Dataplot Vol 1 Vol 2

# ISO 13528 RLP PLOT

Name:
ISO 13528 RLP PLOT
Type:
Graphics Command
Purpose:
Given a response variable containing z-scores and associated variables containing laboratory id's and material id's, generate a plot of relative laboratory performance versus the rescaled sum.
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 ISO 13528 multi-round proficiency studies, the relative laboratory performance (RLP) for a given laboratory with N z-scores (Zi) is defined as

$$\mbox{RLP} = \sqrt{ \frac{\sum_{i=1}^{N}{Z_{i}^{2}}} {\mbox{NMAT}}}$$

where NMAT is the number of materials. An RLP near 1 indicates average performance and an RLP greater than 1.5 indicates that the laboratory may be problematic. An advantage of this statistic is that z-scores of opposite sign do not cancel each other out. A disadvantage is that this statistic is suspectible to outliers in the z-scores.

The rescaled sum (RSZ) is defined as

$$\mbox{RSZ} = \frac{\sum_{i=1}^{N}{Z_{i}}} {\sqrt{N}}$$

So if there are k laboratories, the plot will consist of k points. For each laboratory, the RLP and RSZ are computed over all rounds and all materials. Note that the material id variable enters only in computing the number of distinct materials in the above formulas.

A value of RSZ greater than 2 or less than -2 flags a warning signal with regard to the laboratory. A value of RSZ greater than 3 or less than -3 flags an "action" signal (i.e., similar to an out-of-control signal from a control chart) with regard to the laboratory. An advantage of this statistic is that it has the same interpretation as a z-score. The disadvantage is that z-scores of opposite sign can cancel each other.

Laboratories where the RLP is greater than 1.5 and the |RSZ| > 2 are flagged as problematic. This command automatically defines a sub-region area based on this area. This is demonstrated in the Program example below.

The RSZ statistic is discussed in Thompson, Ellison, and Wood (2006). The RLP statistic is discussed in Uhlig and Lischer (1998).

The RLP and RSZ statistics are examples of combination scores (i.e., the statistic is a combination of many individual z-scores). Although the ISO 13528 standard recommends against using combination scores, these can be helpful in judging the overall performance of a laboratory. A useful way to use this plot is to identify laboratories that are potentially problematic. These laboratories can then be examined more carefully. For example: is the poor performance due to one or a few outliers? is the lab consistently high or consistently low? does the laboratory need to carefully examine their procedures?

Syntax:
ISO 13528 RLP PLOT <z> <labid> <matid>
<SUBSET/EXCEPT/FOR qualification>
where <z> is a response variable containing z-scores;
<labid> is a variable that specifies the lab-id;
<matid> is a variable that specifies the material-id;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
ISO 13528 RLP PLOT Z LABID MATID
Note:
It can be helpful to identify individual laboratories on this plot. You can optionally specify that certain points be labelled with their lab-id. You can use the following command to specify which points are labelled.

SET RLP PLOT LABELS <NONE/ALL/WARNING/ACTION>

where

 NONE => no points are labelled ALL => all points are labelled WARNING => any point where the RLP > 1.5 or the |RSZ| > 2 are labelled ACTION => any point where the RLP > 1.5 or the |RSZ| > 3 are labelled

The default is none. The Program example below demonstrates the ACTION option. Note that you do not have to make any changes to the CHARACTER settings as Dataplot does this automatically. The CHARACTER OFFSET command can be helpful in this context (it is the CHARACTER OFFSET for the second trace that controls the positioning of the lables).

Note:
Some sources recommend capping the maximum value for the z-score when computing the RLP statistic.

To specify this value, enter the command

LET CAPVALUE = <value>

where <value> is typically 3 or 4. Note that the value represents an absolute value. For example, if CAPVALUE is 4, values greater than 4 will be set to 4 and values less than -4 will be set to -4.

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 RLP PLOT command does not automatically compute the z-scores from the original response data.
Default:
None
Synonyms:
None
Related Commands:
 ISO 13528 PLOT = Generate an ISO 13528 plot. ISO 13528 ZSCORE PLOT = Generate an ISO 13528 plot. ISO 13528 CONTROL CHART = Generate an ISO 13528 control chart. ISO 13528 ZSCORE = Compute z-scores as defined in the ISO 13528 standard. ISO 13528 ZPRIME SCORE = Compute z-prime scores as defined in the ISO 13528 standard. ISO 13528 ZETA SCORE = Compute zeta scores as defined in the ISO 13528 standard. CHARACTER = Sets the type for plot characters. LINE = Sets the type for plot lines.
References:
Uhlig and Lischer (1998), "Statistically-based Performance Characteristics in Laboratory Performance Studies", Analyst, 123, pp. 167-172.

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
Program:
. 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 setting
.
case asis
title case asis
title offset 2
label case asis
y1label Relative Laboratory Performance
x1label Rescaled Sum
title ISO 13528 RLP Plot for TURNER.DAT
y1tic mark label decimal 1
xlimits -8  8
major xtic mark number 9
minor xtic mark number 1
x1tic mark offset 0 0
.
set rlp plot labels action
region fill on
region fill color g90
line blank
character circle
character hw 0.5 0.375
character fill on
character offset 0 0 2 0
.
. Step 3:   Generate plot
.
iso 13528 rlp plot z labid matid

Date created: 02/18/2015
Last updated: 12/04/2023