Guarded rejection: 1 Valuable Tool for Reducing the Risk of False Rejection
When assessing the conformity of a product or service to a specified requirement, it is crucial to have a high degree of confidence in the decision.
This is especially true when the consequences of a false rejection or false acceptance are high.
Guarded rejection is a decision rule that can be used to reduce the risk of false rejection.
A Guarded Rejection decision rule is often employed when one wants clear evidence that the limit has been exceeded.
It is a way of setting the rejection criteria so that there is a high degree of confidence that a rejected product or service is actually out of tolerance.
The rejection criteria are typically set wider than the tolerance to implement guarded rejection.
This creates a "guard band" between the tolerance and rejection criteria. As a result, a product or service will only be rejected if it falls outside the guard band.
The guard band would determine the appropriate risk level when rejecting or specifying non-conformance.
JCGM 106 Figure 11
The width of the guard band is determined based on the uncertainty of the measurement and the desired level of confidence in the decision.
JCGM 106:2012 section 8.3.3.1 states the following concerning guarded rejection, "An acceptance limit outside a tolerance interval, as shown in figure 11, can be chosen so as to increase the probability that a rejected item is truly non-conforming. Such a guarded rejection decision rule is often employed when one wants clear evidence that a limit has been exceeded prior to taking a negative action."
Some examples of guarded rejection include:
- Enforcing the Speed Limit where the officer wants to know without a doubt or, say, 99.9 % confidence that someone was speeding.
- Finding the Blood Alcohol or other substances present is within an x % confidence to remove doubt.
- Anti-Doping for Athletes (WADA)
- With DNA, if there is a 20 % chance that the DNA is not a match, is that enough of a chance to get a conviction? If we use guarded rejection, we can set the level to less than a 0.1 % chance, or even less.
JCGM 106:2012 Uses a Speed Limit enforcement example about issuing a ticket.
In highway law enforcement, the speed of motorists is measured by police using devices such as radars and laser guns.
A decision to issue a speeding ticket, which may lead to an appearance in court, must be made with a high degree of confidence that the speed limit has been exceeded.
Using a particular Doppler radar, speed measurements in the field can be performed with a relative standard uncertainty u(v)=v of 2 % in the interval 50 km/h to 150 km/h. Knowledge of a measured speed v in this interval is assumed to be characterized by a normal PDF with expectation v and standard deviation 0.02v.
Equation 1 from JCGM 106
JCGM 106 Example:
This example differs from several others using the guarded rejection formula as the standard measurement uncertainty is of the indicated value. Thus, any solution will account for the standard uncertainty associated with the indicated value.
Above are Excel formulas and the corresponding answers matching the JCGM 106:2012 value of 107 km/h for anyone wanting to implement Guarded Rejection.
The formulas show the probability of 95 % as 0.95, which then would be used with the Excel function for NORMSINV.
If one wanted to reverse solve the equation (i.e., verify the guarded rejection value does indeed back-calculate to 99.9 %), we would have to solve for the standard uncertainty of Vmax = 106.587 609 5 by multiplying Vmax by 2 %.
NORM.DIST(Vmax,Mean,Std Dev * Vmax,TRUE)
NORM.DIST(106.587,100,(2 % *106.587 609 5),TRUE)=0.99900 =99.9 %
Guarded rejection can also be used in manufacturing, quality control, and environmental testing.
It is a valuable tool for reducing the risk of false rejection and ensuring that only products and services that are genuinely out of tolerance are rejected.
However, it can significantly reduce the risk, especially when the uncertainty of the measurement is significant compared to the tolerance.
Benefits of using guarded rejection
There are several benefits to using guarded rejection, including:
- Reduced risk of false rejection: Guarded rejection can significantly reduce the risk of false rejection, especially when the uncertainty of the measurement is significant compared to the tolerance.
- Improved quality: By reducing the risk of false rejection, guarded rejection can help to improve the overall quality of products and services.
- Reduced costs: False rejection can lead to unnecessary costs, such as the cost of rework or scrap. By reducing the risk of false rejection, guarded rejection can help to reduce these costs.
- Improved customer satisfaction: False rejection can lead to dissatisfied customers. By reducing the risk of false rejection, guarded rejection can help to improve customer satisfaction.
How to implement guarded rejection
To implement guarded rejection, the following steps should be taken:
- Determine the uncertainty of the measurement.
- Select a desired level of confidence in the decision.
- Calculate the width of the guard band often using the probability and the NORMINV(Probability) Excel function.
- Set the rejection criteria based on the probability needed.
It is important to note that the guard band should be set wide enough to reduce the risk of false rejection to an acceptable level.
Guarded Rejection - Conclusion
Guarded rejection is a valuable tool for reducing the risk of false rejection.
It can be used in a variety of applications, such as law enforcement, manufacturing, quality control, and environmental testing.
By implementing guarded rejection, organizations can improve the overall quality of their products and services, reduce costs, and improve customer satisfaction.
JCGM 106:2012 Evaluation of measurement data - The role of measurement uncertainty in conformity assessment is a free document to download and can be found here.
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# Guarded Rejection
