1、BSI Standards PublicationBS ISO 7870-6:2016Control chartsPart 6: EWMA control chartsBS ISO 7870-6:2016 BRITISH STANDARDNational forewordThis British Standard is the UK implementation of ISO 7870-6:2016. The UK participation in its preparation was entrusted to TechnicalCommittee SS/4, Statistical Pro
2、cess Management.A list of organizations represented on this committee can be obtained on request to its secretary.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 2016.Publish
3、ed by BSI Standards Limited 2016ISBN 978 0 580 83362 5 ICS 03.120.30 Compliance with a British Standard cannot confer immunity from legal obligations.This British Standard was published under the authority of the Standards Policy and Strategy Committee on 29 February 2016.Amendments/corrigenda issue
4、d since publicationDate T e x t a f f e c t e dBS ISO 7870-6:2016 ISO 2016Control charts Part 6: EWMA control chartsCartes de contrle Partie 6: Cartes de contrle de EWMAINTERNATIONAL STANDARDISO7870-6First edition2016-02-15Reference numberISO 7870-6:2016(E)BS ISO 7870-6:2016ISO 7870-6:2016(E)ii ISO
5、2016 All rights reservedCOPYRIGHT PROTECTED DOCUMENT ISO 2016, Published in SwitzerlandAll 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
6、 internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below or ISOs member body in the country of the requester.ISO copyright officeCh. de Blandonnet 8 CP 401CH-1214 Vernier, Geneva, SwitzerlandTel. +41 22 749 01 11Fax +41 22 749 09 47
7、copyrightiso.orgwww.iso.orgBS ISO 7870-6:2016ISO 7870-6:2016(E)Foreword ivIntroduction v1 Scope . 12 Normative references 13 Symbols and abbreviated terms . 14 EWMA for inspection by variables . 24.1 General . 24.2 Weighted average explained 34.3 Control limits for EWMA control chart 44.4 Constructi
8、on of EWMA control chart 44.5 Example . 65 Choice of the control chart . 95.1 Shewhart control chart versus EWMA control chart . 95.2 Average run length . 105.3 Choice of parameters for EWMA control chart 105.3.1 Choice of . 105.3.2 Choice of Lz115.3.3 Calculation for n. 115.3.4 Example 126 Procedur
9、e for implementing the EWMA control chart 127 Sensitivity of the EWMA to non-normality .138 Advantages and limitations 138.1 Advantages 138.2 Limitations . 13Annex A (informative) Application of the EWMA control chart 14Annex B (normative) EWMA control chart for controlling a proportion of nonconfor
10、ming units .18Annex C (normative) EWMA control charts for a number of nonconformities .20Annex D (informative) Control chart effectiveness 22Bibliography .26 ISO 2016 All rights reserved iiiContents PageBS ISO 7870-6:2016ISO 7870-6:2016(E)ForewordISO (the International Organization for Standardizati
11、on) 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 re
12、presented 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 de
13、velop 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 I
14、SO/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
15、 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 meanin
16、g of ISO specific terms and expressions related to conformity assessment, as well as information about ISOs adherence to the WTO principles in the Technical Barriers to Trade (TBT), see the following URL: Foreword Supplementary information .The committee responsible for this document is ISO/TC 69, A
17、pplications 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: Cumu
18、lative sum charts Part 5: Specialized control charts Part 6: EWMA control chartsA future part on charting techniques for short runs and small mixed batches is planned.iv ISO 2016 All rights reservedBS ISO 7870-6:2016ISO 7870-6:2016(E)IntroductionShewhart control charts are the most widespread statis
19、tical control methods used for controlling a process, but they are slow in signalling shifts of small magnitude in the process parameters. The exponentially weighted moving average10(EWMA) control chart makes possible faster detection of small to moderate shifts.The Shewhart control chart is simple
20、to implement and it rapidly detects shifts of major magnitude. However, it is fairly ineffective for detecting shifts of small or moderate magnitude. It happens quite often that the shift of the process is slow and progressive (in case of continuous processes in particular); this shift has to be det
21、ected very early in order to react before the process deviates seriously from its target value. There are two possibilities for improving the effectiveness of the Shewhart control charts with respect to small and moderate shifts. The simplest, but not the most economical possibility is to increase t
22、he subgroup size. This may not always be possible due to low production rate; time consuming or too costly testing. As a result, it may not be possible to draw samples of size more than 1 or 2. The second possibility is to take into account the results preceding the control under way in order to try
23、 to detect the existence of a shift in the production process. The Shewhart control chart takes into account only the information contained in the last sample observation and it ignores any information given by the entire sequence of points. This feature makes the Shewhart control chart relatively i
24、nsensitive to small process shifts. Its effectiveness may be improved by taking into account the former results.Where it is desired to detect slow, progressive shifts, it is preferable to use specific charts which take into account the past data and which are effective with a moderate control cost.
