1、BRITISH STANDARD BS 5701-2:2003 Guide to quality control and performance improvement using qualitative (attribute) data Part 2: Fundamentals of standard attribute charting for monitoring, control and improvement ICS 03.120.30 BS 5701-2:2003 This British Standard was published under the authority of
2、the Standards Policy and Strategy Committee on 31 October 2003 BSI 31 October 2003 First published as BS 5701 February 1980 The following BSI references relate to the work on this British Standard: Committee reference SS/4 Draft for comment 02/400887 DC ISBN 0 580 42735 8 Committees responsible for
3、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: Association for Road Traffic Safety and Management (ARTSM) BAE Systems British Standards Society (BSS) Clay Pipe De
4、velopment Association (CPDA) Federation of Small Businesses (FSB) Gauge and Tool Makers Association (GTMA) General Domestic Appliances Ltd. Institute of Quality Assurance National Physical Laboratory Royal Statistical Society Amendments issued since publication Amd. No. Date CommentsBS 5701-2:2003 B
5、SI 31 October 2003 i Contents Page Committees responsible Inside front cover Foreword ii 1S c o p e 1 2 Normative references 1 3 Terms, definitions and symbols 1 4 The four types of attribute control charts 1 5 The construction and use of standard control charts for attribute data 1 Annex A (normati
6、ve) Specimen attribute control charts 24 Annex B (normative) Formulae for the control limits 26 Bibliography 27 Figure 1 Standard charts to monitor different types of qualitative data 2 Figure 2 Single characteristic “c” chart 4 Figure 3 “c” chart set up 6 Figure 4 Extension of control limits on “c”
7、 chart 7 Figure 5 “c” chart illustrating a significant change in performance 9 Figure 6 “u” chart 10 Figure 7 Example of adjustment of control limit for variation in sample size 12 Figure 8 Computer-generated chart for unequal sample size 13 Figure 9 Multiple characteristic control chart 14 Figure 1
8、0 Pareto diagram to establish priorities for action 15 Figure 11 “np” control chart 16 Figure 12 “p” chart 19 Figure 13 Computer-generated “p” chart 20 Figure 14 Sudden shift in process average 21 Table B.1 Formulae for the control limits 26BS 5701-2:2003 ii BSI 31 October 2003 Foreword BS 5701-1 de
9、monstrates the business benefits, and the versatility and usefulness, of a very simple, yet powerful, pictorial control chart method for monitoring and interpreting qualitative data. This is done in a practical and largely non-statistical manner. BS 5701-2:2003 partially supersedes BS 5701:1980 and
10、BS 2564:1955 and all four parts of BS 5701 together supersede BS 5701:1980 and BS 2564:1955, which are withdrawn. This qualitative data can range from overall business figures such as percentage profit to detailed operational data, such as percentage absenteeism, individual process parameters and pr
11、oduct/service features. The data can either be expressed sequentially in yes/no, good/bad, present/absent, success/failure format, or as summary measures (e.g. counts of events and proportions). For measured data control charting refer to BS 5702-1. BS 5701-2 continues to focus on the application of
12、 standard control charts to the monitoring, control and improvement of business processes. However, it deals with the application of standard attribute charting at a technical level more suitable for practitioners. Its aim is still to be readily comprehensible to an extensive range of prospective us
13、ers and so facilitate widespread communication, and understanding, of the method. As such, it focuses on a practical statistical treatment of the charting of qualitative data presenting examples of construction and application using a mainly simple pictorial approach. BS 5701-3 provides a more rigor
14、ous, statistical approach to process control and improvement using qualitative data. BS 5701-4 deals with measuring and improving the quality of decision making in the classification process itself. A British Standard does not purport to include all the necessary provisions of a contract. Users of B
15、ritish Standards are responsible for their correct application. Compliance with a British Standard does not of itself confer immunity from legal obligations. Summary of pages This document comprises a front cover, an inside front cover, pages i and ii, pages 1 to 27 and a back cover. The BSI copyrig
16、ht notice displayed in this document indicates when the document was last issued.BS 5701-2:2003 BSI 31 October 2003 1 1 Scope BS 5701-2 describes the fundamentals necessary for the successful application, by practitioners, of standard attribute charting for monitoring, control and improvement of bus
