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 C_{p} for a six-sigma company?

a) 2.0

b) 1.0

c) 3.0

d) 1.3

View Answer

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, C

_{p}≥2.0

2. What should be the position of the process mean for the calculation of the PCR C_{p}?

a) Near to the USL

b) Near to LSL

c) Centered between LSL and USL

d) C_{p} Does not take this into account

View Answer

Explanation: The process capability ratio PCR C

_{p}does not take into account where the process mean is located relative to the specifications.

3. What is the function of C_{p}?

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

View Answer

Explanation: The process capability ratio C

_{p}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

View Answer

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 C_{p} 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

View Answer

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 C_{p}=C_{pk} 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

View Answer

Explanation: Generally, when C

_{p}=C

_{pk}, 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) C_{p} = C_{pk}

b) C_{p} – C_{pk} = C_{pk}

c) C_{p} > C_{pk}

d) C_{p} < C_{pk}

View Answer

Explanation: When the process capability ratio C

_{p}is equal to the process capability ratio C

_{pk}, 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 C

_{p}.

8. Which of these is correct?

a) C_{pk}=min(C_{pu}, C_{p})

b) C_{pk}=min(C_{pu}, C_{pl})

c) C_{pk}=max(C_{pu}, C_{p})

d) C_{pk}=max(C_{p}, C_{pl})

View Answer

Explanation: The process capability ratio C

_{pk}is the minimum of the two, C

_{pu}and C

_{pl}. So,

C

_{pk}=min(C

_{pu}, C

_{pl})

9. Which of these is a correct definition for the C_{pk}?

a) C_{pk} is the one sided PCR for the specification limit nearest to the standard deviation of the process

b) C_{pk} is the one sided PCR for the specification limit farest to the standard deviation of the process

c) C_{pk} is the one sided PCR for the specification limit farest to the average of the process

d) C_{pk} is the one sided PCR for the specification limit nearest to the average of the process

View Answer

Explanation: C

_{pk}is the one sided PCR for the specification limit nearest to the standard deviation of the process.

10. If C_{p}>C_{pk} 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 C_{p}

d) The process can’t perform any better for same C_{p}

View Answer

Explanation: Generally, if C

_{p}> C

_{pk}, 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 C_{pk} for this process?

a) 1.7

b) 2.5

c) 1.0

d) 1.5

View Answer

Explanation: We know that,

C

_{pk}=min(C

_{pu}, C

_{pl})

Calculating the values of C

_{pu}and C

_{pl}, we get C

_{pu}=1.5 and C

_{pl}=2.5. So we get C

_{pk}=1.5.

12. If C_{p}=2.0,C_{pu}=1.5,C_{pl}=2.5 what will be the value of C_{pk}?

a) 2.5

b) 2.0

c) 1.5

d) 0

View Answer

Explanation: The process capability ratio C

_{pk}is expressed by the following equation,

C

_{pk}=min(C

_{pu}, C

_{pl})

Here C

_{pu}=1.5(minimum), so C

_{pk}=1.5.

13. If C_{pk}=1.0 and C_{p}=2.0, what will be the actual fallout for the process in ppm?

a) 200

b) 2700

c) 1

d) 1350

View Answer

Explanation: If C

_{pk}< C

_{p}, C

_{pk}is considered to evaluate the process fallout as the process is off center and the one sided process capability must be used.

14. C_{pk} measures the maximum of the two, C_{pu} and C_{pl}.

a) True

b) False

View Answer

Explanation: As we write,

C

_{pk}=min(C

_{pu}, C

_{pl})

We consider that the value of C

_{pk}will be equal to the one lower than the other between C

_{pk}and C

_{pl}.

15. For the calculation of C_{pk} the quality characteristic should have a lognormal distribution.

a) True

b) False

View Answer

Explanation: PCR C

_{pk}is evaluated using the assumptions made for C

_{p}. So as for C

_{p}, it is assumed that the quality characteristic has a normal distribution, it is also valid for C

_{pk}.

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