SED navigation bar go to SED home page go to Dataplot home page go to NIST home page SED Home Page SED Staff SED Projects SED Products and Publications Search SED Pages
Dataplot Vol 1 Vol 2

ISO 13528 ZSCORE PLOT

Name:
    ISO 13528 ZSCORE PLOT
Type:
    Graphics Command
Purpose:
    Plot the average z-score (or j-score) for each material/round combination. These are also referred to as zone plots.
Description:
    One scenario for proficiency testing described in the ISO 13528 standard is for the case where there are multiple rounds of testing. Given the proficiency data

      Z - a variable containing the response data in z-score units
      MATID - a variable containing the material-id which the plot is generated
      ROUNDID - a variable containing the round-id
      LABID - a variable containing the lab-id

    For a given laboratory, define a grid using the MATID variable for the vertical axis and the ROUNDID variable for the horizontal axis. Then for each material/round cell compute the z-score for the given laboratory. If the laboratory has replicated values, compute the average z-score for the cell.

    Based on the z-score, define the plot symbol for the cell based on

      trace 1:       -2 < Z < +2
      trace 2:       +2 < Z < +3
      trace 3:       -3 < Z < -2
      trace 4:       +3 <= Z
      trace 5:       Z <= -3

    The +/-2 limits typically define a "warning" signal while the +/-3 limits typically define an "action" signal.

    Alternatively, j-scores can be used. The j-score is computed as follows:

    1. If there is replication in the cell, the averages of the z-scores will be used as the z-score for that cell.

      Alternatively, you can request that the most extreme z-score in that cell be used rather than the average.

    2. An initial j-score for the cell is assigned as follows:

        z-score   j-score
        +3 ≤ z   8
        +2 ≤ z < +3   4
        +1 ≤ z < +2   2
        -1 ≤ z < +1   0
        -2 < z ≤ -1   -2
        -3 < z ≤ -2   -4
        -3 ≤ z   -8

    3. We will compute a final j-score for the cell and a cumulative j-score. The cumulative j-score will be used with the initial j-score of the next round to compute the final j-score for the next round.

      To compute the final and cumulative j-scores for the round, do the following:

      • If the initial j-score for the round is 8, then set the final j-score for the round to 8 (if the cumulative j-score from the previous round is positive, then this is added to 8) and reset the cumulative j-score for the next round to 0.

        Likewise, if the j-score for the round is -8, then set the final j-score for the round to -8 (if the cumulative j-score from the previous round is negative, then this is added to -8) and reset the cumulative j-score for the next round to 0.

      • If the j-score for the round is inside the (-8,+8) interval, then compare the signs of the cumulative j-score from the previous round to the j-score for the current round.

        If the signs are the same, then add the cumulative j-score from the previous round to the initial j-score for the round to obtain the final j-score for the round. This will also be the cumulative j-score for the next round.

        If the signs are different, then set the final j-score for the round to initial j-score value. However, set the cumulative j-score for the next round to 0.

    Although the j-score is not part of the 13528 standard, it has been recommended in analyzing 13528-based proficiency studies (see the Thompson and Jaehn references below).

    The j-score combines properties of both the mean control chart and the cusum control charts. Specifically, it can detect both abrupt changes (i.e., j-scores for a given round > 8 or < -8) and drift in the result (i.e., several successive positive j-scores or several successive negative j-scores).

    Based on the final j-score, define the plot symbol for the cell based on

      trace 1:   -2 ≤ J ≤ 2
      trace 2:   +2 < J < +4
      trace 3:   -4 < J < -2
      trace 4:   +4 < J < +6
      trace 5:   -6 < J < -4
      trace 6:   +6 < J < +8
      trace 7:   -8 < J < -6
      trace 8:   +8 <= J
      trace 9:   J <= -8

    The Program example below demonstrates how to set the plot symbols.

    The plots described here are not part of the ISO 13528 standard. However, they are described in Thompson, Ellison, and Wood (2006) and in Jaehn (1991) (see References below) and are used in the context of ISO 13528 multi-round proficiency studies. These plots are alternatives to the control charts given in the ISO 13528 standard. Thompson, Ellison, and Wood refer to the z-score and j-score plots described here as zone plots.

Syntax 1:
    ISO 13528 ZSCORE PLOT <z> <matid> <roundid>
                            <SUBSET/EXCEPT/FOR qualification>
    where <z> is a response variable containing z-scores;
                <matid> is a variable that specifies the material-id;
                <roundid> is a variable that specifies the round-id;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    This syntax is used to generate the z-score version of the plot.

    The SUBSET clause is typically used to specify a single laboratory (see the Examples below). If no laboratory is specified on the SUBSET clause, then the different laboratories are treated like replications from a single laboratory.

Syntax 2:
    ISO 13528 JSCORE PLOT <z> <matid> <roundid>
                            <SUBSET/EXCEPT/FOR qualification>
    where <z> is a response variable containing z-scores;
                <matid> is a variable that specifies the material-id;
                <roundid> is a variable that specifies the round-id;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    This syntax is used to generate the j-score version of the plot.

    The SUBSET clause is typically used to specify a single laboratory (see the Examples below). If no laboratory is specified on the SUBSET clause, then the different laboratories are treated like replications from a single laboratory.

