# Statistical Quality Control Questions and Answers – Variable Charts – Control Charts for x̅ and R – 1

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This set of Statistical Quality Control Multiple Choice Questions & Answers (MCQs) focuses on “Variable Charts – Control Charts for x̅ and R – 1”.

1. Quantities that can be numerically measured, can be plotted on a _________ control chart.
a) X bar
b) P chart
c) C chart
d) np chart

Explanation: A quantity that is measured on a continuous scale, i.e. it is numerically measured, can be plotted on a control chart type named, X bar control chart.

2. A single measureable quality characteristic, such as dimension, weight, or volume, is called ________
a) Variable
b) Attribute
c) Variable and an Attribute
d) Mean and variablility

Explanation: A single measurable quality characteristic is that CTQ that can be measured on a continuous scale. So it is also called a variable, be it a dimension or a weight measurement of a product unit.

3. A variable quality characteristic will have both __________
a) Mean and variability
b) Discrete and continuous values
c) Zero and infinite value
d) One or zero

Explanation: A variable quality characteristic will vary on a continuous scale. So it will have both, a mean and its variability.

4. Control of the process average or mean quality level is usually done with the ___________ control chart.
a) X bar control chart
b) S control chart
c) R chart
d) P chart

Explanation: If a quality characteristic has a mean and variability, it is called a variable. If the control of process average or mean quality level is to be done for a variable, an x bar variable control chart is used.

5. S chart is used to monitor _________ of a quality characteristic.
a) Mean
b) Range
c) Variability
d) Attributes

Explanation: S chart is a control chart used to monitor the variability of a process quality characteristic. It is variable chart as it is used for monitor variability of variables.

6. Toughness of a bolt mount on a tank is __________
a) An attribute
b) A variable
c) Variable and an attribute
d) Variability

Explanation: A quality characteristic having a numerical measurement on a continuous scale is called a variable. As the toughness of a bolt is a continuous quality characteristic, it is called a variable.

7. X chart is a ____________
a) Attribute control chart
b) Variable control chart
c) Neither a variable control chart nor an attribute control chart
d) Falls in the category of both variable and attribute control charts

Explanation: Mean is only an asset of a variable quality characteristic. As x denotes mean of a variable, x chart is counted in the variable control chart category.

8. If a process is said to be in control, what can we say about the variation?
a) Random
b) Normal
c) Attribute
d) Assignable

Explanation: If a process is said to be in control, its sample data will have a random pattern. So when plotted on a control chart, they will appear to have a random distribution.

9. Tolerances are said to be ________
a) limits of natural variability
b) Statistical limits of variability
c) Limits determined by the customers of the product
d) Limits of inherent process variability

Explanation: The natural variability varies from a certain highest value to some lowest value. These limits of natural variability are also called as Tolerance.

10. Upper control limit for a x chart is expressed by ________
a) $$\bar{\bar{x}} + A_2 R$$
b) $$\bar{\bar{x}} – A_2 R$$
c) $$\bar{\bar{x}} + A_2 \bar{R}$$
d) $$\bar{\bar{x}} + A_3 R$$

Explanation: The expression for the upper control limit of the x chart is $$\bar{\bar{x}} + A_2 R$$

11. The center line for a $$\bar{\bar{x}}$$ chart denotes ________
a) Mean of any sample
b) Mean of means of the sample
c) Mean of any sample + 0.5
d) (Mean of any sample) / 0.5

Explanation: The center line for a $$\bar{\bar{x}}$$ chart is generally mean of means of all the samples taken from a process. This gives more accurate results than choosing the mean of any sample to be taken as Center line.

12. Specifications have the same meaning as ____________
a) Control limits
b) UCL
c) LCL
d) Tolerances

Explanation: The tolerance for a variable quality characteristic is generally having the same meaning as specifications of a product, i.e. the desired values for that quality characteristic.

13. For a random variable having a normal distribution, the ratio of its range to the standard deviation is called ____________
a) Relative range
b) Absolute range
c) Major range
d) Minor range

Explanation: For a normal random variable, the ratio of its range to the standard deviation is called the relative range for that random variable.

14. Process variability can only be described and monitored by the s control chart.
a) True
b) False

Explanation: The process variability can be monitored with either a control chart for standard deviation, called the s control chart, or a control chart for the range, called an R control chart.

15. The lower control limit for an x bar control chart is lesser than the mean of means of the samples taken.
a) True
b) False

Explanation: The lower control limit for any control chart is expressed by
LCL = $$\bar{\bar{x}} – A_2 R$$
So it is lower than process mean or the mean of means of samples taken.

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