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1、STDaJIS Z 902L-ENGL 1998 D 4933b08 0554922 b32 D JIS t 2) X-R (moving range) control chart ; 3) median chart and R chart. b) Attributes control charts 1) fraction nonconforming (p) chart or number of nonconforming units (np) chart ; 2) number of nonconformities (c) chart or nonconformities per unit
2、(u chart. Informative reference : Nonconforming is not to be in compliance with a spe- cific requirements. In addition nonconformin units _- - 2 _- -_- g are the items having one or more nonconformities and the number of nonconformities is the number of the places of nonconformity. Therefore, . -_-_
3、-_ _- Number of nonconforming units Subgroup size , and - - Number of nonconformities per unit - Number of nonconforming units - Number of units of subgroup . 4.2 Control charts where no standard values are given The purpose here is to discover whether observed values of the plotted characteristics,
4、 such as x, R or any other statistic, vary among themselves by an amount greater than that which should be attributed to chance alone. Control charts based entirely on the data col- lected from samples are used for detecting those variations caused other than by chance. 4.3 Control charts with respe
5、ct to given standard values The purpose here is to identify whether the observed values of x, etc., for several subgroups of n ob- servations each, differ from the respective standard values X, (or p0), etc. by amounts greater than that expected to be due to chance causes only. The difference betwee
6、n charts with standards given and those where no standards are given is the additional requirement concerning the location of the centre and variation of the process. The specified values may be based on experience obtained by using control charts with no prior information or specified standard valu
7、es. They may also be based on economic values established upon consideration of the need for service and cost of production or be nominal values designated by the product specifications. Copyright Japanese Standards Association Provided by IHS under license with JSALicensee=IHS Employees/1111111001,
8、 User=Wing, Bernie Not for Resale, 03/12/2007 22:07:45 MDTNo reproduction or networking permitted without license from IHS -,-,- STD-JIS Z 902L-ENGL 1998 - 4933b08 0554931 b45 6 Z 9021 : 1998 Preferably, the specified values should be determined through an investigation of preliminary data that is s
9、upposed to be typical of all future data. The standard val- ues should be compatible with the inherent process variability for effective function- ing of the control charts. Control charts based on such standard values are used particularly during manufacture to control processes and to maintain pro
10、duct unifor- mity at the desired level. 5 Variables control charts 5.1 Outline of variable control charts Variables data represent observations obtained by measuring and recording the numerical magnitude of a characteristic for each of the units in the subgroup under consideration. Examples of varia
11、bles mea- surements are length in meters, resistance in ohms, noise in decibels, etc. Variables charts - and especially their most customary forms, the and R charts - represent the classic application of control charting to process control. Control charts for variables are particularly useful for se
12、veral reasons. Most processes and their output have characteristics that are measurable, so the potential applicability is broad. A measurement value contains more information than a simple yes - no state- ment. The performance of a process can be analyzed without regard to the specifica- tion. The
13、charts start with the process itself and give an independent picture of what the process can do. Afterwards, the process may or may not be compared with the specification. Although obtaining one piece of measured data is generally more costly than obtaining one piece of goho go data, the subgroup si
14、zes for variables are almost always much smaller than those for attributes, and so are more efficient. This helps to reduce the total inspection cost in some cases and to shorten the time gap between the production of parts and corrective action. Informative reference : The reduction of the total in
