1、BRITISH STANDARD BS 5701-3:2003 Guide to quality control and performance improvement using qualitative (attribute) data Part 3: Technical aspects of attribute charting: special situation handling ICS 03.120.30 BS 5701-3:2003 This British Standard was published under the authority of the Standards Po
2、licy 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 42736 6 Committees responsible for this British Sta
3、ndard 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 Development Associ
4、ation (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 5701-3:2003 BSI 31 October 20
5、03 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 Qualitative data fundamentals 1 5 Limitations of standard control chart limits: appropriate counter-measures 3 6 Specialized design control charts 18 7
6、Attribute charts for measured data situations 22 Annex A (normative) Poisson and binomial tests 26 Annex B (normative) Poisson-based control chart limits 28 Bibliography 31 Figure 1 Illustration of the variation in distribution shape with changes in the mean 5 Figure 2 Count data control limit selec
7、tion flow chart 6 Figure 3 “c” chart for accidents 7 Figure 4 “c” chart for orders per day 9 Figure 5 Histogram of adjustment data 10 Figure 6 Normal probability plot of adjustment data 10 Figure 7 Control chart for number of adjustments per unit 11 Figure 8 Histogram of fabric fault data 12 Figure
8、9 Run chart of fabric faults indicating significant improvement in performance 12 Figure 10 Control chart for number of faults per roll 13 Figure 11 Change in shape of the binomial distribution with different means 14 Figure 12 Classified data distribution selection flow chart 15 Figure 13 Control c
9、hart for non-conforming weld data 18 Figure 14 Universal “u” chart for stud threads 20 Figure 15 How to select the appropriate control chart for measurable data 22 Figure 16a) Two-way attribute control chart 23 Figure 16b) Illustration of process diagnosis using two-way control charts 24 Table 1 Eff
10、ect of method of calculation of action control limits in terms of value of the mean 4 Table 2 Example of difference between conventional and Poisson-based control limits 7 Table 3 Conventional v Poisson control limits 8 Table 4 Binomial probabilities for n = 500: p = 0.019 8 17 Table 5 Plotting data
11、 for standardized control charts 18 Table 6 Example of tabulation for setting up a universal “u” chart 19 Table 7 Formulae for setting up a demerits attribute chart 20 Table 8 Results of twenty consecutive audits in multiple characteristic control chart format 21 Table A.1 Critical values of varianc
12、e ratio for testing binomial or Poisson distribution assumptions 27 Table B.1 Poisson-based upper action control limits (set at 0.001 35 probability) 28 Table B.2 Poisson-based lower action control limits (set at 0.001 35 probability) 29 Table B.3 Poisson-based upper warning control limits (set at 0
13、.022 8 probability) 29 Table B.4 Poisson-based lower warning limits (set at 0.022 8 probability) 29BS 5701-3:2003 ii BSI 31 October 2003 Foreword BS 5701-3:2003 partially supersedes BS 5701:1980 and BS 2564:1955 and all four parts of BS 5701 together supersede BS 5701:1980 and BS 2564:1955, which ar
14、e withdrawn. Qualitative data can range from overall business figures such as percentage profit to detailed operational data, such as percentage absenteeism, individual process parameters and product/service features. The data can either be expressed sequentially in yes/no, good/bad, present/absent,
15、 success/failure format, or as summary measures (e.g. counts of events and proportions). For measured data control charting refer to BS 5702-1. The focus throughout the BS 5701 family of standards is on the application of attribute control charts to monitoring, control and improvement. The roles of
16、associated, mainly pictorial, diagnostic, presentation and performance improvement tools, such as priority (Pareto) diagrams, cause and effect diagrams and flow charts are also indicated. This aim of BS 5701 is to be readily comprehensible to the very extensive range of prospective users and so faci
17、litate widespread communication, and understanding, of the method. As such, it focuses to the greatest extent possible on a practical non-statistical treatment of the gathering and charting of qualitative data. BS 5701-1 demonstrates the business benefits, and the versatility and usefulness of a ver
18、y simple, yet powerful, pictorial control chart method for monitoring and interpreting qualitative data. In BS 5701-1, the treatment of charting of qualitative data is essentially at appreciation level. However, it is intended to provide adequate information for a gainful first application, by a typ
19、ical less statistically inclined user, in many everyday situations. BS 5701-2 continues to focus on the application of standard attribute charts to the monitoring, control and improvement of business processes. This is done at a technical level more suitable for practitioners. BS 5701-3 concentrates
20、 on the statistical basis of, and technical rationale for, attribute control charting. It also gives guidance on dealing with special situations. 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 i
21、nclude all the necessary provisions of a contract. Users of British 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, pa
22、ges i and ii, pages 1 to 31 and a back cover. The BSI copyright notice displayed in this document indicates when the document was last issued.BS 5701-3:2003 BSI 31 October 2003 1 1 Scope BS 5701-3 describes the technical and statistical foundations of attribute control charting. It also gives guidan
23、ce on dealing with special situations. 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 amendmen
24、ts) applies. BS EN ISO 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
25、For the purposes of this 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 with one exception. The exception is intended for purposes of simplicity. It relates to the symbols for population parameters, sample statistics
26、and their realized values. It is standard statistical practice for population parameters to be symbolized by lower case Greek letters in italics. For example, mean and standard deviation are denoted by and . A population parameter is a summary measure of the value of some characteristic of a populat
27、ion. A sample statistic is a summary measure of some observed value of a sample. Sample statistics are symbolized by upper case Latin letters in italics. For example, mean and standard deviation are denoted by and . Realized values of sample statistics to be symbolized by lower case Latin letters in
28、 italics. For example, mean and deviation are denoted by and . Upper case Latin letters in italics are used in Annex A and its applications. 4 Qualitative data fundamentals 4.1 General Two general classifications of data are quantitative data and qualitative data. This standard focuses on qualitativ
29、e data. Qualitative data are divided for convenience, into two categories, classified data and count data. 4.2 Classified data and the binomial distribution With classified data, each item of data is classified as being one of a number of categories. Frequently the number of categories is two, i.e.
