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Dataplot Vol 1 Vol 2

CONTROL CHART

Name:
    ... CONTROL CHART
Type:
    Graphics Command
Purpose:
    Generates the following types of univariate control charts:

    1. Mean (or xbar)
    2. Range (or R)
    3. Standard deviation (or S)

    4. Moving average
    5. Moving range
    6. Moving standard deviation

    7. Cumulative sum (or CUSUM)
    8. Exponentially weighted moving average (or EWMA)

    9. Binomial proportion (or P)
    10. Binomial counts (or NP)
    11. Poisson counts for constant area and equal sub-group sizes (or C)
    12. Poisson counts where area or sub-group sizes are not neccessarily equal (or U)

    13. ISO 13528
Description:
    A control chart, introduced by Walter Shewart, is a data analysis technique for determining if a measurement process has gone out of statistical control. For continuous data, most of the standard control charts attempt to detect either a change in location or a change in variation. The binomial and Poisson control charts have been developed for the cases when the data consist of proportions or counts rather than a continuous response variable.

    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 (sub-groups) and the appropriate statistic is computed and plotted for each sub-group. The MOVING control charts are used for the case when the data are not divided into sub-groups.

    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:

      Vertical axis: the mean, range, standard deviation, or other appropriate statistic for each sub-group;
      Horizontal axis: sub-group designation.

    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.

Syntax 1:
    <stat> CONTROL CHART <y> <x>             <SUBSET/EXCEPT/FOR qualification>
    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 sub-group 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.

Syntax 2:
    MOVING <stat> CONTROL CHART <y>             <SUBSET/EXCEPT/FOR qualification>
    where <stat> is one of AVERAGE, RANGE, or SD;
                <y> is the response variable;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 3:
    <P/NP> CHART <y> <size> <x>             <SUBSET/EXCEPT/FOR qualification>
    where <y> is the response variable containing the number of defectives for each sub-group;
                <size> is a variable containing the sample size for each sub-group;
                <x> is a variable containing the sub-group 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.

Syntax 4:
    C CHART <y> <x>             <SUBSET/EXCEPT/FOR qualification>
    where <y> is the response variable containing the number of defectives for each sub-group;
                <x> is a variable containing the sub-group 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 sub-groups have constant area (or equal sample size).

Syntax 5:
    U CHART <y> <area> <x>             <SUBSET/EXCEPT/FOR qualification>
    where <y> is the response variable containing the number of defectives for each sub-group;
                <area> is a variable containing the sample size or area adjustment for each sub-group;
                <x> is a variable containing the sub-group 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 sub-groups have unequal area (or unequal sample size).

Syntax 6:
    ISO 13528 CONTROL CHART <y> <x>             <SUBSET/EXCEPT/FOR qualification>
    where <y> is the response variable;
                <x> is a variable containing the sub-group 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:

    1. Use a z-score for the response variable. Since the ISO 13528 standard allows several variants of the z-score (e.g., you may use a reference value rather than the sample mean in computing the z-score), it is assumed that the response variable is already a z-score (i.e., the z-score will not automatically be computed from the raw data).

    2. If there is replication, compute a mean for each group. If there is no replication, just use the single data value as the estimate of the mean.

    3. Control limits are set at +/-2 and +/- 3.

    For the ISO 13528 control chart, the sub-groups 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.

Examples:
    MEAN CONTROL CHART Y X
    RANGE CONTROL CHART Y X
    S CONTROL CHART Y X
    MOVING AVERAGE CONTROL CHART Y X
Note:
    Control charts were introduced as an alternative to acceptance sampling. In acceptance sampling, some sample of units are inspected after production. Then based on the number of defective units, the entire lot is either accepted or rejected.

    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.

Note:
    Dataplot normally sets the control limits automatically. However, you can enter your own control limits if you wish. This is usually based on historical data or specific engineering requirements. User control limits are entered with the commands:

      LET TARGET = <value>
      LET USL = <value>
      LET LSL = <value>

    This sets the target value, the upper control limit, and the lower control limit respectively.

Note:
    For the mean, range, standard deviation, cusum, and EWMA control charts, the response variable is assumed to follow an approximately normal distribution. This assumption is the basis for calculating the upper and lower control limits.
Note:
    You can control the appearance of this chart by setting the switches for the LINE, CHARACTER, SPIKE, and BAR commands appropriately. Specifically, for the mean, range, and standard deviation control charts,

      Trace 1 = the value of the statistic for each sub-group
      Trace 2 = the mean of the statistic over the sub-groups
      Trace 3 = the Dataplot calculated upper control limit
      Trace 4 = the Dataplot calculated lower control limit
      Trace 5 = the user-specified target value
      Trace 6 = the user-specified upper control limit
      Trace 7 = the user-specified lower control limit

    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 user-specified 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.

Note:
    The control charts documented here are univariate control charts. That is, they monitor a single response variable.

    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.

Note:
    There have been numerous proposals for signaling when a process is out of control. For the mean, range, and standard deviation control charts, critierion developed by Western Electric have some popularity. These rules are as follow:

    1. Any point > 3*\( \sigma \) or < 3*\( \sigma \)

    2. Two of the last threee points > 2*\( \sigma \)
      Two of the last threee points < 2*\( \sigma \)

    3. Four of the last five points > 1*\( \sigma \)
      Four of the last five points < 1*\( \sigma \)

    4. Eight consecutive points above the center line or eight consecutive points below the center line

    The command

      SET CONTROL CHART LIMITS <DEFAULT/WECO/ISO 13528>

    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 z-score).

    Note that the if the WECO rules are turned on, the following is done:

    1. The standard control limits are drawn (traces 2, 3, and 4).

    2. The individual plot points that signal an out of control point according to the WECO rules are drawn using trace 5. So you can control how these points are drawn by setting the attributes for trace 5. This is demonstrated in the Program 3 example below.

    The WECO rules have been criticized for generating too many false positives.

Note:
    In some situations, you may want to highlight certain points on the control chart. For example, you may want to flag points that are outside the control limits or you may want to flag a particular sub-group (e.g., if a new batch of data is being added to historical data, you may want to emphasize the new data).

    The 2012/02 version added the HIGHLIGHT option. This is demonstrated in the Program 2 example below.

Default:
    None
Synonyms:
    XBAR CONTROL CHART for MEAN CONTROL CHART
    STANDARD DEVIATION CONTROL CHART for S CONTROL CHART
Related Commands: References:
    Walter Shewart (1931), "Economic Control of Quality of Manufactured Product", Van Nordstrom.

    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, 2005-09-01.

Applications:
    Quality Control
Implementation Date:
    Pre-1987
    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
Program 1:
     
    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 HORIZONTAL
        
    plot generated by sample program
Program 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
    .
    
    plot generated by sample program
    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 TAG
        
    plot generated by sample program
Program 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 X
        
    plot generated by sample program
Program 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 z-score
    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
        
    plot generated by sample program
    .
    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 matid
        
    plot generated by sample program
Program 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 "group-id" 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 Z-Score
        
    plot generated by sample program
Program 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 z-score
    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
        
    plot generated by sample program
    .
    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
        
    plot generated by sample program
    .
    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
        
    plot generated by sample program
Date created: 02/10/2015
Last updated: 12/04/2023

Please email comments on this WWW page to alan.heckert@nist.gov.