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 2 Vol 1

ISO 13528 PA SCORE

Name:
    ISO 13528 PA SCORE (LET)
Type:
    Let Subcommand
Purpose:
    Generate a percentage of allowed deviation (PA) score based on the ISO 13528 standard.
Description:
    The ISO 13528 standard for proficiency testing defines the following PA score

      \( Pa_{i} = \frac{x_{i} - x_{ref}}{\delta_{E}} 100 \)

    with xref and \(\delta_{E}\) denoting the "assigned value" and the pre-defined allowance for measurement error, respectively. The multiplication by 100 is to express the score as a percentage.

    The Pa statistic is a performance score discussed in the ISO 13528 standard (2015 second edition pp. 25-26). Values of Pa ≤ -100 and Pa ≥ 100 indicate an action signal (i.e., unacceptable performance).

    Note that xref and \(\delta_{E}\) are not computed from the current data. The xref is considered the "true" value (or the best guess for the true value). The ISO 13528 standard discusses numerous ways of determining this value. The \( \delta_{E} \) is an "acceptable" error.

    Although the ISO 13258 standard does not define a specific method for determing \( \delta_{E} \), if estimates for the repeatability and reproducibility are available, then ISO 13528 suggests the following (p. 22)

      \( \sigma_{pt} = \sqrt{\sigma_{R}^2 - \sigma_{r}^2 (1 - 1/m)} \)

    where

      \( \sigma_{pt} \) = standard deviation for proficiency assessment
      \( \sigma_{R} \) = repeatability standard deviation
      \( \sigma_{r} \) = reproducibility standard deviation
      m = number of replicate measurements for each participant

    Then

      \( \delta_{E} = 3 \sigma_{pt} \)

    The justification for this is that this corresponds to an action signal of +/-3 for z-scores.

    In some cases, \( \sigma_{pt} \) may be based on fitness for purpose or data from prior rounds.

    The Pa score is only one of several possible performance scores discussed in the ISO 13528 standard.

Syntax:
    LET <y> = ISO 13528 PA SCORE <x> <xref> <deltae>
                            <SUBSET/EXCEPT/FOR qualification>
    where <x> is the response variable;
                <xref> is a parameter that defines the assigned value;
                <deltae> is a parameter that defines the DELTAe value;
                <y> is a variable where the Pa score values are stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET PA = ISO 13528 PA SCORE X XREF DELTAE
Default:
    None
Synonyms:
    ISO 13528 PA is a synonym for ISO 13528 PA SCORE
    PA is a synonym for ISO 13528 PA SCORE
Related Commands: Reference:
    ISO 13528, Second Edition, Statistical Methods for Use in Proficiency Testing by Interlaboratory Comparisons, 2015, pp. 22, 25-26.
Applications:
    Proficiency Testing
Implementation Date:
    2016/2
Program:
     
    . Step 1:   Read the Data
    .
    skip 25
    read e2489a.dat labid y
    .
    . Step 2:   Compute and print the Pa values
    .
    let xref   = median y
    let sd     = sd y
    let deltae = 3*sd
    let deltae = round(deltae,2)
    .
    let pa    = iso 13528 pa  y xref deltae
    .
    set write decimals 3
    print y pa
    .
    . Step 3:   Plot the Pa values
    .
    tic mark offset units screen
    tic mark offset 3 3
    case asis
    label case ais
    title case asis
    title offset 2
    .
    y1label Percentage of Allowed Deviation (Pa)
    x1label Laboratory
    x2label Assigned Value: ^xref
    x3label DeltaE: ^deltae
    title Pa for E2489A.DAT
    line blank solid dash dash
    spike on
    line color black black red red
    .
    let xmax = maximum labid
    let xtemp = data 1 xmax
    let ymax  = data 100 100
    let ymin  = data -100 -100
    let yzero = data 0 0
    plot pa labid and
    plot yzero xtemp and
    plot ymax xtemp and
    plot ymin xtemp
        
    The following output is generated
    ------------------------------
                  Y             PA
    ------------------------------
              1.220         -6.466
              1.620         10.776
              1.820         19.397
              0.600        -33.190
              2.750         59.483
              1.550          7.759
              1.170         -8.621
              1.760         16.810
              1.350         -0.862
              1.180         -8.190
              1.190         -7.759
              1.710         14.655
              2.030         28.448
              1.100        -11.638
              1.840         20.259
              1.390          0.862
              1.130        -10.345
              1.660         12.500
              1.280         -3.879
              1.240         -5.603
              0.690        -29.310
              1.540          7.328
              1.430          2.586
              0.840        -22.845
              0.980        -16.810
              1.970         25.862
              4.890        151.724
              1.850         20.690
              1.090        -12.069
              1.070        -12.931
        
    plot generated by sample program

Privacy Policy/Security Notice
Disclaimer | FOIA

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

Date created: 04/11/2016
Last updated: 04/11/2016

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