# Presentation: 754128

## DQOs and the Development of MQOs

- Carl V. Gogolak
- USDOE
- Environmental Measurements Lab

## Data Quality Objectives

- DQOs define the *performance* criteria that limit the probabilities of making *decision errors* by:
-  considering the purpose of collecting the data;
-  defining the appropriate type of data needed;
-  and specifying tolerable probabilities of making decision errors.

## Measurement Quality Objectives

- 	MQOs are statements of *performance* objectives or requirements for a particular analytical method performance characteristic.
- MQOs are acceptance criteria for quality attributes, usually measured by project DQIs.
- One of the most important of these is the analytical measurement uncertainty (accuracy).

## Uncertainty

***Uncertainty*** is defined in the ISO Guide to the Expression of Uncertainty in Measurement (GUM) as:
- “a parameter associated with the result of a measurement that characterizes the dispersion of values that could reasonably be attributed to the measurand.”

## Uncertainty

- The uncertainty of a measured value is typically expressed as an estimated standard deviation, called a ***standard uncertainty.***
- The standard uncertainty of a calculated result is usually obtained by propagating the standard uncertainties of a number of other measured values. In this case it is called a ***combined standard uncertainty.***

## DQOs and Uncertainty 

- No measurement program or sampling plan can be adequately designed without some estimate of the uncertainty in the data relative to the action level.

## Uncertainty and the Action Level

- Relatively large uncertainty can be tolerated:

- Either more accuracy or more samples are needed:

## Connecting the MQOs to the DQOs

- Decision errors are made because there is uncertainty in the data
- One component of the uncertainty is analytical measurement uncertainty
- To limit decision errors, the analytical measurement uncertainty should be limited to a level appropriate to the DQOs

## MARLAP emphasizes Method Uncertainty as an MQO.

***Method Uncertainty*** refers to the predicted uncertainty of a measured value that would be calculated if the method were applied to a hypothetical laboratory sample with a specified analyte concentration.
- The Method Uncertainty is a characteristic of the analytical method and the measurement process.

## Developing MQOs for Method Uncertainty

- Data are collected so that decisions can be made...
- Decisions can be made about individual samples
*...**as for bioassays*
- Decisions can be made about the mean of a sampled population
*...**as for MARSSIM final status surveys*

## Decisions made about individual samples

- H0: Sample contains no radioactivity
- Ha: Sample contains radioactivity
- Type I error: Decide there is radioactivity when there isn’t
- Type II error: Decide there is no radioactivity when there is
*This is the familiar framework for LLD calculations.*

## Desired Limits on Decision Errors

- Concentration

- Probability of Detection

- AL

- 0

- Gray Region:
- The probability of detection
- decreases with
- decreasing
- concentration

- Limit the probability
- of missing a sample
- above the action level

- Limit the probability
- of flagging a blank sample

## Lower Limit of Detection

## The probability of detection increases with increasing concentration

## Power Curve

## The MQO for Method Uncertainty

- The width of the gray region is  = AL – 0 = AL.
- To limit the probability of decision errors,
-  and , to 0.05, we have to limit the
- standard deviation of the analytical method, M
- So that  / M > 1.645 + 1.645 = 3.29.
- The performance requirement is that the *upper bound* for the measurement standard deviation is
- MR  =  / 3.29 = AL / 3.29.
*This is essentially the same as requiring that the minimum detectable concentration (MDC) not exceed the action level.*

## Required Method Uncertainty

- The true standard deviation of the measurement process, M , is a theoretical quantity and is never known exactly.
- The laboratories estimate of M is denoted *u*M, the method uncertainty.
- The value MR is the required upper bound for the unknown M.
- Therefore _*in practice *_MR is an upper bound on *u*M, the method uncertainty.
- Used this way, MR is called the required method uncertainty and is denoted by *u*MR.

## Decisions made about the mean of a sampled population

- H0: The mean exceeds the action level.
- Ha: The mean is below the action level.
- Type I error: Decide mean exceeds AL when it doesn’t.
- Type II error: Decide mean does not exceed AL when it does.

## Desired Limits on Decision Errors

- Mean Concentration

- Probability of Deciding Mean < AL

- AL

-  DL

- 0

- Limit the probability
- of missing a mean
- above the action level

- Limit the probability
- of missing a mean
- below the DL

- Gray Region

- The width
- of the gray
- region, ,
- represents the smallest
- concentration difference that it is important to detect.

## Power Curve

- Mean Concentration

- Probability of Deciding Mean < AL

- AL

-  DL

- 0

- Gray Region

## The MQO for Method Uncertainty

- The width of the gray region is  = AL – DL.
- The total variance of the data is

-  The sampling standard deviation, S , depends on the variability in the spatial distribution of the analyte concentrations and other factors having to do with how the sampling is performed.
-  The analytical standard deviation, M , is affected by laboratory sample preparation, subsampling and analysis procedures.

## The MQO for Method Uncertainty

- The sample size needed to conduct the hypothesis test with specified limits on  and  depends on the relative shift,  /  .
- To keep sample sizes reasonable,  should be such that 1<  /  < 3. Ideally,  /   3.
- The cost in samples rises rapidly when   /  < 1, but there is little benefit from increasing  /  above 3.

## The MQO for Method Uncertainty

- Generally it is easier to control M than S.
- If S is large, then the best one can do is make M small relative to S.
- If M ~ S/3, then the analytical method variance is contributing less than 10% to the total variance 2. Reducing it further will not reduce  very much.
- This implies that the upper bound for M should be

## Required Method Uncertainty

- If the lower bound of the gray region is zero, then the required method uncertainty is

*This is essentially the same as requiring that the relative standard deviation of the measurements near the action level be 10%.*
*In other words, the minimum quantifiable concentration MQC should be no larger than the action level.*

## Required Method Uncertainty

- The required method uncertainty is specified at the Action Level
- At concentrations below the action level, the bound on the standard deviation Req = MR is constant.
- At concentrations above the action level, the bound on the *relative* standard deviation Req = MR = MR/AL is constant.
- The combined standard uncertainty *u**c* of each result may be compared to these bounds.

## Slide 26

## Required Method Uncertainty

- The required method uncertainty, *u**MR* , and the required method relative uncertainty, ***MR *, can be used for both method selection and to develop acceptance criteria for QC sample results.