1、BRITISH STANDARD BS 5702-1:2001 Guide to statistical process control (SPC) charts for variables Part 1: Charts for mean, median, range and standard deviation ICS 21.060.10; 21.060.20 NO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAWBS 5702-1:2001 This British Standard, having be
2、en prepared under the direction of the Management Systems Sector Committee, was published under the authority of the Standards Board and comes into effect on 15 April 2001 BSI 04-2001 The following BSI references relate to the work on this standard: Committee reference SS/4 Draft for comment 94/4089
3、16 DC ISBN 0 580 33229 2 Committees responsible for this British Standard The preparation of this British Standard was entrusted to Technical Committee SS/4, Statistical process control, upon which the following bodies were represented: BEAMA Limited British Standards Society Cable and Wireless Comm
4、unications plc Clay Pipe Development Association Limited Federation of Small Businesses Gauge and Tool Makers Association General Domestic Appliances Limited Institute of Quality Assurance Royal Statistical Society Society of Motor Manufacturers and Traders Limited Amendments issued since publicatio
5、n Amd. No. Date of issue CommentsBS 5702-1:2001 BSI 04-2001 i Contents Page Committees responsible Inside front cover Foreword ii Introduction 1 1S c o p e 1 2 Normative references 2 3 Definitions 2 4S y m b o l s 3 5 Preparation for control charting 4 6 Types of variables charts 8 7 Setting up the
6、control chart 9 8 Using the control chart 18 Annex A (normative) Analysis of subgroup data 23 Annex B (informative) Control charts with probabilistic action lines and warning lines 27 Annex C (informative) Tables of values of c 4 /c 4 and c 4 33 Bibliography 37 Figure 1 Recommended control chart lay
7、out for /R chart 7 Figure 2 Flowchart for the collection and analysis of preliminary data to set up a control chart 12 Figure 3 Example of a typical reaction plan for a production process 20 Figure 4 Typical patterns and trends to look for in the analysis of range control charts 21 Figure A.1 Range
8、control charts 23 Figure A.2 Processes out-of-control for ranges with patterns or trends within the control lines 24 Figure A.3 Average ( ) charts 26 Figure A.4 Process out-of-control for averages with patterns or trends within the control lines 26 Table 1 X scale as a function of subgroup size 8 Ta
9、ble 2 Factors for the calculation of control and warning lines 17 Table A.1 Significant run lengths 24 Table B.1 Factors for the calculation of probabilistic control limits of plots 31 Table B.2 Factors for the calculation of probabilistic control limits for R and s charts 32 Table C.1 Values of c 4
10、 /c 4 3 3 Table C.2 Values of c 4 3 5 X X XBS 5702-1:2001 ii BSI 04-2001 Foreword This part of BS 5702 has been prepared by Technical Committee SS/4. It is envisaged that, ultimately, BS 5702 will consist of the following parts: Part 0: General introduction to control charts for measurements; Part 1
11、: Charts for mean, median, range and standard deviation; Part 2: Charts for individual values and moving range and for moving averages and moving ranges/standard deviations; Part 3: Charting techniques for short production runs and small batches; Part 4: Charting techniques for special situations. A
12、 new British Standard on process capability is in the course of preparation and this subject is not included in this standard. A British Standard does not purport to include all necessary provisions of a contract. Users of British Standards are responsible for their correct application. Compliance w
13、ith a British Standard does not of itself confer immunity from legal obligation. Summary of pages This document comprises a front cover, an inside front cover, pages i and ii, pages 1 to 36, an inside back cover and a back cover. The BSI copyright notice displayed in this document indicates when the
14、 document was last issued.BS 5702-1:2001 BSI 04-2001 1 Introduction The business aim of statistical process control (SPC) is to control and improve quality, increase productivity and reduce cost. This is achieved through the analysis of the variation of a process or its outputs in order to take appr
15、opriate actions to: achieve and maintain a state of statistical control; provide a quantitative measure of process performance; improve process capability. The variation in a quality characteristic of a process is due to two types of causes: assignable (special): systematic cause or causes that are
16、not part of the process all the time but arise due to special circumstances; random (common): non-systematic causes that are inherent in the process. The principal tool of SPC is the control chart. There are two main types of control chart, Shewhart and cusum (Cumulative SUM). NOTE Cusum charts are
17、dealt with in BS 5703. The Shewhart control chart provides a graphical representation of a process showing plotted values of a representative statistic of the characteristic (e.g. count, mean, range, standard deviation), a centre line, and one or more control lines. The control line(s) and centre li