17、iness processes. 2 Normative references The following 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 EN ISO
18、 9000:2000, Quality management systems Fundamentals and vocabulary. BS ISO 3534-1, Statistics Vocabulary and symbols Part 1: Probability and general statistical terms. BS ISO 3534-2, Statistics Vocabulary and symbols Part 2: Applied statistics. 3 Terms, definitions and symbols For the purposes of th
19、is part of BS 5701, the terms, definitions and symbols given in BS ISO 3534-1, BS ISO 3534-2 and BS EN ISO 9000:2000, Clause 3 apply. 4 The four types of attribute control charts Qualitative data are divided for convenience, into two categories, classified data and count data. In conventional statis
20、tical process control, classified and countable data are handled using a: 1) “p” chart for proportion of entities (e.g. units or items), having a particular attribute (e.g. non-conforming), particularly when the sample size is variable; 2) “np” chart for numbers of entities (e.g. units or items), ha
21、ving a particular attribute (e.g. non-conforming), from samples of constant size; 3) “u” chart for number of events (e.g. non-conformities) per sample, particularly when the sample size is variable; 4) “c” charts for number of events (e.g. non-conformities) for samples of constant size. Figure 1 ill
22、ustrates the appropriate standard chart to choose to monitor different types of qualitative data. NOTE 1 Refer to BS 5703 for cumulative sum (CUSUM) methods for handling both discrete and continuous data. Whilst the four standard discrete data charts of Figure 1 have peculiar names or labels (i.e. “
23、c”, “u” etc.), these labels are in standard use throughout the world. The charts are extremely easy to set up and apply and provide a pictorial window of the behaviour of the chosen characteristic readily understandable to all. NOTE 2 See Annex A. 5 The construction and use of standard control chart
24、s for attribute data 5.1 The “c” chart 5.1.1 General The “c” chart is one of the simplest control charts to construct and use. Samples of a constant size are taken from a process and the number of non-conformities present within each sample counted. These observations (known as “c” numbers) can be r
25、ecorded and plotted onto a control chart and so provide a way of monitoring the process for statistical control. A procedure for setting up such a control chart is given in 5.1.2 to 5.1.11.BS 5701-2:2003 2 BSI 31 October 2003 Figure 1 Standard charts to monitor different types of qualitative data Di
26、screte (attribute) (qualitative) See BS 5702 Continuous (measured) (quantitative) Type of Data Classified into categories (e.g. good/bad) Count of events (e.g. non-conformities) Constant sample size Variable sample size Constant sample size Variable sample size “c“ chart “u“ chart “p“ chart “np“ cha
27、rt Type of ChartsBS 5701-2:2003 BSI 31 October 2003 3 5.1.2 Step 1 Select the sample size and frequency Select a sample size that is large enough so that the expected number of non-conformities (c) observed per sample is more than four. A useful source of information to assist this selection is any
28、recent history of the process. It can be in the form of inspection records. From such or similar information it can be possible to establish a level of occurrence of the non-conformity, e.g. the total number of non-conformities recorded divided by the total number of items inspected. From this value
29、, it would be possible to estimate a sample size that would have an expected number of non-conformities greater than four. For example, if past records indicate that of the most recent inspections 2 545 items had been taken and 140 non-conformities had been observed amongst them. The level of occurr
30、ence of the non-conformity can be estimated as 0.055, i.e. 140/2 545. Using this estimate, if a sample of 75 were selected, the expected number of non-conformities per sample would be 4.125, i.e. 0.055 75. The minimum sample size required is 4/0.005 5 = 72.7, rounded up to 73. After running the char
31、t for a while, a review should be undertaken to check the appropriateness of the selected sample size and adjust it as necessary. If there is no information, it is suggested that an audit is carried out on the process. During this audit, a random sample is taken from the output of the process and in
32、spected for the non-conformity. The result is used as described above. The selection of the frequency of sampling should be determined according to those events within the process that are likely to have an impact on the occurrence of the non-conformity, e.g. a change of operator or a shift change.
