1、BS 5702-3:2008Guide to statistical process control (SPC) charts for variables Part 3: Charting techniques for short runs and small mixed batchesICS 03.120.30NO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAWBRITISH STANDARDPublishing and copyright informationThe BSI copyright not
2、ice displayed in this document indicates when the document was last issued. BSI 2008ISBN 978 0 580 53004 3The following BSI references relate to the work on this standard:Committee reference SS/4Draft for comment 03/102261 DCPublication historyFirst published April 2008Amendments issued since public
3、ationAmd. no. Date Text affectedBS 5702-3:2008 BSI 2008 iBS 5702-3:2008ContentsForeword iiiIntroduction 11 Scope 22 Normative references 23 Terms, definitions, abbreviations and symbols 34 How to select the correct type of Shewhart control chart for measured data 55 How to prepare for short-run, sma
4、ll mixed batch control charting 86 How to establish and apply short-run, small mixed batch, control charts 17AnnexesAnnex A (informative) Reproducible copies of control chart forms and normal probability worksheet 28Bibliography 33List of figuresFigure 1 Diagram distinguishing between a population p
5、arameter and a sample statistic 3Figure 2 Shewhart control chart selection flow chart for measured data 6Figure 3 Control chart selection flow chart for short runs and small batches 7Figure 4 Four different scenarios with a single observed measurement 10Figure 5 Preliminary process stability check 1
6、5Figure 6 Normal probability worksheet 16Figure 7 Variable aim, individual and moving range control chart 19Figure 8 Variable aim, moving mean and moving range control chart 21Figure 9 Universal, individual and moving mean chart 25Figure 10 Universal, moving mean chart for short runs 27Figure A.1 Va
7、riable aim, individual and moving range chart 28Figure A.2 Variable aim, moving mean and moving range control chart 29Figure A.3 Universal, individual and moving range chart 30Figure A.4 Universal, moving mean and moving range control chart 31Figure A.5 Example normal probability worksheet 32List of
8、 tablesTable 1 Chart selection table for short runs and small batches 7Table 2 Four scenarios when a single measurement is taken at set up 11Table 3 Range of critical set up acceptance values for t 11Table 4 % probability plotting positions for sample sizes of 3 to 20 14Table 5 Data for normal proba
9、bility plot 15Table 6 Key data for constructing a variable aim, individual and moving range chart 18Table 7 Data and calculations for variable aim, individual and moving range chart 19BS 5702-3:2008ii BSI 2008Table 8 Key data for constructing a variable aim, moving mean and moving range control char
10、t 21Table 9 Data and calculations for variable aim, moving mean and moving range chart 21Table 10 Key data for constructing a universal, individual and moving range chart 23Table 11 Data and calculations for universal, individual and moving range chart 24Table 12 Key data for constructing a universa
11、l, moving mean and moving range control chart 26Table 13 Data and calculations for universal, moving mean and moving range chart 27Summary of pagesThis document comprises a front cover, an inside front cover, pages i to iv, pages 1 to 33 and a back cover. BSI 2008 iiiBS 5702-3:2008ForewordPublishing
12、 informationThis part of BS 5702 was published by BSI and came into effect on 30 April 2008. It was prepared by Technical Committee SS/4, Statistical process control. A list of organizations represented on this committee can be obtained on request to its secretary.Relationship with other publication
13、sIt is envisaged that, ultimately, BS 5702 will consist of the following parts: Part 0: General introduction to control charts for measurements; Part 1: Charts for mean, median, range and standard deviation; Part 2: Charts for individual values; Part 3: Charting techniques for short runs and small b
14、atches;BS 5702-3 is self-contained in respect to the specific subject matter. It also provides essential links to, and is consistent in approach, format and style with, BS 5702-1 and BS 5702-2, BS 5701 Parts 1 to 4, BS 600 and BS 5703 Parts 1 to 4.Use of this documentBSI permits the reproduction of
15、Figures A.1, A.2, A.3, A.4 and A.5, on pages 29 to 33 of BS 5702-3. This reproduction is only permitted where it is necessary for the user to record findings on the figures during each application of the standard.As a guide, this part of BS 5702 takes the form of guidance and recommendations. It sho
16、uld not be quoted as if it were a specification and particular care should be taken to ensure that claims of compliance are not misleading.Any user claiming compliance with this part of BS 5702 is expected to be able to justify any course of action that deviates from its recommendations.Presentation
