# Statistical Quality Control Questions and Answers – Gauge and Measurement System Capability Studies – 4

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This set of Statistical Quality Control Multiple Choice Questions & Answers (MCQs) focuses on “Gauge and Measurement System Capability Studies – 4”.

1. What is reproducibility?
a) Variability due to different operators using the gauge or different time periods, or environments
b) Variability due to error in process
c) Variability reflecting the basic inherent precision of the gauge itself
d) Variability reflecting the basic inherent precision of the process

Explanation: Reproducibility is defined as the variability due to different operators using the gauge, or different time periods, or different environments, or in general, different conditions.

2. What is repeatability?
a) Variability due to different operators using the gauge or different time periods, or environments
b) Variability due to error in process
c) Variability reflecting the basic inherent precision of the gauge itself
d) Variability reflecting the basic inherent precision of the process

Explanation: Repeatability is defined as reflecting the basic inherent precision of the gauge itself, through which we are measuring the unit.

3. What can we write the variance in measurement error or gauge in the terms of variance in repeatability, and variance of reproducibility?
a) $$\sigma_{gauge}^2=\sigma_{repeatability}^2-\sigma_{reproducibility}^2$$
b) $$\sigma_{gauge}^2=\sigma_{repeatability}^2+\sigma_{reproducibility}^2$$
c) $$\sigma_{gauge}^2=\sigma_{repeatability}+\sigma_{reproducibility}^2$$
d) $$\sigma_{gauge}^2=\sigma_{repeatability}-\sigma_{reproducibility}^2$$

Explanation: We can write the measurement error or gauge error variance as follows,
$$\sigma_{gauge}^2=\sigma_{repeatability}^2+\sigma_{reproducibility}^2$$.

4. Which of these is called an R & R study?
a) Experiment used to measure components of $$\sigma_{gauge}^2$$
b) Experiment used to measure components of $$\sigma_{Total}^2$$
c) Experiment used to measure components of $$\sigma_{P}^2$$
d) Experiment used to measure components of $$\sigma_{repeatability}^2$$

Explanation: The experiment used to measure the components of $$\sigma_{gauge}^2$$ is usually called a gauge R & R study, for two components of $$\sigma_{gauge}^2$$.

5. What is the other name of random effects model analysis of variance?
a) ANOVA
b) RENOVA
c) FNOVA
d) MENOVA

Explanation: The random effects model analysis of variance is also called the ANOVA model analysis. This is a part of analysis of variance method.

6. If the value of the variance of the product variability increases, what will be the effect on the variance of the gauge?
a) Increase
b) Decrease
c) No change
d) Can’t be predicted (no dependency over each other)

Explanation: As there is no dependency of the variance of the gauge on the product variability, even if the product variability increases, we cannot predict the changes in gauge variability variance.

7. If the variance of the total observed measurement is constant and the gauge capability ratio ρ_M is increased, what will be change in the gauge measurement variance?
a) Increase
b) Decrease
c) No change
d) Can’t be predicted (no dependency over each other)

Explanation: As we know,
$$ρ_M=\left(\frac{\sigma_{gauge}^2}{\sigma_{Total}^2}\right)$$
So if the variance of the total observed measurement is kept constant with the gauge capability ratio ρM increasing, the variance of gauge measurement will be increased.

8. If the variance of product variability is increased while keeping the total observed measurement variance constant, what will be effect on the gauge capability ratio ρP?
a) Increase
b) Decrease
c) No change
d) Can’t be predicted (no dependency over each other)

Explanation: As we know,
ρP∝ σp2
So, the gauge capability ratio ρP will increase with increase with increase in the variance in product variability σp2.

9. If the value of product variance is increased with the variance of the total observed measurement kept constant, the value of the gauge capability ratio ρM increases.
a) True
b) False

Explanation: As we know,
$$\sigma_{Total}^2 = \sigma_{gauge}^2 + \sigma_P^2; ρ_M=\frac{\sigma_{gauge}^2}{\sigma_{Total}^2}$$
Putting the equations together, we get to know that the value of ρM increases with decrease in the product variance.

10. A DR of value 5.89 indicates an adequate measurement system.
a) True
b) False