 2: Cartes de contrle de ShewhartINTERNATIONAL STANDARDISO7870-2First edition2013-04-01Reference numberISO 7870-2:2013(E)BS ISO 7870-2:2013ISO 7870-2:2013(E)ii ISO 2013 All rights reservedCOPYRIGHT PROTECTED DOCUMENT ISO 2013All rights reserved. Unless otherwise specified,
6、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 ISOs mem
7、ber 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 copyrightiso.orgWeb www.iso.orgPublished in SwitzerlandBS ISO 7870-2:2013ISO 7870-2:2013(E) ISO 2013 All rights reserved iiiContents PageForeword ivIntroduc
8、tion v1 Scope . 12 Normative references 13 Terms, definitions and symbols 13.1 General . 13.2 Symbols . 14 Nature of Shewhart control charts . 35 Types of control charts. 55.1 Control charts where no pre-specified values are given . 55.2 Control charts with respect to given pre-specified values 65.3
9、 Types of variables and attributes control charts . 66 Variables control charts 76.1 Mean ( X ) chart and range (R) chart or mean ( X ) chart and standard deviation (s) chart 86.2 Control chart for individuals (X) and control chart for moving ranges (Rm) 96.3 Control charts for medians (X ) 107 Cont
10、rol procedure and interpretation for variables control charts 117.1 Collect preliminary data 117.2 Examine the s (or R) chart 117.3 Remove assignable causes and revise the chart 117.4 Examine the X chart . 127.5 Ongoing monitoring of process . 128 Pattern tests for assignable causes of variation .12
11、9 Process control, process capability, and process improvement.1310 Attributes control charts .1511 Preliminary considerations before starting a control chart 1711.1 Choice of critical to quality (CTQ) characteristics describing the process to control .1711.2 Analysis of the process 1711.3 Choice of
12、 rational subgroups . 1711.4 Frequency and size of subgroups . 1811.5 Preliminary data collection . 1811.6 Out of control action plan . 1812 Steps in the construction of control charts 1812.1 Determine data collection strategy 1912.2 Data collection and computation . 2012.3 Plotting X chart and R ch
13、art . 2013 Caution with Shewhart control charts 2013.1 General caution 2113.2 Correlated data 2213.3 Use of alternative rule to the three-sigma rule 22Annex A (informative) Illustrative examples 24Annex B (informative) Practical notices on the pattern tests for assignable causes of variation .42Bibl
14、iography .44BS ISO 7870-2:2013ISO 7870-2:2013(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 me
15、mber 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 E
16、lectrotechnical 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 adop
17、ted 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 paten
18、t rights. ISO shall not be held responsible for identifying any or all such patent rights.ISO 7870-2 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods, Subcommittee SC 4, Applications of statistical methods in process management.This first edition cancels and replace
19、s ISO 8258:1991, 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 chartsEWMA cont
20、rol charts will from the subject of a future Part 6.iv ISO 2013 All rights reservedBS ISO 7870-2:2013ISO 7870-2:2013(E)IntroductionA traditional approach to manufacturing has been to depend on production to make the product and on quality control to inspect the final product and screen out items not
21、 meeting specifications. This strategy of detection is often wasteful and uneconomical because it involves after-the-event inspection when the wasteful production has already occurred. Instead, it is much more effective to institute a strategy of prevention to avoid waste by not producing unusable o
22、utput in the first place. This can be accomplished by gathering process information and analysing it so that timely action can be taken on the process itself.Dr. Walter Shewhart in 1924 proposed the control chart as a graphical means of applying the statistical principles of significance to the cont
23、rol of a process. Control chart theory recognizes two kinds of variability. The first kind is random variability due to “chance causes” (also known as “common/natural/ random/inherent/uncontrollable causes”). This is due to the wide variety of causes that are consistently present and not readily ide
24、ntifiable, each of which constitutes a very small component of the total variability but none of which contributes any significant amount. Nevertheless, the sum of the contributions of all of these unidentifiable random causes is measurable and is assumed to be inherent to the process. The eliminati
25、on or correction of common causes may well require a decision to allocate resources to fundamentally change the process and system.The second kind of variability represents a real change in the process. Such a change can be attributed to some identifiable causes that are not an inherent part of the
26、process and which can, at least theoretically, be eliminated. These identifiable causes are referred to as “assignable causes” (also known as special/unnatural/systematic/controllable causes) of variation. They may be attributable to such matters as the lack of uniformity in material, a broken tool,
27、 workmanship or procedures, the irregular performance of equipment, or environmental changes.A process is said to be in statistical control, or simply “in control”, when the process variability results only from random causes. Once this level of variation is determined, any deviation from this level
28、 is assumed to be the result of assignable causes that should be identified and eliminated.Statistical process control is a methodology for establishing and maintaining a process at an acceptable and stable level so as to ensure conformity of products and services to specified requirements. The majo
29、r statistical tool used to do this is the control chart, which is a graphical method of presenting and comparing information based on a sequence of observations representing the current state of a process against limits established after consideration of inherent process variability called process c
