# Statistical Quality Control Questions and Answers – Process Capability Ratios – 1

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This set of Statistical Quality Control Multiple Choice Questions & Answers (MCQs) focuses on “Process Capability Ratios – 1”.

1. Process capability ratio is expressed as ____________
a) $$C_p=\frac{USL-LSL}{6σ}$$
b) $$C_p=\frac{USL-2LSL}{6σ}$$
c) $$C_p=\frac{2USL-LSL}{6σ}$$
d) $$C_p=\frac{USL+LSL}{6σ}$$

Explanation: Process capability ratio (PCR) is denoted as Cp and expressed as,
$$C_p=\frac{USL-LSL}{6σ}$$

2. USL in the formula of PCR is ____________
a) Upper safe limit
b) Ultimate safe limit
c) Upper specification limit
d) Ultimate specification limit

Explanation: USL in the formula of PCR or process capability ratio is the Upper Specification Limit. This denotes the maximum tolerable value for a quality characteristic.

3. The LSL in the Cp is called ____________
a) Lower safe limit
b) Largest safe limit
c) Largest specification limit
d) Lower specification limit

Explanation: The LSL, in the formula of the Process Capability Ratio, Cp is the Lower Specification Limit value of the quality characteristic. It specifies the lowest possible value for the quality characteristic for the process to be in statistical control.

4. When the process standard deviation σ is unknown for a process, to calculate the PCR we use _____________
a) The mean
b) The variance
c) The sample average
d) The estimate of σ

Explanation: It is common that the process standard deviation is not known for the process. In this case, to calculate the PCR, we use the estimate of the process standard deviation.

5. We use _____________ to calculate the estimate of the process standard deviation.
a) Sample standard deviation
b) Sample average
c) Sample variance
d) Sample mean

Explanation: When the process standard deviation is not known, we use the estimate of the process standard deviation. This estimate is calculated by using the sample standard deviation, s.

6. How is s (Sample standard deviation) calculated?
a) s = R/2
b) s = R/2d2
c) s = R/d2
d) s = 2R/d2

Explanation: The sample standard deviation, s, used for the estimation of the process standard deviation, is calculated by the formula:
s = R/d2.

7. The estimate of the Cp is calculated by ______________
a) $$\frac{USL-LSL}{6\hat{\sigma}}$$
b) $$\frac{USL-LSL}{3\hat{\sigma}}$$
c) $$\frac{USL-LSL}{\hat{\sigma}}$$
d) $$\frac{USL-LSL}{12\hat{\sigma}}$$

Explanation: The estimate of the process capability ratio Cp is calculated by,
$$\widehat{C_P} = \frac{USL-LSL}{6\hat{\sigma}}$$

8. If the estimate of the process standard deviation is 0.1368, and the USL for the quality characteristic is 2.00, and the LSL=2.00, what will be the value of the estimate of PCR Cp is _____________
a) 1.21
b) 1.19
c) 1.13
d) 1.31

Explanation: We know that,
$$\widehat{C_P} = \frac{USL-LSL}{6\hat{\sigma}}$$
So, when we put values, we get, $$\widehat{C_P}$$=1.192.

9. The percentage of the specification band used by the process is calculated by formula _______________
a) P=Cp
b) P=$$\frac{1}{C_p}$$*100
c) P=Cp*100
d) P=$$\frac{1}{C_p}$$

Explanation: The percentages of the specification band used by any process is calculated by the following formula,
P=$$\frac{1}{C_p}$$*100

10. If the process capability ratio Cp is 1.532, what percentages of the specification band will be used by the process?
a) 65.27%
b) 75.11%
c) 44.21%
d) 21.42%

Explanation: The percentages of specification band used by the process is calculated by,
P=$$\frac{1}{C_p}$$*100
When we put values, we get, P=65.27%.

11. The one sided process capability ratio that uses the USL of the quality characteristic, is written as ____
a) $$C_{pu}=\frac{USL+μ}{3σ}$$
b) $$C_{pu}=\frac{USL+μ}{6σ}$$
c) $$C_{pu}=\frac{USL-μ}{6σ}$$
d) $$C_{pu}=\frac{USL-μ}{3σ}$$

Explanation: The one sided process capability ratio that uses the USL of the quality characteristic is written as,
$$C_{pu}=\frac{USL-μ}{3σ}$$

12. For a process, the process standard deviation is 32. If the mean of the process is 364, and the upper specification limit is 400, what will be the one side process capability ratio which uses USL of the quality characteristic?
a) 1.242
b) 1.135
c) 1.125
d) 0.991

Explanation: We know that,
$$C_{pu}=\frac{USL-μ}{3σ}$$
Putting values, we get, Cpu=1.125.

13. What is the formula to calculate the one sided process capability which uses lower specification limit?
a) $$C_{pl}=\frac{μ+LSL}{σ}$$
b) $$C_{pl}=\frac{μ-LSL}{6σ}$$
c) $$C_{pl}=\frac{μ-LSL}{3σ}$$
d) $$C_{pl}=\frac{μ-LSL}{6σ}$$

Explanation: The formula to calculate the one sided process capability which uses lower specification limit of the quality characteristic,
$$C_{pl}=\frac{μ-LSL}{3σ}$$

14. Process capability ratio Cp cannot be zero.
a) True
b) False

Explanation: Process capability ratio Cp cannot be zero as the USL and LSL difference can’t be zero and the standard deviation of the process also can’t be infinite. So we can say that that Cp can’t be zero.

15. Increase in process capability ratio Cp states that there is an increase in the percentage of the specification band used.
a) True
b) False

Explanation: We know that,
P=$$\frac{1}{C_p}$$*100
So an increase in the PCR Cp shows a decrease in the percentage of the specification band used.

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