25、Two very effective alternatives to the Shewhart control chart in such situations area) Cumulative Sum (CUSUM) control chart. This chart is described in ISO 7870-4. The CUSUM control chart reacts more sensitively than the X-bar chart to a shift of the mean value in the range of half or two sigma. If
26、one plots the cumulative sum of deviations of successive sample means from a specified target, even minor, permanent shifts in the process mean will eventually lead to a sizable cumulative sum of deviations. Thus, this chart is particularly well-suited for detecting such small permanent shifts that
27、may go undetected when using the X-bar chart.b) Exponentially Weighted Moving Average (EWMA) control chart which is covered by this document. This chart is presented like the Shewhart control chart; however, instead of placing on the chart the successive averages of the samples, one monitors a weigh
28、ted average of the current average and of the previous averages.EWMA control charts are generally used for detecting small shifts in the process mean. They will detect shifts of half sigma to two sigma much faster. They are, however, slower in detecting large shifts in the process mean. EWMA control
29、 charts may also be preferred when the subgroups are of size n = 1.The joint use of an EWMA control chart with a small value of lambda and a Shewhart control chart has been recommended as a means of guaranteeing fast detection of both small and large shifts. The EWMA control chart monitors only the
30、process mean; monitoring the process variability requires the use of some other technique. ISO 2016 All rights reserved vBS ISO 7870-6:2016BS ISO 7870-6:2016Control charts Part 6: EWMA control charts1 ScopeThis International Standard covers EWMA control charts as a statistical process control techni
31、que to detect small shifts in the process mean. It makes possible the faster detection of small to moderate shifts in the process average. In this chart, the process average is evaluated in terms of exponentially weighted moving average of all prior sample means. EWMA weights samples in geometricall
32、y decreasing order so that the most recent samples are weighted most highly while the most distant samples contribute very little depending upon the smoothing parameter ().NOTE 1 The basic objective is the same as that of the Shewhart control chart described in ISO 7870-2.The Shewhart control charts
33、 application is worthwhile in the rare situations when production rate is slow, sampling and inspection procedure is complex and time consuming, testing is expensive, and it involves safety risks.NOTE 2 Variables control charts can be constructed for individual observations taken from the production
34、 line, rather than samples of observations. This is sometimes necessary when testing samples of multiple observations would be too expensive, inconvenient, or impossible. For example, the number of customer complaints or product returns may only be available on a monthly basis; yet, one would like t
35、o chart those numbers to detect quality problems. Another common application of these charts occurs in cases when automated testing devices inspect every single unit that is produced. In that case, one is often primarily interested in detecting small shifts in the product quality (for example, gradu
36、al deterioration of quality due to machine wear).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
37、 of the referenced document (including any amendments) applies.ISO 7870-1, Control charts Part 1: General guidelinesISO 7870-2, Control charts Part 2: Shewhart control chartsISO 7870-4, Control charts Part 4: Cumulative sum charts3 Symbols and abbreviated terms0Target value for the average of the pr
38、ocessU, LUpper rejectable value of the average, lower rejectable value of the averagexiMean of the sample iN Number of units in a sample (sample size)INTERNATIONAL STANDARD ISO 7870-6:2016(E) ISO 2016 All rights reserved 1BS ISO 7870-6:2016ISO 7870-6:2016(E)ziEWMA value placed on the control chartz0
39、Initial value of zi Value of the smoothing parameterLzParameter used to establish the control limit for zi(expressed in number of standard deviations of z)s Estimator of the standard deviation True standard deviation of the distribution of x0True standard deviation of binomial distribution for P = p
40、0xStandard deviation of the averages of n individual observations; xn= /zStandard deviation of ziwhen i tends towards infinity Drift related to the average expressed in number of standard deviations1Maximum acceptable drift of the average, expressed in number of standard deviationsp Proportion of no
41、nconforming units of the processp0Target value for the proportion of nonconforming units of the processp1Upper refusable value of the proportion of nonconforming unitspiProportion of nonconforming units in the ith samplec Average number of nonconformitiesc0Target value for the average number of nonc
42、onformitiesc1Refusable average of nonconformitiesciNumber of nonconforming units in the ith sampleUCLUpper control limit value for the EWMA control chartLCLLower control limit value for the EWMA control chart. If LCLis negative, then it is taken as zeroARL Average Run LengthARL0Average Run Length of
43、 the process in controlARL1Average Run Length of the process with setting driftCL Centre line of the control limitMAXRL Maximum Run Length (5 % overrun probability), expressed as an integer4 EWMA for inspection by variables4.1 GeneralAn EWMA control chart plots geometric moving averages of past and
44、current data in which the values being averaged are assigned weights that decrease exponentially from the present into the past. Consequently, the average values are influenced more by recent process performance. The exponentially weighted moving average is defined as Formula (1):zi= xi+ (1 - ) zi-1
45、(1)NOTE 1 When the EWMA control chart is used with rational subgroups of size n 1 then xiis simply replaced with xi.Where 0 5.The maximum acceptable drift, 1, is: 1= (p1 p0)/s0, where p1is the maximum permissible proportion of nonconforming units in the production.B.3 ExampleA welding operation is m
46、onitored by control chart of the proportion of nonconforming units. The preliminary study enabled to estimate the average proportion p0of the properly set and stable process at 0,019 45 (1,945 %). The sample size n is constant and equal to 1 600.When the condition np0 5 is amply fulfilled; the techn
47、ique defined above and Table 4 can be used. With the same size of samples, an EWMA attributes chart, which has a run length of 370 when P = p0and which rapidly detects a proportion of nonconforming units equal to 0,028, can be obtained. See Formula (B.5):spp00010138 1=()= , (B.5)Hence,10 028 0 019 4
48、5 0 138 11600 248n =()=, , (B.6)For ARL0= 370, the following values are found in Table 4:125n = , ; = 0,54;Lz= 2,98;ARL1= 2,38.The control limits are deduced following Formulae (B.7) and (B.8):UCL=+=0 019 452980138 11 60005420540 025 0, (B.7)LCL=0 019 452980138 11 60005420540 013 2, (B.8)The same EW
49、MA control chart expressed in number of nonconforming units in the samples, provided that the size of samples does not vary or varies little, has the following parameters:z0= np0= 31,12 31 units;ns0= 220,96 221 units;UCL= 41,12 41 units;LCL= 21,12 21 units.The calculations for ziwill be made with the number of nonconforming units in each sample. ISO 2016 All rights reserved 19BS ISO 7870-6:2016ISO 7870-6:2016(E)Annex C (normative) EWMA control charts for a number of nonconformitiesC
