250+ TOP MCQs on Process Capability Ratios – 3 and Answers

Statistical Quality Control Assessment Questions and Answers 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
Answer: a
Clarification: 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
Answer: d
Clarification: 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
Answer: d
Clarification: 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
Answer: c
Clarification: 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
Answer: a
Clarification: 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
Answer: c
Clarification: 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
Answer: a
Clarification: 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)
Answer: b
Clarification: 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
Answer: a
Clarification: 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
Answer: b
Clarification: 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
Answer: d
Clarification: 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
Answer: c
Clarification: 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
Answer: d
Clarification: 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
Answer: b
Clarification: 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
Answer: b
Clarification: 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.