1、BSI Standards PublicationBS 5700:2015Guide to the selection ofcharting methods andcapability assessment foruse in statistical processcontrolPublishing and copyright informationThe BSI copyright notice displayed in this document indicates when the documentwas last issued. The British Standards Instit
2、ution 2015Published by BSI Standards Limited 2015ISBN 978 0 580 83714 2ICS 03.120.30; 25.040.40The following BSI references relate to the work on this document:Committee reference SS/4Draft for comment 15/30286921 DCPublication historyFirst published March 1984Second (present) edition September 2015
3、Amendments issued since publicationDate Text affectedBS 5700:2015 BRITISH STANDARDContentsForeword iiIntroduction 11 Scope 12 Terms, definitions and symbols 13 Control charts, performance and capability analysis 34 Charting discrete data 95 Charts for continuous variables 156 Process capability 21Bi
4、bliography 23List of figuresFigure 1 Example of an Xcontrol chart of washer diameters 3Figure 2 Example of a histogram of continuous data 5Figure 3 Example of a histogram of continuous data with specification limitssuperimposed 5Figure 4 Example of a histogram of continuous data with specification l
5、imitsand a normal distribution model displayed 6Figure 5 Example of a histogram of discrete data 7Figure 6 Flow chart for control chart selection 8Figure 7 Flow chart for selecting capability and performance measures 9Figure 8 Example of a c chart of the counts of non-conformities in a monthlynewsle
6、tter 11Figure 9 Example of a p chart of the proportion non-conforming 13Figure 10 Example cusum chart for golf attribute data 14Figure 11 Example Xchart 17Figure 12 Example R chart 18Figure 13 Example of a cusum for protein content data 20Figure 14 Example of a histogram of data with specification l
7、imits and normaldistribution model displayed 21List of tablesTable 1 Non-conformity counts in a monthly newsletter 10Table 2 Non-conforming circuit boards 12Table 3 Example of a cusum of golf data 13Table 4 Charts for discrete variables or attributes and which standard torefer to 15Table 5 Sampled d
8、ata 16Table 6 Protein content of blood plasma 18Table 7 Charts for continuous variables and which standard to refer to 20Summary of pagesThis document comprises a front cover, an inside front cover, pages i to ii, pages1 to 24, an inside back cover and a back cover.BRITISH STANDARD BS 5700:2015 The
9、British Standards Institution 2015 iForewordPublishing informationThis British Standard is published by BSI Standards Limited, under licence fromThe British Standards Institution, and came into effect on 30 September 2015. Itwas prepared by Technical Committee SS/4, Statistical process management.Al
10、ist of organizations represented on this committee can be obtained on requestto its secretary.SupersessionThis British Standard supersedes BS 5700:1984, which is withdrawn.Use of this documentAs a guide, this British Standard takes the form of guidance andrecommendations. It should not be quoted as
11、if it were a specification or a codeof practice and claims of compliance cannot be made to it.Presentational conventionsThe guidance in this standard is presented in roman (i.e. upright) type. Anyrecommendations are expressed in sentences in which the principal auxiliaryverb is “should”.Commentary,
12、explanation and general informative material is presented insmaller italic type, and does not constitute a normative element.Contractual and legal considerationsThis publication does not purport to include all the necessary provisions of acontract. Users are responsible for its correct application.C
13、ompliance with a British Standard cannot confer immunity from legalobligations.BRITISH STANDARDBS 5700:2015ii The British Standards Institution 2015IntroductionBS 5700 is a guide for any organization wanting to use control charts andcapability analysis to control a process, report performance, or me
14、asure resultsof an improvement programme. The application of control charts and capabilityanalysis is a vital step in the management and improvement of processes.Business processes can be many and varied, including applications inmanufacturing and in services, ranging from health and finance to cust
15、omercare.When followed correctly, statistical process control (SPC) can deliver a definable,measureable, and recognized way to monitor processes and produce accurateperformance reporting. These are important tools in the delivery ofimprovement programmes.The application of SPC offers many benefits t
16、o an organization beyond that ofcontrolling and improving processes SPC has an important role in developingstaff and helping them to engage with processes. For the methods to beeffective, it is important that senior management and other stakeholders act ina consistent and proactive manner on the mes
17、sages arising from the applicationof the methods.To improve a process it needs to be understood and to do so, take data from akey characteristic that describes the process. For example, if dimensions such asheight, length and thickness are to be monitored, the data needs to be charted.For this type