30、apability. The control chart method helps first to evaluate whether or not a process has attained, or continues in, a state of statistical control. When in such a state the process is deemed to be stable and predictable and further analysis as to the ability of the process to satisfy the requirement
31、s of the customer can then be conducted. The control chart also can be used to provide a continuous record of a quality characteristic of the process output while process activity is ongoing. Control charts aid in the detection of unnatural patterns of variation in data resulting from repetitive pro
32、cesses and provide criteria for detecting a lack of statistical control. The use of a control chart and its careful analysis leads to a better understanding of the process and will often result in the identification of ways to make valuable improvements. ISO 2013 All rights reserved vBS ISO 7870-2:2
33、013BS ISO 7870-2:2013Control charts Part 2: Shewhart control charts1 ScopeThis International Standard establishes a guide to the use and understanding of the Shewhart control chart approach to the methods for statistical control of a process.This International Standard is limited to the treatment of
34、 statistical process control methods using only the Shewhart system of charts. Some supplementary material that is consistent with the Shewhart approach, such as the use of warning limits, analysis of trend patterns and process capability is briefly introduced. There are, however, several other type
35、s of control chart procedures, a general description of which can be found in ISO 7870-1.2 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
36、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 statisticsISO 16269-4, Statistical interpretation of data Part 4: Detection and treatment of outliersISO 5479, Statistical i
37、nterpretation of data Tests for departure from the normal distributionISO 22514 (all parts), Statistical methods in process management Capability and performance3 Terms, definitions and symbols3.1 GeneralFor the purposes of this document, the terms and definitions given in ISO 3534-2:2006 apply.3.2
38、SymbolsNOTE The ISO/IEC Directives makes it necessary to depart from common SPC usage in respect to the differentiation between abbreviated terms and symbols. In ISO standards an abbreviated term and its symbol can differ in appearance in two ways: by font and by layout. To distinguish between abbre
39、viated terms and symbols, abbreviated terms are given in Cambria upright and symbols in Cambria or Greek italics, as applicable. Whereas abbreviated terms can contain multiple letters, symbols consist only of a single letter. For example, the conventional abbreviation of upper control limit, UCL, is
40、 valid but its symbol in equations becomes UCL. The reason for this is to avoid misinterpretation of compound letters as an indication of multiplication.In cases of long established practice where a symbol and/or abbreviated term means different things in different applications, it is necessary to u
41、se a field limiter, thus , to distinguish between them. This avoids the alienation of practitioners by the creation of unfamiliar abbreviated terms and symbols in their particular field that are unlike all related texts, operational manuals and dedicated software programs. An example is the abbrevia
42、ted term R and symbol R which means different things in metrology from that in acceptance sampling and statistical process control. The abbreviated term R is differentiated thus:INTERNATIONAL STANDARD ISO 7870-2:2013(E) ISO 2013 All rights reserved 1BS ISO 7870-2:2013ISO 7870-2:2013(E)R metrology re
43、producibility limitR SPC and acceptance sampling rangeFor the purposes of this document, the following symbols apply.n Subgroup size; the number of sample observations per subgroupk Number of subgroupsLLower specification limitLCLLower control limitUUpper specification limitUCLUpper control limitX M
44、easured quality characteristic (individual values are expressed as (X1, X2, X3,.). Sometimes the symbol Y is used instead of XX(X bar) Subgroup averageX(X double bar) Average of the subgroup averages True process mean value True process standard deviation value0A given value of XMedian of a subgroup
45、XAverage of the subgroup mediansR Subgroup range: difference between the largest observation and smallest observation of a subgroupRAverage of the R values for all subgroupsRmMoving range: the absolute value of the difference between two successive values |X1 X2|,|X2 X3|, etc.RmAverage of the (n 1)
46、Rmvalues in a set of n observed valuess Sample standard deviation obtained from values within a subgroup:sXXni=()21s Average of the subgroup sample standard deviations Estimated process standard deviation valuep Proportion or fraction of units in a subgroup with a given classificationp Average value
47、 of the proportion or fractionnp Number of units with a given classification in a subgroup2 ISO 2013 All rights reservedBS ISO 7870-2:2013ISO 7870-2:2013(E)p0A given value of pnp0A given value of np (for a given p0)c Number of incidences in a subgroupc0A given value of ccAverage value of the c value
48、s for all subgroupsu Number of incidences per unit in a subgroupuAverage value of the u valuesu0A given value of u4 Nature of Shewhart control chartsA Shewhart control chart is a graph that is used to display a statistical measure obtained from either variables or attribute data. The control chart r
49、equires data from rational subgroups to be taken at approximately regular intervals from the process. The intervals may be defined in terms of time (for example hourly) or quantity (every lot). Usually, the data are obtained from the process in the form of samples or subgroups consisting of the same process characteristic, product or service with the same measurable units and the same subgroup size. From each subgroup, one or more subgroup characteristics are derived, such as the subgroup average, X , and the subgro