15、spection cost is reasonable to _-. _-_-._ be- onsiriereb- as- the reduction- of the -tote!- ontroi O S L A normal (Gaussian) distribution is assumed for within-sample variability for all variables control chart applications considered in this Standard and departures from this assumption will affect
16、the performance of the charts. The factors for computing control limits were derived using the assumption of normality. Since most control limits are used as empirical guides in making decisions, reasonably small departures from normality should not cause concern. In any case, because of the central
17、 limit theorem, averages tend to be normally distributed even when individual observations are not; this makes it reasonable to assume normality for charts, even for sample sizes as small as 4 or 5 for evaluating control. When dealing with individual observations for capability study purposes, the t
18、rue form of the distribution is important. Periodic checks on the continuing validity of such assumptions are advisable, particularly for ensuring that only data from a single population are being used. It should be noted that the distribution of the ranges and standard deviations are not normal, al
19、though approximate normality was as- sumed in the estimation of the constants for the calculation of control limits, which is satisfactory for an empirical decision procedure. Copyright Japanese Standards Association Provided by IHS under license with JSALicensee=IHS Employees/1111111001, User=Wing,
20、 Bernie Not for Resale, 03/12/2007 22:07:45 MDTNo reproduction or networking permitted without license from IHS -,-,- STD-JIS 2 9021-ENGL 1998 4933608 0554932 581 I 7 Z 9021 : 1998 Statistic 5.2 K - R control chart or - 8 control chart Variables charts can describe process data in terms of both spre
21、ad (piece-to-piece variability) and location (process average). Because of this, control charts for variables are almost always prepared and analyzed in pairs - one chart for location and another for spread. The most commonly used pair is the x and R charts. Table 1 and Table 2 give the control limi
22、t formulae and the factors for variables control charts respectively. I Remarks : XO, Ro, SO, p and 00 are given standard values. I Table 1 Control limit formulae for Shewhart variables control charts Central line I UCL and LCL Central line I UCL and LCL Statistic Central line x x R R S S x R S UCL
23、and LCL Central line UCL and LCL 3 f AzR or j? f A33 Ro or dzoo B33, B a Copyright Japanese Standards Association Provided by IHS under license with JSALicensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 03/12/2007 22:07:45 MDTNo reproduction or networking permitted without license
24、from IHS -,-,- STD-JIS Z 902L-ENGL 1998 4933bO8 0554933 418 8 2 9021 : 1998 Table 2 Factors for computing control chart lines - lbservs .ions in xubpui n 2 3 4 5 - 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 - A 2.121 1.732 1.500 1.342 - 1.225 1.134 1 .o61 1.OOO O. 949 O. 905 O. 866 O. 8
25、32 O. 802 O. 775 O. 750 O. 728 O. 707 0.688 O. 671 O. 655 0.640 O. 626 O. 612 0.600 - A, - 1.880 1.023 O. 729 O. 577 0.483 O. 419 O. 373 O. 337 0.308 O. 285 0.266 O. 249 O. 235 O. 223 0.212 O. 203 O. 194 O. 187 O. 180 O. 173 O. 167 O. 162 O. 157 O. 153 - A, - 2.659 1.954 1.628 1.427 1.287 1.182 1 .O
26、99 1.032 O. 975 0.927 O. 886 O. 850 O. 817 O. 789 O. 763 O. 739 0.718 O. 698 O. 680 0.663 0.647 O. 633 O. 619 0.606 - B S 0.000 0.000 0.000 0.000 - O. 030 O. 118 O. 185 O. 239 0.284 0.321 O. 354 O. 382 0.406 O. 428 0 . M 0.466 0.482 O. 497 O. 510 O. 523 O. 534 O. 545 O. 555 O. 565 - Factors for cont
27、rol limits B 4 3.267 2.568 2.266 2.089 - 1.970 1.882 1.815 1.761 1.716 1.679 1.646 1.618 1.594 1.572 1.552 1.534 1.518 1.503 1 ,490 1.477 1.466 1.455 1.445 1.435 - Source : ASTM, Philadelphia, PA, USA B 5 0.OOO o, O00 0.000 0.OOO - O. 029 0.113 0.179 O. 232 O. 276 0.313 0.346 O. 374 0.399 0.421 0.44
28、0 0.458 O. 475 O. 490 0.504 O. 516 O. 528 O. 539 O. 549 O. 559 - B 6 2.606 2.276 2.088 1.964. - 1.874 1.806 1.751 1.707 1.669 1.637 1.610 1.585 1.563 1.544 1.526 1.511 1.496 1.483 1.470 1.459 1.448 1.438 1.429 1.420 - - Dl 0.000 0.000 o. O00 0.OOO - 0.OOO O. 204 O. 388 O. 547 O. 687 0.811 O. 922 1.0
29、25 1.118 1.203 1.282 1.356 1.424 1.487 1.549 1.605 1.659 1.710 1.759 1.806 - 4 3.686 4.358 4.698 4.918 - 5.078 5.204 5.306 5.393 5.469 5.535 5.594 5.647 5.696 5.741 5.782 5.820 5.856 5.891 5.921 5.951 5.979 6.006 6.031 6.056 - - 0 3 0.OOO 0.OOO 0.OOO 0.OOO - 0.000 O. 076 O. 136 0.184 O. 223 0.256 O.