18、of data, variable charts are used. If the characteristic of interest is acount, such as the number of scratches or a proportion such as the number ofparcels with incorrect addresses, an attribute chart is appropriate. It is alsoimportant to measure process performance outcomes and assess capability
19、ofthe process so improvement can be assessed. This British Standard acts as aguide to selecting the correct type of chart, performance measurement andcapability analysis for the process and the relevant standard to refer to.NOTE If the wrong characteristic for measurement has been selected, success
20、is notguaranteed.1 ScopeThis British Standard provides guidance on the selection and application ofcontrol chart methods that are expanded upon in all parts of BS 5701,BS 5702 and BS ISO 7870.This British Standard also provides information on capability and performanceassessment as given in BS ISO 2
21、2514 (all parts) for the purpose of monitoring,understanding, reporting and improving processes.2 Terms, definitions and symbols2.1 Terms and definitionsFor the purposes of this British Standard, the terms and definitions given inBS ISO 3534 (all parts) apply.NOTE However, the terminology used in qu
22、ality control is subject to a continuingprocess of development in response to market demand.2.2 SymbolsFor the purposes of this British Standard the following symbols apply.Cpcapability indexCpkminima of CpkUand CpkLBRITISH STANDARD BS 5700:2015 The British Standards Institution 2015 1CpkLlower capa
23、bility indexCpkUupper capability indexc count number of non-conformitiesc average count number of non-conformitiesD demerit scoreD3coefficient to calculate the lower control limit of a range chartD4coefficient to calculate the upper control limit of a range chartd distance on a V-maskd2coefficient t
24、o estimate standard deviation from average sample rangei index counterk number of subgroupsL lower specification limitLCLlower control limitn, N subgroup, sample sizenp number non-conformingPpperformance indexPpkminima of PpkUand PpkLPpkLlower performance indexPpkUupper performance indexp proportion
25、 non-conformingp average proportion non-conformingR ranges standard deviationU upper specification limitUCLupper control limitV varianceXithe ithreading in a subgroup or samplex, Xsubgroup, sample, mean valuex,Xaverage of the subgroup meanso summation population mean population standard deviationstt
26、otal standard deviationxStandard error of the meanBRITISH STANDARDBS 5700:20152 The British Standards Institution 20153 Control charts, performance and capabilityanalysis3.1 Control charts3.1.1 GeneralObservations of the process should be made at regular intervals and plotted. Ifthe control limits w
27、hich are set at the process mean 3 standard errors of theprocess variation are exceeded then the process is deemed to be out of controland to have changed as a consequence of an assignable cause.Figure 1 illustrates a process variable (in this case the interior diameter of awasher specified to be 12
28、.00 0.06 mm).Figure 1 Example of an Xcontrol chart of washer diametersNOTE This chart was constructed from drawing samples of five washers every 30 minutes and plotting theaverage on the chart (further detail on chart construction is given in 5.3). The process mean, derived from samplemeasures was f
29、ound to be 12.01 mm with a standard error of 0.0133 mm. This sets the control lines at 11.97 mmand 12.05 mm that are within specification limits indicating that this might be a capable process, but it has goneout of control.Assignable causes can also occur if there is a systematic pattern within the
30、control lines, meaning that if the process is behaving as desired, points shouldappear at random within the control lines. For a continuous variable that isdistributed according to the normal distribution this would mean that if thereare no assignable causes, the chance of exceeding the control line
31、s is very small(less than a probability of 0.003). In addition, the user should expect around twothirds of the observations to be within 1 standard error of the process meanand 95% of the sample means to lie within 2 standard errors of the processaverage (almost equivalent to a 95% confidence interv
32、al). The width betweenthe control lines is reflective of the inherent variation (or common causevariation) in the process.BRITISH STANDARD BS 5700:2015 The British Standards Institution 2015 3NOTE For further discussion of assignable and common cause variation see Deming1 and Wheeler 2. When these c
33、harts were developed, sample measures weretaken by the process operator, at regular intervals, who then calculated the meanand the range (the difference between the highest and lowest sample measurement,taken as a simplified measure of variability). The operator then plotted thesecalculated values o
