ISO-7873-1993.pdf
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1、INTERNATIONAL STANDARD IS0 7873 First edition 1993-l 2-l 5 Control charts for arithmetic average with warning limits Cartes de contr8le de la moyenne arithmdtique A limites de surveillance Reference number IS0 7873.1993(E) Foreword IS0 (the International Organization for Standardization) is a worldw
2、ide federation of national standards bodies (IS0 member bodies). The work of preparing International Standards is normally carried out through IS0 technical committees. Each member body interested in a subject for which a technical committee has been established has the right to be represented on th
3、at committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. IS0 collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization. Draft International Standards adopted b
4、y the technical committees are circulated to the member bodies for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote. International Standard IS0 7873 was prepared by Technical Committee ISO/TC 69, Applications of statistical metho
5、ds, Sub-Committee SC 4, Statistical process control. Annex A forms an integral part of this International Standard. Annexes B, C and D are for information only. 0 IS0 1993 All rights reserved. No part of this publication may be reproduced or utilized in any form or by any means, electronic or mechan
6、ical, including photocopying and microfilm, without per- mission in writing from the publisher. International Organization for Standardization Case Postale 56 l CH-1211 Geneve 20 l Switzerland Printed in Switzerland ii -,-,- IS0 7873:1993(E) Introduction The statistical control of processes using ar
7、ithmetic average control charts with warning limits is a modification of Shewhart control charts. Control charts for the arithmetic average using both warning and action limits are characterized by higher sensitivity to a process level shift. Arithmetic average control charts with warning limits are
8、 able to reveal smaller shifts of the mean value of the controlled quality measure because of additional information obtained from the points being accumulated in the warning zone. In addition, sudden large shifts in process level are de- tectable if sample average values fall beyond action limits.
9、In comparison with Shewhart control charts, they are more sensitive in the case of minor and slowly forming biases of the quality measure (that is, shifts not ex- ceeding 2,5a/ Jn, where (T is the standard deviation of the quality measure and n is the sample size). . . . III INTERNATIONAL STANDARD I
10、S0 7873:1993(E) Control charts for arithmetic average with warning limits 1 Scope This International Standard specifies procedures for the statistical control of processes by using control charts based on calculating the arithmetic average of a sample and using warning limits and action limits. It i
11、s assumed that for large lots and for the mass output of piece and batch production, such a measure of quality is a random variable following a normal dis- tribution. However, when averages of four or more items are plotted, this assumption of a normal dis- tribution is not necessary for control pur
12、poses (see 4.2). 2 Normative references The following standards contain provisions which, through reference in this text, constitute provisions of this International Standard. At the time of publi- cation, the editions indicated were valid. All standards are subject to revision, and parties to agree
13、ments based on this International Standard are encouraged to investigate the possibility of applying the most re- cent editions of the standards indicated below. Members of IEC and IS0 maintain registers of cur- rently valid International Standards. IS0 3534-l :1993, Statistics - Vocabulary and sym-
14、 bols - Part 1: Probability and general statistical terms. IS0 3534-2:1993, Statistics - Vocabulary and sym- bols - Part 2: Statistical quality control. 3 Definitions For the purposes of this International Standard, the definitions given in IS0 3534-l and IS0 3534-2 apply. 4 Conditions of applicatio
15、n 4.1 The implementation of the statistical methods of process control should be preceded by statistical analysis during a base period of the quality measure to be controlled in order to provide a basis for con- structing relationships between a process (the oper- ations) and product quality, as wel
16、l as for producing recommendations for the adjustment of the process. If the statistical analysis shows that the process is out of control, and the process capability does not meet specified requirements, it is necessary to determine the causes of level shifts ) and ways of adjusting the process. 4.
17、2 In order to apply the rules of this International Standard, it is necessary first to establish the follow- ing. a) The arithmetic average X approximates a normal distribution. Except for extremely unusual circum- stances, averages of samples of four or more items will, under the Central Limit Theo
18、rem, follow approximately a normal distribution even though the individual observations may not. b) For best results, the individual observations aver- aged to obtain X are made by scale-measuring in- struments with scale divisions not exceeding a/2. c) The underlying, but unknown, mean value p of t
19、he sample x values defines the current process level. If the process level shifts, then so will p. The pro- cess level should then be adjusted. d) The target level cl0 corresponds to the value of the middle line of the tolerance zone of the quality measure specified in the documents when the two-sid
20、ed criterion is used. 1) “Level shifts” means a case in which p becomes equal to p, or pml. 1 -,-,- IS0 7873:1993(E) e) The standard deviation u of the quality measure is assumed to remain constant and acceptable. This assumption must be verified by using sample standard deviation or range control c
21、harts. f) 9) In the case of the one-sided criterion p1 cl0 or p-, p. and Jo, 1 the ARL for the two-sided criterion coin- cides numerically with the ARL for the one-sided cri- terion (see table C.l). 7.2.4 For the values of 6 Jn missing from tables 1 to 4, the corresponding L, values are obtained thr
22、ough linear interpolation. 7.3 The sample size n affects the ARL curves, as shown through the formulae in annex C, as well as the parameters po, p+, and/or pL- , g and K. Moreover, for the same total number of observations or measurements the control chart can be designed with a long sampling period
23、, t, and a small sample size n, or conversely. In each specific application, various trial combinations of n and t should be investigated during design of the control chart to determine the resulting values of Lo and L,. The design should be evaluated in terms of the elapsed process time associated
24、with the result- ing values of L, and L,. In most cases, the pre-existing sampling plan in, A will be the “base” trial combination, and other trial designs should be compared with the base design with respect to performance Cr, and L,) and cost. 7.4 Tables 1 to 4 are used for choosing a plan of the
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