30、 283 O. 307 O. 328 O. 347 O. 363 O. 378 0.391 0.433 O. 415 O. 425 O. 434 0.443 0.451 O. 459 - - 0 4 3.267 2.574 2.282 2.114 - 2.04 1.924 1.864. 1.816 1.777 1.744 1.717 1.693 1.672 1.653 1.637 1.622 1.608 1.597 1.585 1.575 1.566 1.557 1.548 1.541 - Factors for central c 4 0.797 9 0.886 2 0.921 3 0.94
31、00 0.951 5 0.959 4 0.9650 0.969 3 0.972 7 0.975 4 0.9776 0.9794 0.981 O 0.9823 0.983 5 0.9845 0.985 4 0.986 2 0.986 9 0.987 6 0.988 2 0.988 7 0.989 2 0.9896 1/C4 1.2533 1.1284 1.0854 1.0638 1 .O51 O 1.0423 1 .O36 3 1 .O31 7 1 .O28 1 1.025 2 1 .o22 9 1.021 o 1.0194 1.0180 1.0168 1.0157 1.0148 1.0140
32、1.0133 1.0126 1.011 9 1.011 4 1 .O10 9 1 .O10 5 - d2 1.128 1.693 2.059 2.326 - 2.534 2.704 2.847 2.970 3.078 3.173 3.258 3.336 3.437 3.472 3.532 .3.588 3.40 3.689 3.735 3.778 3.819 3.858 3.895 3.931 5.2.1 Steps in the construction of x -R control charts (when no standard values are given) The steps
33、involved in the construction of the xchart and the R chart, for the case when no standard values are given, are described in a) to f). They are described in the form of an example in 5.2.2. In the construction of other control charts, the same basic steps shall be followed but the constants for the
34、computations are different (see Table 1 and Table 2). A general format of a stan- dard control chart form is shown in Figure 2. Modifications to this form can be made in concert with the particular requirements of a process control situation. line i/ their subgroup average and range values are calcu
35、lated (see Table 4) and plotted with the control limits calcu- lated above (see Figure 5). The charts, shown in Figure 5, indicate that the process is out of control at the desired level because there is a sequence of 13 points below the central line in the x chart and 16 points above the central li
36、ne in the R chart. The cause of such a long sequence of low values of the mean should be investigated and eliminated. Copyright Japanese Standards Association Provided by IHS under license with JSALicensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 03/12/2007 22:07:45 MDTNo reproduc
37、tion or networking permitted without license from IHS -,-,- STD*JIS Z 902L-ENGL 1998 W 4933b08 0554940 b58 15 Z 9021 : 1998 Table 4 Tea packing process Subgroup No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Subgroup average x 100.6 101.3 99.6 100.5 99.9 99.5 100.4 100.5 101.1
38、 100.3 100.1 99.6 99.2 99.4 99.4 99.6 99.3 99.9 100.5 99.5 100.1 100.4 101.1 99.9 99.7 Subgroup range R 3.4 4.0 2.2 4.5 4.8 3.8 4.1 1.7 2.2 4.6 5 .O 6.1 3.5 5.1 4.5 4.1 4.7 5.0 3.9 4.7 4.6 4.4 4.9 4.7 3.4 Copyright Japanese Standards Association Provided by IHS under license with JSALicensee=IHS Emp
39、loyees/1111111001, User=Wing, Bernie Not for Resale, 03/12/2007 22:07:45 MDTNo reproduction or networking permitted without license from IHS -,-,- 16 Z 9021 : 1998 z 100 14 X0=100.6 O1 4 5 10 15 20 25 Subgroup number Figure 5 -R chart for data given in Table 4 5.3 X control chart In some process con
40、trol situations, it is either impossible or impractical to take rational subgroups. The time or cost required to measure a single observation is so great that repeat observations cannot be considered. This would typically occur when the measurements are expensive (e.g. in a destructive test) or when
41、 the output at any time is relatively homogeneous. In other situations there is only one possible value, e.g. an instrument reading or a property of a batch of input material. In such situations, it is necessary for process control to be based on indi- vidual readings. In the case of X control chart
42、s, since there are no rational subgroups to provide an estimate of within-batch variability, control limits are based on a variation measure obtained from moving ranges of, often, two observations. A moving range is the absolute difference between successive pairs of measurements in a series ; i.e.
43、the difference between the first and second measurements, then between the second and third, and so on. From the moving ranges, the average moving range is calculated and used for the construction of control charts. Also, from the entire data, the overall average is calculated. Table 5 gives the con
44、trol limit formulae for control charts for individuals. Copyright Japanese Standards Association Provided by IHS under license with JSALicensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 03/12/2007 22:07:45 MDTNo reproduction or networking permitted without license from IHS -,-,- ST
45、D-JIS Z 9021-ENGL 1998 4933608 0554942 420 = Statistic Individual, Moving range, R 17 Z 9021 : 1998 No standard values given Standard values given Central line UCL and LCL Central line UCL and LCL - - X X I E2R x o or P x o f 300 R D4R, DBR Ro or d 2 0 o D200, D l 0 0 - Table 5 Control limit formula
46、e for control charts for individuals a) The X charts are not as sensitive to process changes as are the x - R charts. b) Care shall be taken in the interpretation of X charts if the process distribution is not normal. c) X charts do not isolate the piece-to-piece repeatability of the process and, th
47、ere- fore, it may be better in some applications to use a conventional x - R chart with small subgroup sample sizes (2 to 4) even if this requires a larger period between subgroups. 5 . 3 . 1 Example of X control chart and moving range : No standard values given Table 6 gives the results of laborato
48、ry analysis of “percent moisture” of samples from 10 successive lots of skin milk powder. A sample of skim milk pow- der, representing a lot, is analyzed in the laboratory for such various characteristics as fat, moisture, acidity, solubility index, sedimentation, bacteria and whey protein. It was intended to control the percentage of moisture below 4 % for this process. The sampling variation within a single lot was found to be negligible, so it was decided to take only one