Q: A laboratory is preparing a control chart for a new analytical method. The mean of 20 replicate measurements is 100, and the standard deviation is 5. What is the value of the upper action line for the mean if $$n=4$$ per subgroup?

$$100 + 3 \times 5 / \sqrt{4} = 107.5$$

Question 1

Which of the following best describes the purpose of a Shewhart control chart in analytical chemistry?

Accepted Answer

To monitor the stability and quality of analytical measurements over time.

Question 2

In a Shewhart chart for mean values, what is the formula for the upper action line?

Accepted Answer

$$\mu_0$ + 3\sigma/\sqrt{n}$$

Question 3

A laboratory is using a Shewhart chart to monitor the range of replicate measurements. If the target value for the range is $$\bar{R}$$, which line represents the threshold for immediate investigation?

Accepted Answer

Upper action line: $$\bar{R}_{A2}$$

Question 4

If a series of mean values on a Shewhart chart consistently fall between the upper and lower warning lines but show a clear upward trend, what does this indicate?

Accepted Answer

There may be a systematic error or drift developing in the process.

Question 5

The Horwitz trumpet (Figure 4.10) is used to illustrate the relationship between which two variables in analytical chemistry?

Accepted Answer

Concentration and % relative standard deviation

Question 6

A laboratory's Shewhart chart for means has an upper action line at 66.5, a target value at 57, and a lower action line at 49.5. If a measurement of 68 is recorded, what should the analyst do?

Accepted Answer

Initiate an immediate investigation, as the value exceeds the upper action line.

Question 7

Which of the following statements about warning and action lines on a Shewhart chart is correct?

Accepted Answer

Action lines are set at $$\pm 3\sigma$$ from the mean.

Question 8

A CUSUM (cumulative sum) chart is particularly useful for detecting which type of error in analytical measurements?

Accepted Answer

Small, persistent shifts in the process mean

Question 9

In the context of proficiency testing (PT), as shown in Figure 4.11, what does a histogram of laboratory results help to identify?

Accepted Answer

The distribution and potential bias of results among laboratories

Question 10

A laboratory is preparing a control chart for a new analytical method. The mean of 20 replicate measurements is 100, and the standard deviation is 5. What is the value of the upper action line for the mean if $$n=4$$ per subgroup?

Accepted Answer

$$100 + 3 	imes 5 / \sqrt{4} = 107.5$$

Question 11

Which of the following scenarios would most likely trigger an investigation according to Shewhart chart rules?

Accepted Answer

A single point falls outside the action line.

Question 12

Why is it important to use both mean and range charts together in quality control of analytical measurements?

Accepted Answer

To detect both shifts in the process mean and changes in measurement variability.

Question 13

The Horwitz trumpet shows that as analyte concentration decreases, the % relative standard deviation:

Accepted Answer

Increases.

Question 14

A laboratory's control chart shows a sudden increase in the range of replicate measurements, but the mean remains within control limits. What is the most likely cause?

Accepted Answer

An increase in random error or imprecision.

Question 15

If a laboratory consistently reports results above the target value in a proficiency test (PT) round, what does this suggest?

Accepted Answer

The laboratory has a positive bias in its measurements.

Question 16

Which of the following best describes the function of warning lines on a Shewhart chart?

Accepted Answer

They serve as an early alert to potential problems, prompting increased monitoring.

Question 17

A CUSUM chart for a laboratory process shows a steady downward trend in the cumulative sum. What does this most likely indicate?

Accepted Answer

The process mean is drifting lower over time.

Question 18

In the context of analytical quality control, what is the main advantage of using control charts over simply calculating the mean and standard deviation of a data set?

Accepted Answer

Control charts allow for real-time monitoring and detection of trends or shifts in the process.

Question 19

A laboratory is evaluating compliance with a specification limit using uncertainty analysis. If the measured value plus its expanded uncertainty exceeds the specification limit, what should the laboratory conclude?

Accepted Answer

The result is not compliant with the specification.

Quality of Analytical Measurements: Control Charts and Statistical Tools in Analytical Chemistry

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