17、al conventionsThe provisions in this standard are presented in roman (i.e. upright) type. Its recommendations are expressed in sentences in which the principal auxiliary verb is “should”.Commentary, explanation and general informative material is presented in smaller italic type, and does not consti
18、tute a normative element.Contractual and legal considerationsThis publication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application.Compliance with a British Standard cannot confer immunity from legal obligations.iv BSI 2008 This pa
19、ge deliberately left blankBS 5702-3:2008 BSI 2008 1BS 5702-3:2008IntroductionBS 5702-1 makes the general recommendation that at least 25 subgroups of data be collected, and plotted, before any constructive analysis can take place to form the basis for establishing standard traditional measured data
20、control charts. This represents best practice for the application of standard statistical process control (SPC) charts to long production runs of a single product characteristic (e.g. diameter) or process parameter (e.g. temperature). However, it presents a problem in many potential applications of
21、SPC.In the business environment there is an increasing need for versatility and flexibility in highly efficient systems. These support just-in-time inventories and create greater product variety, with smaller batches and shorter runs. The consequent ever-increasing resets, changeovers, die changes,
22、etc., bring new challenges to the meaningful application of SPC. These occur at a critical time when the pressure for continual performance improvement has never been greater.Processes accommodate many part numbers, often of similar shape but different nominal sizes at best, and part configurations
23、having multiple characteristics with different specified nominal values, units of measure and tolerances. For example a bolt maker with short runs of various size bolts (diameter and length), or a tube extruder with tubes of different size outside diameter, inside diameter and wall thickness. The cu
24、stomary approach is to put a different standard SPC chart on each characteristic of each part number. The consequences of this administratively cumbersome, product-focused, procedure would include the generation of large numbers of run charts each containing data too sparse to be useful, either for
25、control or improvement.In the same way that other functions have responded to the challenge, e.g. the introduction of lean methods and single minute exchange of die (SMED) in production, so the SPC facilitating function responds. This situation presents both a problem and an opportunity.The problem
26、arises because, in many organizations, production runs are often too small to generate enough data to apply traditional control charts. This can occur in two ways. Firstly, there is the case where the batch, or lot, size itself is very small. Secondly, there is the situation where the run is very sh
27、ort, e.g. the high speed stamping operation that may run only for a short period. It is frequently not practicable, in either case, to generate enough sub-groups to make the control chart meaningful.The opportunity arises because much current statistical process control is actually statistical produ
28、ct control, i.e. SPC implementation is often product- rather than process-focused. Different products, which are generated by a single or similar process, are looked upon as dissimilar entities. Consequently, sources of process variation can be overlooked when analysing the product-orientated contro
29、l chart. Due to the sparseness of product information in short-run, small-batch situations, focus has to be on the common element, the process. Short-run SPC provides the means to transform a succession of short-run product-related jobs into a long-term process. An example is the jobbing shop that d
30、oes not make many of the same part, but has a number of processes that are continually being employed. They turn many shafts, BS 5702-3:20082 BSI 2008drill many holes, etc., continually. The grouping of drilling, turning, grinding processes and the like, or their corresponding facilities, e.g. machi
31、ne tools, could make good candidates for the application of short-run SPC.Some basic statistical concepts, terminology and symbols are introduced in this part of BS 5702; however, these are kept to a minimum. The language chosen is that of the workplace rather than that of the statistician. The aim
32、is to make this standard readily comprehensible to the extensive range of prospective users and so facilitate widespread communication and understanding of the method.It is advisable that those who are not familiar with the control chart technique read both BS 5702-1 and BS 5702-2 before reading BS
33、5702-3.1 ScopeThis part of BS 5702 describes ways of applying measured data statistical process control (SPC) charts to short runs and small mixed batches where the sample size for monitoring is restricted to one. It provides a set of tools to facilitate the understanding of sources of variation in