18、ne are used as a basis for judging the stability of the process, namely, whether or not the process is in statistical control. Control limits are derived from the performance of the process and are not to be confused with specification limits or specified tolerances. Shewhart control charts provide
19、a common international language for communicating technical information on the performance of a process. Control charts are effective tools in understanding process behaviour. They distinguish between random and assignable causes of variation. When no assignable causes are present, the process is sa
20、id to be in statistical control. When a process is in statistical control its performance is predictable and can be assessed. This performance can be improved by reducing random cause variation and improving process centring (targeting). The control chart has wide applicability throughout an organiz
21、ation, ranging from marketing, sales, finance, administration to manufacturing or service. There are essentially two main classes of Shewhart control chart, namely attribute charts and variable charts. Attributes charts are dealt with in BS 5701. This part of BS 5702 deals solely with the control as
22、pects of Shewhart-type variables charts for mean, median, range and standard deviation, using both Shewhart and probabilistic control limits. 1 Scope This part of BS 5702 describes a method of statistical process control that involves charting measurements of a given characteristic. It sets out acce
23、pted methods of sampling and charting that are easy to use and that often can safely and profitably replace routine inspection. These charts indicate both the level and variability of the characteristic. The control aspects of Shewhart-type variables charts for mean, median, range and standard devia
24、tion, using both Shewhart and probabilistic control limits, are described. Guidance is given to persons concerned with making decisions on products and processes. The charting techniques outlined may be employed to establish and maintain process control over the charted characteristic. No attempt is
25、 made to deal at length with the statistical principles underlying the methods described in this standard.BS 5702-1:2001 2 BSI 04-2001 2 Normative references The following normative documents contain provisions which, through reference in this text, constitute provisions of this part of BS 5702. For
26、 dated references, subsequent amendments to, or revisions of, any of these publications do not apply. For undated references, the latest edition of the publication referred to applies. BS ISO 3534-1:1993, Statistics Vocabulary and symbols Part 1: Probability and general statistical terms. BS ISO 353
27、4-2:1993, Statistics Vocabulary and symbols Part 2: Statistical quality control. BS EN ISO 8402:1995, Quality management and quality assurance Vocabulary. 3 Definitions For the purposes of this part of BS 5702, the definitions given in BS EN ISO 8402:1995, BS ISO 3534-1:1993, BS ISO 3534-2:1993 and
28、the following apply. 3.1 control line (action line) line drawn on a control chart to indicate a control limit NOTE 1 Users of probabilistic control limits usually employ the term “action line“ instead of “control line“, a practice which has also been adopted in this standard in the discussion of pro
29、babilistic control charts. NOTE 2 In loose day-to-day usage the terms “control line“ and “control limit“ are often used indiscriminately, meant to denote the same thing. In this standard the terms are used with their specific meaning. The term “control limits” is defined in BS ISO 3534-2 (see 3.4.1)
30、. They are calculated numerical values that define the location of the control lines on the chart. 3.2 random causes (of variation) factors, generally many in number but each of relatively small importance, contributing to variation, which have not necessarily been identified NOTE Synonyms used to d
31、esignate the factors responsible for inherent variation in characteristics of product items are “chance causes” and “common causes”. In this standard the term “random causes“ is used exclusively. 3.3 assignable cause (of variation) factor (usually systematic) that can be detected and identified as c
32、ontributing to a change in a quality characteristic or process level NOTE Synonymous term used to designate variation attributable to a specific factor is “special cause”. However, this standard will only use the term “assignable cause“. 3.4 control chart chart normally consisting of two plots one t
33、o depict how over time the subgroup averages vary in relation to the target process mean, the other to indicate the extent of the variation within the subgroups over time 3.5 process any activity that operates upon an input and as a result produces an outputBS 5702-1:2001 BSI 04-2001 3 4 Symbols The
