
CONTROL CHARTName:
For each of the supported control charts, limits have been determined for signaling when a response is "out of control". That is, if the points on the control chart are within the control limits, the data is considered "in control". When a point is outside these control limits, the data is considered "out of control" and the process should be examined to determine the cause. In developing the control limits, an effort is made to balance quick detection while minimizing "false positives" (i.e., signaling that a process is out of control when it is in fact still in control). Quick detection is desired to minimize the number of potentially bad units produced. Minimizing false positives is desired since shutting down the process can result in unnecessarily lost production (and possibly significant cost). The mean control chart is the most commonly used control chart for detecting a change in location. The CUSUM and EWMA charts were developed to detect small shifts of location. The standard deviation control chart and range control chart are the primary control charts for detecting a change in the variability of a process. Typically, the data for control charts is divided into batches (subgroups) and the appropriate statistic is computed and plotted for each subgroup. The MOVING control charts are used for the case when the data are not divided into subgroups. The ISO control chart is a variant of control charts used in the ISO 13528 standard for proficiency studies for multiple rounds. There is separate documentation for the mean, standard deviation, range, cusum, ewma, and the various proportion and counts control charts. This documentation may contain more details for that specific type of control chart. The control chart consists of:
In addition, horizontal lines are drawn at the mean (i.e., the mean of the means, ranges, standard deviations, or other appropriate statistic) and at the upper and lower control limits.
where <stat> is one of XBAR (or MEAN), R (or RANGE), S (or SD), CUSUM, or EWMA; <y> is the response variable; <x> is a variable containing the subgroup identifications; and where the <SUBSET/EXCEPT/FOR qualification> is optional. Enter one of MEAN, RANGE, S, CUSUM, or EWMA to specify what type of control chart to generate.
where <stat> is one of AVERAGE, RANGE, or SD; <y> is the response variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
where <y> is the response variable containing the number of defectives for each subgroup; <size> is a variable containing the sample size for each subgroup; <x> is a variable containing the subgroup identifications; and where the <SUBSET/EXCEPT/FOR qualification> is optional. If P is specified, then the percentage of defectives is plotted. If NP is specified, then the number of defectives is plotted.
where <y> is the response variable containing the number of defectives for each subgroup; <x> is a variable containing the subgroup identifications; and where the <SUBSET/EXCEPT/FOR qualification> is optional. The C chart is used for Poisson counts. For the Poisson counts case, you can have either an area of material that is being inspected or a sample size. The C chart is used when the subgroups have constant area (or equal sample size).
where <y> is the response variable containing the number of defectives for each subgroup; <area> is a variable containing the sample size or area adjustment for each subgroup; <x> is a variable containing the subgroup identifications; and where the <SUBSET/EXCEPT/FOR qualification> is optional. The U chart is used for Poisson counts. For the Poisson counts case, you can have either an area of material that is being inspected or a sample size. The U chart is used when the subgroups have unequal area (or unequal sample size).
where <y> is the response variable; <x> is a variable containing the subgroup identifications; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This is a variant of the mean control chart. This chart is constructed as follows:
For the ISO 13528 control chart, the subgroups are typically the different laboratories. The ISO 13528 control chart is used to identify laboratories that are not consistent with the other laboratories in the proficiency study.
RANGE CONTROL CHART Y X S CONTROL CHART Y X MOVING AVERAGE CONTROL CHART Y X
One of the motivations for control charts is to detect problems during production rather than after production. That is, if a production problem can be detected early, then this can help minimize the number of defective units produced.
LET USL = <value> LET LSL = <value> This sets the target value, the upper control limit, and the lower control limit respectively.
For example, some analysts prefer to draw the value of the statistic as a character or spike rather than a connected line. If you include both Dataplot calculated and userspecified limits, you may want to draw them with different colors or different line styles. For the other control charts, the documentation for the specific control charts provides a similar listing for the mapping of traces to chart features. These may vary somewhat from the above list.
The HOTELLING CONTROL CHART can be used to simultaneously monitor multiple response variables for a shift in location. Although you can monitor multiple response variables with individual mean control charts, this assumes that the response variables are independent. The Hotelling control chart takes the correlation structure into account.
The command
can be used to specify the control limits used. DEFAULT uses the standard control chart limits. WECO uses the Western Electric guidlines. ISO 13528 uses the +/2 and +/3 limits (this assumes the response variable has been transformed to a zscore). Note that the if the WECO rules are turned on, the following is done:
The WECO rules have been criticized for generating too many false positives.
The 2012/02 version added the HIGHLIGHT option. This is demonstrated in the Program 2 example below.
STANDARD DEVIATION CONTROL CHART for S CONTROL CHART
Kaoru Ishikawa (1982), "Guide to Quality Control," Asian Productivity Organization, (Chapter 7). Thomas Ryan (1989), "Statistical Methods for Quality Improvement", Wiley. Douglas Montgomery (2001), "Introduction to Statistical Quality Control", Fourth Edition, Wiley. ISO 13528 (2005), "Statistical Methods for use in proficiency testing by interlaboratory comparisons," First Edition, 20050901.