Examples:
    ISO 13528 ZSCORE PLOT Z MATID ROUNDID SUBSET LABID = 32
    ISO 13528 JSCORE PLOT Z MATID ROUNDID SUBSET LABID = 32
Note:
    The ISO 13528 standard defines a number of methods for computing the z-scores (enter HELP ISO 13528 ZSCORE, HELP ISO 13528 ZPRIME SCORE, and HELP ISO 13528 ZETA SCORE for details). For this reason, the ISO 13528 ZSCORE PLOT command does not automatically compute the z-scores from the original response data.
Default:
    None
Synonyms:
    None
Related Commands: References:
    Michael Thompson, Stephen Ellison, Roger Wood (2006), The International Harmonized Protocol for the Proficiency Testing of Analytical Chemistry Laboratories, Pure Applied Chemistry, Vol. 78, No. 1, pp. 145-196.

    Jaehn (1991), "The Zone Control Chart", Quality Progress, 24, pp. 65-68.

    Howarth, Richard J. (2003), "The J-chart: a simple plot that combines the capabilities of Shewart and cusum charts, for use in analytical quality control," AMC Technical Brief, Royal Society of Chemistry, No. 12.

    ISO 13528 (2005), "Statistical Methods for use in proficiency testing by interlaboratory comparisons," First Edition, 2005-09-01.

Applications:
    Multi-Round Proficiency Testing
Implementation Date:
    2012/2
    2015/10: Correction to j-score computation
Program 1:
     
    . Step 1:   Read the data
    .
    dimension 40 columns
    skip 25
    read allergen.dat z labid matid year quarter
    let roundid = year + (quarter-1)/4
    skip 0
    .
    . Step 2:   Set plot control setting
    .
    case asis
    title case asis
    title offset 2
    .
    line blank all
    character circle tria revtri tria revtri
    character hw 0.5 0.375 2.0 1.50 2.0 1.50 4 3 4 3
    character fill on all
    .
    tic mark offset units data
    tic mark offset 0.5 0.5
    .
    . Step 3:   Generate plot
    .
    y1label Material
    x1label Round
    title Z-Score Zone Plot for ALLERGEN.DAT
    iso 13528 zscore plot z matid roundid
    .
    line solid all
    character blank all
    justification center
    fill on
    font simplex
    hw 4 3
    move 87.5 86
    text tria()
    hw 2 1.5
    move 87.5 83
    text tria()
    hw 0.5 0.375
    move 87.5 80
    text circ()
    hw 2 1.5
    move 87.5 76
    text revt()
    hw 4 3
    move 87.5 71
    text revt()
    justification left
    fill off
    font tektronix
    .
    hw 2 1
    move 91 88
    text z > 3
    move 91 83.5
    text 2 < z < 3
    move 91 79.5
    text -2 < z < 2
    move 91 76
    text -2 < z < -3
    move 91 71.5
    text z < -3
        
    plot generated by sample program
Program 2:
     
    . Step 1:   Read the data
    .
    dimension 40 columns
    skip 25
    read allergen.dat z labid matid year quarter
    let roundid = year + (quarter-1)/4
    skip 0
    .
    . Step 2:   Set plot control setting
    .
    case asis
    title case asis
    title offset 2
    .
    line blank all
    character circle tria revtri tria revtri tria revtri tria revtri
    character hw 0.5 0.375 1.0 0.75 1.0 0.75 2.0 1.50 2.0 1.50 ...
                 3.0 2.25 3.0 2.25 4 3 4 3
    character fill on all
    .
    tic mark offset units data
    tic mark offset 0.5 0.5
    .
    y1label Material
    x1label Round
    title J-Score Zone Plot for ALLERGEN.DAT
    iso 13528 jscore plot z matid roundid
    .
    line solid all
    character blank all
    justification center
    fill on
    font simplex
    .
    hw 4 3
    move 87.5 86
    text tria()
    .
    hw 3 2.25
    move 87.5 82
    text tria()
    .
    hw 2 1.5
    move 87.5 78
    text tria()
    .
    hw 1 0.75
    move 87.5 74
    text tria()
    .
    hw 0.5 0.375
    move 87.5 70
    text circ()
    .
    hw 1 0.75
    move 87.5 66
    text revt()
    .
    hw 2 1.5
    move 87.5 62
    text revt()
    .
    hw 3 2.25
    move 87.5 58
    text revt()
    .
    hw 4 3
    move 87.5 54
    text revt()
    .
    justification left
    fill off
    font tektronix
    .
    hw 2 1
    move 91 88
    text j > 8
    move 91 83
    text 6 < j < 8
    move 91 78.5
    text 4 < j < 6
    move 91 74
    text 2 < j < 4
    move 91 69.5
    text -2 < j < 2
    move 91 65.5
    text -4 < j < -2
    move 91 62
    text -6 < j < -4
    move 91 59
    text -8 < j < -2
    move 91 54.5
    text j < -8
        
    plot generated by sample program

Privacy Policy/Security Notice
Disclaimer | FOIA

NIST is an agency of the U.S. Commerce Department.

Date created: 02/18/2015
Last updated: 10/29/2015

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