33、This is sometimes known as the assessment of process dominance. The sampling scheme should be selected so that the full effect of such process events will be observed. The sampling frequency also needs to take account of any production rate. It would be nonsense to specify a sample size so large tha
34、t the production rate would not produce that quantity in the time allowed. A further consideration about the sampling frequency is how quickly information about the process will be collected. Clearly, a shorter time interval with a smaller sample size will provide more rapid information but will not
35、 be as powerful at detecting lesser special causes. A larger sample taken over a longer time interval is more powerful but is not so rapid. Figure 2 illustrates where this information can be recorded on a control chart. See “Step 1” in the figure. 5.1.3 Step 2 Record the sample information In the ap
36、propriate rows and columns, record the information concerning each sample. The chart requires the date, sample size (n) and the number of non-conformities (c). In the case of a “c” chart, the sample size is a constant and so it can be entered as shown in Figure 2. All subsidiary information relevant
37、 to the process should also be collected. For example, if it is thought important to record information such as a batch number or which shift was working at a particular time then other rows can be added to the chart. 5.1.4 Step 3 Select a scale for the control chart The vertical scale of the chart
38、should be labelled according to the non-conformity that the samples are inspected for. The scaling should be selected to begin at zero and extent to about three times the expected average number of non-conformities . This scale should be enough to enable control lines to be drawn and most sample obs
39、ervations to be plotted. 5.1.5 Step 4 Plot the number of non-conformities Plot the number of non-conformities (c) for each sample. Ensure that every plotted point is joined to its neighbours by straight lines. This is so that trends can be more easily identified and should any points be missing, the
40、y will be more obvious. c ()BS 5701-2:2003 4 BSI 31 October 2003 Figure 2 Single characteristic “c” chart Average = UCL = LCL = Target Sample Size: Frequency: Plant Area Part ID Operation np p c u 51 01 52 02 53 03 5 Date and/or Time Sample Size (n) Number (np,c) Proportion (p,u) Control Chart for A
41、ttribute Data - Single Characteristic 8.25 16.87 - 150 per day 22 20 18 16 14 12 10 8 6 4 2 0 Number of Brass Particles Production G752 Controller Final Assembly 19 20 21 22 23 26 27 28 29 30 150 14 10 6 6 16 8 4 11 86 8 4 9981 26866 15 16 567 8 91 21 31 4 June Step 1 Step 2 Step 3 Step 4 Data Colle
42、ctionBS 5701-2:2003 BSI 31 October 2003 5 5.1.6 Step 5 Calculate the process average To establish the level of the process average, data gathering should be done over a suitably long enough period. This period should be at least 20 samples long and the period should be indicated on the control chart
43、. In Figure 2, it has been written at the bottom of the chart. The average number of non-conformities can be found by summing all of the non-conformities observed during the data collection period. Divide this sum by the number of samples (k) taken. For example, from the data given in Figure 2: wher
44、e k = 20, here. This calculation can be recorded at the top of the chart, as shown in Figure 3. 5.1.7 Step 6 Calculate the control limits Annex B provides the formulae for the control limits. The use of the formulae is illustrated in Figure 3. Here, the calculated value for the lower control limit (
45、LCL) is less than zero. Since this is an illogical result, because the number of non-conformities can never be less than zero, the lower control limit (LCL) is not plotted. The technical reasons for this are explained in BS 5701-3. 5.1.8 Step 7 Draw the control and centre lines onto the chart Draw t
46、he centre and control lines as follows: centre line draw the process average onto the chart using a dashed horizontal line. Some practitioners prefer to draw this line in a green colour if a colour coding system is chosen. control lines draw the upper (and lower, if applicable) control line onto the
47、 chart using a solid horizontal line. This line is often drawn in red. 5.1.9 Step 8 Establish the control limits for on-going control Review the chart for any out-of-control signals for the data gathered during the data collection period. If there are no out-of-control signals during this period, th
48、e calculated limits can be used for the future control of the process. The centre line and the control lines can be drawn forwards on the control chart as shown in Figure 4. Should some of the plotted points gathered during the data collection period produce out-of-control signals, it will be necess
49、ary to investigate the reason. Depending on the outcome, a further data collection period might be necessary. If such a reason is found, and should action be taken to prevent a future occurrence of the same, then the control limits can be recalculated excluding the sample that contained the “special cause”. If the remaining samples now indicate an “in-control” pattern within the revised limits, these revised limits can then be used for o