1988/01: Support for P, PN, U, and C charts 1990/07: Support for user specified control limits 1997/03: Support for CUSUM and EWMA charts 1997/03: Support for moving average, moving range and moving sd charts 2012/01: Support for highlighting option 2012/01: Support for WECO and ISO 13528 control limits 2012/02: Support for ISO 13528 control chart SKIP 25 READ CROARK3.DAT Y X . MULTIPLOT CORNER COORDINATES 2 2 98 98 MULTIPLOT SCALE FACTOR 2 MULTIPLOT 2 2 TITLE CASE ASIS CASE ASIS TITLE OFFSET 2 LINE BLANK SOLID DASH DASH DOTT DOTT CHARACTER CIRCLE CHARACTER FILL ON CHARACTER HW 1 0.75 . YLIMIT 0.5 0.6 MAJOR YTIC MARK NUMBER 6 Y1TIC MARK LABEL DECIMAL 2 XLIMITS 0 100 X1TIC MARK OFFSET 0 20 TITLE Raw Data PLOT Y . YLIMIT MAJOR YTIC MARK NUMBER Y1TIC MARK LABEL DECIMAL XLIMITS 0 40 X1TIC MARK OFFSET 0 0 TITLE Mean Control Chart MEAN CONTROL CHART Y X . TITLE Range Control Chart RANGE CONTROL CHART Y X . TITLE SD Control Chart STANDARD DEVIATION CONTROL CHART Y X . END OF MULTIPLOT MOVE 50 98 JUSTIFICATION CENTER TEXT Control Charts for Magnification Standard for SEMs (CROARK3.DAT) MOVE 50 2 TEXT Batch DIRECTION VERTICAL MOVE 2 50 TEXT Distance (Micrometers) DIRECTION HORIZONTALProgram 2: SKIP 25 READ CROARK3.DAT Y X LET N = SIZE Y LET TAG = 0 FOR I = 1 1 N LET TAG = 1 SUBSET Y > 0.58 . SET WRITE DECIMALS 3 LABEL CASE ASIS CASE ASIS TITLE Magnification Standard for SEMs Y1LABEL Distance (Micrometers) XLIMITS 0 40 X3LABEL AUTOMATIC LINE SOLID SOLID DASH DASH BLANK CHARACTER BLANK BLANK BLANK BLANK CIRCLE CHARACTER FILL ON ALL CHARACTER HW 1 0.75 ALL CHARACTER COLOR RED ALL . HIGHLIGHT MEAN CONTROL CHART Y X TAG . LET TAG = 0 FOR I = 1 1 N LET TAG = 1 SUBSET Y > 0.58 LIMITS XLIMITS 0 100 XTIC MARK OFFSET 0 10 HIGHLIGHT MOVING MEAN CONTROL CHART Y TAGProgram 3: LET X = SEQUENCE 1 10 1 50 LET Y = NORMAL RANDOM NUMBERS FOR I = 1 1 500 LET Y2 = Y LET Y2 = 7*Y FOR I = 351 1 425 LET Y = Y2 . SET WRITE DECIMALS 3 LABEL CASE ASIS CASE ASIS Y1LABEL Normal Random Numbers TITLE AUTOMATIC LINE SOLID SOLID DASH DASH BLANK CHARACTER BL BL BL BL CIRCLE CHARACTER FILL ON ALL CHARACTER HW 0.5 0.375 ALL CHARACTER COLOR RED ALL XLIMITS 0 50 XTIC MARK OFFSET 1 2 . SET CONTROL CHART LIMITS WECO MEAN CONTROL CHART Y XProgram 4: skip 25 read croark3.dat y roundid skip 0 let n = size y . let z = zscore y roundid let z = zscore y let matid = sequence 1 1 3 for i = 1 1 n . label case asis y1label zscore x1label batch xlimits 0 35 x1tic mark offset 0 2 y1tic mark offset 0.2 0.2 title case asis title offset 2 title ISO 13528 Control Chart line solid solid dash dash dash dash blank character blank blank blank blank blank blank blank character hw 1 0.75 all character fill on all . iso 13528 control chart z roundid . line blank solid dash dash dash dash blank blank blank character circl blank blank blank blank blank 1 2 3 highlight iso 13528 control chart z roundid matidProgram 5: . Read data: Year is essentially the round and there are 10 . materials. skip 25 read turner.dat labid z year quart matid matave skip 0 . . Note that we want to generate the control chart treating . laboratory as the "groupid" variable. Generate a separate . plot for each material. . case asis label case asis title case asis title offset 2 line blank solid solid solid solid solid blank line color black black blue blue red red black character circle blank blank blank blank blank blank character hw 1 0.75 all character fill on all . multiplot corner coordinates 2 2 98 98 multiplot scale factor 3 multiplot 3 4 . xlimits 0 90 major xtic mark number 4 ylimits 4 4 major ytic mark number 5 let nmat = unique matid loop for k = 1 1 nmat title Material ^k iso 13528 control chart z labid subset matid k end of loop end of multiplot . justification center move 50 98 text ISO 13528 Control Chart for TURNER.DAT move 50 2 text Laboratory direction vertical move 2 50 text ZScoreProgram 6: . Step 1: Read the data . dimension 40 columns skip 25 read turner.dat labid z year quarter matid matave let roundid = year skip 0 . . Step 2: Set plot control settings . case asis label case asis title case asis title offset 2 . y1label zscore x1label Laboratory ID xlimits 0 90 x1tic mark offset 2 0 ytic mark offset 0.2 0.2 . line blank solid solid solid solid solid blank line color black black blue blue red red black character circle blank blank blank blank blank blank character hw 1 0.75 character fill on . . Step 3: Generate 13528 Control Charts . title ISO 13528 Control Chart  Combine Materials iso 13528 control chart z labid . line solid solid dash dash dash dash blank character blank blank blank blank blank blank circle title ISO 13528 Control Chart  Show Individual Materials iso 13528 control chart z labid . line blank all line solid solid dash dash dash dash character blank blank blank blank blank blank 1 2 3 4 5 6 7 8 9 10 title ISO 13528 Control Chart  Identify Materials highlight iso 13528 control chart z labid matid  
Date created: 02/10/2015 Last updated: 12/04/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 