34、such processes so that the processes can be better managed.The charts described are process- rather than product-focused. The user can plot, monitor and control similar characteristics on different items, or different characteristics on an item, on a single control chart.2 Normative referencesThe fo
35、llowing referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.BS 600:2000, A guide to the application of statistical m
36、ethods to quality and standardizationBS 5702-1:2001, Guide to statistical process control (SPC) charts for variables Part 1: Charts for mean, median, range and standard deviationBS 5702-2:2008, Guide to statistical process control (SPC) charts for variables Part 2: Charts for individual valuesBS ISO
37、 3534-2:2006, Statistics Vocabulary and symbols Part 2: Applied statistics BSI 2008 3BS 5702-3:20083 Terms, definitions, abbreviations and symbols3.1 GeneralFor the purposes of this part of BS 5702, the terms, definitions, abbreviations and symbols given in BS ISO 3534-2:2006 and the following apply
38、.NOTE Whilst the rigour of the statistical treatment in this standard is kept to a minimum it is essential that there is a clear understanding of the distinction between what is a “population parameter” and what is a “sample statistic”, together with the associated notation. This is illustrated in F
39、igure 1.As an illustration of the application of this diagram and the distinguishing between “A”, “B” and “C”:a) The lower case Greek letter sigma, , a population parameter, represents the standard deviation of a population;b) S, a sample statistic, represents the sample estimate of the standard dev
40、iation;c) s represents the realized, or measured value, of the sample statistic, S.Figure 1 Diagram distinguishing between a population parameter and a sample statisticKeyA Population parameters are symbolized by lower case Greek letters in italics.B Sample statistics are symbolized by upper case La
41、tin letters in italics.C Realized values of sample statistics are symbolized by lower case Latin letters in italics.Describe the populationwith probability distributionPopulationPopulation parameterEstimatepopulationparameterTake a sample4231ABSample statisticIdentify a sample statisticRealized valu
42、eof sample statisticCSampleBS 5702-3:20084 BSI 2008Similarly:1) the lower case Greek letter mu, , a population parameter, represents the arithmetic mean of the population;2) , a sample statistic, represents the sample estimate of the arithmetic mean;3) represents the realized, or measured, value of
43、the sample statistic .3.2 Terms and definitions3.2.1 aimvalue from which departure in level is to be detectedNOTE The aim can be the nominal value, the desired or expected value, or the overall mean value experienced or estimated. It is not necessarily the most desirable or preferred value. It is si
44、mply a convenient target value for constructing a control chart.3.2.2 population parametersummary measure of the values of some characteristic of a populationEXAMPLES Population mean = ; population standard deviation = .NOTE Population parameters are usually symbolized by lower case Greek letters in
45、 italics.3.2.3 sample statisticsummary measure of some observed value of a sampleNOTE 1 Sample statistics (random variables) are symbolized by upper case Latin letters in italics (e.g. and S) whereas the actual realization of sample statistics (observed values) are symbolized by lower case Latin let
46、ters in italics (e.g. and s). This contrasts with population parameters symbolized by lower case Greek letters in italics (e.g. and ).NOTE 2 Observed values may be combined to form a test result or measurement result. For instance, the density of a bar may involve the combining of observed values of
47、 length, diameter and mass.3.3 Abbreviations and symbolsXxXXxCL centre line of a control chartLCL , and , are the lower control limits for individuals, mean and range, respectivelyRmovingmoving range, the range of each two consecutive range valuesm number of subgroupsn number in a sample or subgroup
48、 R range of two consecutive valuesRaimthe aimed value of the range of a particular characteristicS, s respectively the general form of the estimator of the process standard deviation and its realized valuet test statistic for set-up acceptanceUCL ,and , are the upper control limits for individuals,
49、mean and range, respectivelyX, x respectively a symbol representing a general value of a quality characteristic and a realization of it, respectively the general form of the estimator of the process mean and its realized valueLCLXLCLXLCLRUCLXUCLXUCLRX x BSI 2008 5BS 5702-3:20084 How to select the correct type of Shewhart control chart for measured data4.1 GeneralThe business aim of statistical process control (SPC) is to control and improve qua
