# Statistical Quality Control Questions and Answers – Process Capability Ratios – 3

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This set of Statistical Quality Control Assessment Questions and Answers focuses on ” Process Capability Ratios – 3″.

1. What should be the minimum value of PCR Cp for a six-sigma company?
a) 2.0
b) 1.0
c) 3.0
d) 1.3

Explanation: A six-sigma company would require the process mean, when in control, will not be closer to than the six-sigma deviations from the nearest specification limit. For this, Cp≥2.0

2. What should be the position of the process mean for the calculation of the PCR Cp?
a) Near to the USL
b) Near to LSL
c) Centered between LSL and USL
d) Cp Does not take this into account

Explanation: The process capability ratio PCR Cp does not take into account where the process mean is located relative to the specifications.

3. What is the function of Cp?
a) To measure the value of process mean
b) To measure the value of the process standard deviation
c) To measure the USL and LSL of the quality characteristic
d) To measure the spread of the specifications relative to the six sigma spread

Explanation: The process capability ratio Cp does not take into account the process centering. It simply measures the spread of the specifications relative to the six sigma spread of the process.

4. Which one of the processes performs the best?
a) The one which operates near the USL
b) The one which operates near the LSL
c) The one which operates at the midpoint of the interval between the specifications
d) The one which operates outside the specifications

Explanation: The process which operates at the midpoint of the interval between the specifications, has the best performance among all the processes.

5. 4 processes have same value of Cp and the USL and LSL values equal to 62 and 38 respectively. Which one of those performs the best?
a) Centered at 50
b) Centered at 44
c) Centered at 54
d) Centered at 63

Explanation: The process, which is centered at the midpoint of the interval between the specifications limits, has the maximum probability of performing the best.
midpoint=$$\frac{USL+LSL}{2}$$

6. If Cp=Cpk which of these is true?
a) Process is centered at the LSL of the specifications
b) Process is centered at the USL of the specifications
c) Process is centered at the midpoint of the specification
d) Process is centered at the outside the specification limits

Explanation: Generally, when Cp=Cpk, the process is centered at the midpoint of the specifications. This means the process performance is a lot better.

7. Which of these gives the best performance of the process?
a) Cp = Cpk
b) Cp – Cpk = Cpk
c) Cp > Cpk
d) Cp < Cpk

Explanation: When the process capability ratio Cp is equal to the process capability ratio Cpk, it is generally stating that the process is centered at the midpoint of the specifications. This gives the best performance of the process at a particular value of Cp.

8. Which of these is correct?
a) Cpk=min⁡(Cpu, Cp)
b) Cpk=min⁡(Cpu, Cpl)
c) Cpk=max⁡(Cpu, Cp)
d) Cpk=max⁡(Cp, Cpl)

Explanation: The process capability ratio Cpk is the minimum of the two, Cpu and Cpl. So,
Cpk=min⁡(Cpu, Cpl)

9. Which of these is a correct definition for the Cpk?
a) Cpk is the one sided PCR for the specification limit nearest to the standard deviation of the process
b) Cpk is the one sided PCR for the specification limit farest to the standard deviation of the process
c) Cpk is the one sided PCR for the specification limit farest to the average of the process
d) Cpk is the one sided PCR for the specification limit nearest to the average of the process

Explanation: Cpk is the one sided PCR for the specification limit nearest to the standard deviation of the process.

10. If Cp>Cpk what conclusion can be carried out about the process?
a) The process has its operation at the midpoint of the interval between the specifications
b) The process operates off-center
c) The process performance is the best possible for that Cp
d) The process can’t perform any better for same Cp

Explanation: Generally, if Cp > Cpk, we can say that the process is not centered at the midpoint of the specifications, i.e. the process operates off-center.

11. For a process, the upper specification limit and lower specification limits are 62 and 38 respectively. If the process has its mean equal to 53, and its standard deviation 2, what is the value of Cpk for this process?
a) 1.7
b) 2.5
c) 1.0
d) 1.5

Explanation: We know that,
Cpk=min⁡(Cpu, Cpl)
Calculating the values of Cpu and Cpl, we get Cpu=1.5 and Cpl=2.5. So we get Cpk=1.5.

12. If Cp=2.0,Cpu=1.5,Cpl=2.5 what will be the value of Cpk?
a) 2.5
b) 2.0
c) 1.5
d) 0

Explanation: The process capability ratio Cpk is expressed by the following equation,
Cpk=min⁡(Cpu, Cpl)
Here Cpu=1.5(minimum), so Cpk=1.5.

13. If Cpk=1.0 and Cp=2.0, what will be the actual fallout for the process in ppm?
a) 200
b) 2700
c) 1
d) 1350

Explanation: If Cpk < Cp, Cpk is considered to evaluate the process fallout as the process is off center and the one sided process capability must be used.

14. Cpk measures the maximum of the two, Cpu and Cpl.
a) True
b) False

Explanation: As we write,
Cpk=min⁡(Cpu, Cpl)
We consider that the value of Cpk will be equal to the one lower than the other between Cpk and Cpl.

15. For the calculation of Cpk the quality characteristic should have a lognormal distribution.
a) True
b) False 