34、 following symbols and abbreviated terms are used in this part of BS 5702. NOTE 1 The symbol represents the arithmetic mean of a number of individual subgroup standard deviations and is used to obtain a (biased) estimate of the process standard deviation. An alternative method which is less biased i
35、s to take the square root of the arithmetic mean of the squares of the subgroup standard deviations. The correct, but awkward, expression for the latter would therefore be . In this part of BS 5702 the symbol is used in place of . (See also 7.2.2.2.1.) NOTE 2 The symbol is the notation generally emp
36、loyed to denote an estimate of a population standard deviation and it should be noted that the use of this symbol in this part of BS 5702 is more specific than this. NOTE 3 In several places of this part of BS 5702 the term “standard error“ has been used (and denoted by e ). In the context of this p
37、art of BS 5702 the term represents the standard deviation of the distribution of a statistic, e.g. the standard deviation of the subgroup means, the subgroup medians or the subgroup ranges. CL Centre line UCL Upper centre line LCL Lower control line UWL Upper warning line LWL Lower warning line UAL
38、Upper action line (see Annex B) LAL Lower action line (see Annex B) i Counter for items in a subgroup j Counter for subgroups in a sequence k Number of subgroups n Subgroup size n j Number of items in the j thsubgroup X Individual value of the characteristic for items in a subgroup X ij Value of the
39、 characteristic for the i thitem of the j thsubgroup X max Highest value in a subgroup X min Lowest value in a subgroup Arithmetic mean of the characteristic for all items in a subgroup Arithmetic mean of a number of values of (i.e. arithmetic mean of the characteristic for all subgroups combined) R
40、 Subgroup range (X max- X min ) Arithmetic mean of subgroup range values Subgroup median Arithmetic mean of subgroup median values True process mean value 0 Nominal value for the process mean R Process arithmetic mean of the range in subgroups of size n s Process arithmetic mean of the standard devi
41、ation in subgroups of size n True process standard deviation 0 Assumed true process standard deviation Unbiased estimate of the process standard deviation e Standard error of the plotted characteristic (see NOTE 3 below) R Process standard deviation of the range in subgroups of size n s Standard dev
42、iation of the process standard deviation in subgroups of size n s Subgroup standard deviation Arithmetic mean of a number of subgroup standard deviations (see NOTE 1 below) Square root of the arithmetic mean of s 2over a number of subgroups (see NOTE 1 below) X = X X R X X s s s s 2 s s 2 BS 5702-1:
43、2001 4 BSI 04-2001 5 Preparation for control charting 5.1 General Any statistical method will fail to achieve a desired objective unless management has prepared a responsive environment. Open communication should be developed. A team approach should be used, and training and resources should be prov
44、ided to support improvement actions. This clause outlines the steps to be taken to ensure that a suitable environment for control charting is established. 5.2 Analysis of the process 5.2.1 Concept of process The definition of “process” for the purposes of this standard is given in 3.5. The process s
45、hould be understood in terms of its relationship to other operations in the system and in terms of the individual process elements. Irregularities may arise from a variety of causes associated with equipment, materials, methods, human factors, etc., and these may have effects at different stages. Me
46、thods of presentation such as process flow diagrams may help to clarify such relationships. 5.2.2 Minimization of variation Unnecessary external causes of variation should be reduced before charting begins. This could simply mean ensuring that the process is being operated as intended, or it could m
47、ean conducting a designed experiment with known input materials, constant control settings, etc. The purpose is to avoid problems that should be corrected beforehand, including excessive process adjustment or over-control. In all cases a process log should be kept, noting all relevant events such as
48、 tool changes, new raw material lots, etc. 5.2.3 Identification of output The process should be considered as a single stream having a single set of causes. If there are two or more distinct streams, the usual practice is for each to be treated separately in the control programme because they come f
49、rom different systems, e.g. different conveyor or machine lines. Alternatively, methods of control that recognize the differences between streams may be used. 5.3 Choice of characteristics 5.3.1 Determination of characteristics to be managed Attention should be concentrated on those characteristics that are most promising for process improvement or which give the clearest indications of subsequent performance. Several considerations are appropriate as follows. a) The customers