30、a binary situation where, for instance, results are usually expressed as 0 and 1, or as, good/bad, success/failure, profit/loss, in/out, or presence/absence of a particular characteristic. Data having two classes is termed “binomial” (binomial = “two names”) data. A measure can be inherently binomia
31、l, e.g. where a profit or loss is made, or of someone is in or out. Sometimes it is arrived at indirectly by categorizing some other numerical measure. Take, for instance, a case where telephone calls are classified on whether or not they last more than 10 min or, perhaps, whether or not they are an
32、swered within six rings. The binomial distribution is a statistical distribution giving the probability of obtaining a specified number of particular outcomes (e.g. successes) in a specified number of independent trials with a constant probability of success in each. X S x sBS 5701-3:2003 2 BSI 31 O
33、ctober 2003 The conditions that need to be satisfied for a binomial distribution are: a) there is a fixed number of trials, n; b) only two possible outcomes are possible at each trial; c) the trials are independent; d) there is a constant probability of a particular outcome e.g. success, “p”, in eac
34、h trial; e) the variable is the total number of successes in n trials. The binomial distribution is very cumbersome to calculate. When dealing with control limits other distributions can be used as approximations to the binomial. For example, if p is small, in Equation 2, (1 p) approaches 1 and the
35、standard deviation of the binomial distribution approximates to the square root of its mean. Equations (1) and (2) then become identical to equations (3) and (4) of the Poisson distribution. In standard statistical process control methodology, binomial data is monitored using: i) “p” charts for prop
36、ortions, particularly when the sample size is variable; and ii) “np” charts for numbers from samples of constant size. 4.3 Count data and the Poisson distribution Count data relates to counts of events where each item of data is the count of the number of particular events per given period of time o
37、r quantity of product. Instances are: number of accidents or absentees per month, number of operations or sorties per day, number of incoming telephone calls per minute, or number of non-conformities per unit or batch. The Poisson distribution has two principal parts to play in this standard: i) as
38、an approximation to the more cumbersome binomial when: ii) as a distribution in its own right. The binomial distribution applies to the situation where an item, say, is classified as conforming or non-conforming. Here one can count either the number of items non-conforming or the number of items con
39、forming. Poisson data arises when one can count only, say, the number of faults in an item not the number of non-faults. The conditions that need to be satisfied for a Poisson distribution are that events occur randomly, singly, uniformly and independently. The validity of the Poisson model hinges o
40、n the independence of events and their occurrence at an average rate that is assumed to be stable (in the absence of special causes). Two fundamental features of the Poisson distribution are: a) the connection between its standard deviation and mean; and b) the results of summation of two independen
41、t Poisson variables. Regarding a), the mean and standard deviation of a Poisson distribution are given by: This relationship is useful for establishing the validity of the Poisson model for a particular set of data. Whilst many real life situations can suggest that Poisson is a reasonable underlying
42、 model it would be unwise to take this for granted. Sometimes a degree of clustering of events is present, for example, of accidents and faults. This has the effect of increasing the spread beyond that of the Poisson distribution. This wider spread, termed over-dispersion, can gives rise to a higher
43、 false alarm rate when monitoring using control charts. To reduce the risk of assuming an incorrect model a simple “dispersion” test is often recommended (see Annex A). This involves comparing the sample variance of the data with the mean. mean = np (1) standard deviation = (2) n is large and p is s
44、mall, say, n 20 and p k 0.1 (i.e. k 10 %); mean = m (3) standard deviation = (4) np 1 p () mBS 5701-3:2003 BSI 31 October 2003 3 Equation (4) indicates that the variance (the square of the standard variation) is equal to the mean for a Poisson distribution. Hence if: a) sample variance equals the me
45、an, the Poisson model is plausible; b) sample variance is “much greater or smaller than” the mean, the Poisson model is implausible. This variance comparison can be supported by other methods such as a graphical evaluation of the data and by goodness of fit tests such as the chi-squared test for dif
46、ferences between expected and observed frequencies. Regarding b), distribution of the sum of independent Poisson variables is still Poisson. For example: “if two sets of Poisson data are independent with separate means m 1and m 2 , their sum is also Poisson with mean, (m 1+ m 2 )”. This fact has con
47、siderable impact on counts where multiple characteristics are involved. Instances are adding together different types of flaws, absenteeism for different reasons and injuries of different kinds. Another application is where events of a particular kind have a very small mean so that counts are freque
48、ntly zero. This enables one to increase the number of sampled items (e.g. counts per month rather than per day or week). In standard statistical process control, Poisson data is monitored using: 1) “c” charts for numbers (counts of events) from samples of constant size; and 2) “u” charts for proport
49、ions (number of events per sample), particularly when the sample size is variable. 5 Limitations of standard control chart limits: appropriate counter-measures 5.1 Bases for selection of control chart limits for count data 5.1.1 Introduction It is common practice throughout the world to base standard control chart limits on the assumption of normality of data. Control limits are then calculated thus: a) action control limits = mean