34、nto the charts. This had an additional benefit of involving theoperator and allowing him or her to take responsibility (See Shewhart 3 andWheeler 2).BS 5701, BS 5702 and BS ISO 7870-4 detail the theory and use of control chartsand explain how the performance of these charts is assessed by using them
35、easure “average run length” (ARL) that a chart will take to detect a change.3.1.2 Count and proportion charts covered in BS 5701Generally, those who manage processes use qualitative or attribute data such asthe number of blemishes on the paint work of a car, the number of errors in theinitial proces
36、sing of a legal document, or the proportion of a production batchthat is in some way defective. Charts to allow the monitoring of such attributesare count (c) and proportion (p) charts and are introduced in Clause 4 and arecovered in BS 5701.3.1.3 Mean and range (or standard deviation) charts covere
37、d in BS 5702For continuous measures, the user also needs to monitor variation in the processas well as changes in the process average. For this, range (R) or standarddeviation (s) charts should be used. These, along with Xcharts, are covered inBS 5702.3.1.4 Cusum charts covered in BS ISO 7870-4The c
38、harts described in 3.1.1 and 3.1.2 tend to perform well if changes in theprocess are reasonably substantial. When changes are small and gradual, a chartthat plots the cumulative deviation from the process average performs betterand should be used. These charts are called cusum charts and are detaile
39、d inBS ISO 7870-4, and are covered in more detail in Clause 4 and Clause 5.3.2 Performance3.2.1 Continuous variablesPD ISO/TR 22514-4 describes the performance assessment of continuousvariables. An example of a histogram of continuous data is shown in Figure 2.BRITISH STANDARDBS 5700:20154 The Briti
40、sh Standards Institution 2015Figure 2 Example of a histogram of continuous dataIn Figure 2, there is no order for the data and no control chart was used.Therefore, if the specification limits for the process are 40 to 60, whensuperimposed over the histogram, as in Figure 3, the output of the process
41、clearly exceeds the specification limits.Figure 3 Example of a histogram of continuous data with specification limits superimposedNOTE It is the end users decision to specify what the actual permissible proportion of results will be, but mostcontractual circumstances would allow a maximum of 0.0134%
42、 defective per limit, i.e. 0.0268% in total.BRITISH STANDARD BS 5700:2015 The British Standards Institution 2015 5As detailed in PD ISO/TR 22514-4, a suitable model should be found thatdescribes the total output. For the data in Figures 2 and 3 the normaldistribution provides a good model and it has
43、 been superimposed over the dataand shown in Figure 4.Figure 4 Example of a histogram of continuous data with specification limits and a normaldistribution model displayedPD ISO/TR 22514-4 defines indices that are typically used for performanceassessment.In the case of the example data shown in Figu
44、re 4 being modelled by thenormal distribution, the equations are:Pp=U2L6tPpkU5U23tPpkL52L3tIf a process has an index of 1.33 it would be regarded in most circumstances tobe barely acceptable. The higher the index value the better.From the data given in Figure 3 and Figure 4, the mean is 50.13 and th
45、estandard deviation is 4.95. Thus the indices are:Pp=60 4064.95= 0.67PpkU560 50.1334.95= 0.66BRITISH STANDARDBS 5700:20156 The British Standards Institution 2015PpkL550.13 4034.95= 0.68The low value of these indices indicates a large proportion of non-conformingitems have been produced.3.2.2 Discret
46、e variablesIf the variable in question is of a discrete type, e.g. the number of blemishesfound per 10 m length of a carpet, as shown in Figure 5, the equations referredto in PD ISO/TR 22514-4 should not be used. Instead, it is usual to simply statethe achieved average level of the non-conformity. I
47、n this example the averageis 1.3 blemishes per 10 m length.Figure 5 Example of a histogram of discrete data3.3 Process capabilityIf a process is in control then process capability can be assessed. Processcapability is the degree to which customer agreed specifications, or sometimesinternally set spe
48、cifications, are met. Capability can be assessed for continuousdata and methods which are under development for discrete data.See BS ISO 25514 for more information.3.4 How to choose an appropriate chart and capability analysis3.4.1 GeneralWhen the data is a set of continuous measures such as tempera
49、ture, weight,length or diameter then the user should choose from a set of charts known asvariable charts as illustrated in Figure 6.BRITISH STANDARD BS 5700:2015 The British Standards Institution 2015 7Figure 6 Flow chart for control chart selection3.4.2 Xand range chartsIf the user can take sample batches of a process characteristic, they shouldconsider using Xand range charts. If it is only possible to obtain individualmeasures then the user should choose individual and
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