# Industrial Engineering Questions and Answers – Control Charts and their Applications – Set 4

This set of Industrial Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Control Charts and their Applications – Set 4”.

1. Match the following.

 p) C chart i) c + 3 √c q) U chart ii) $$\frac {USL-LSL}{6\sigma }$$ r) Capability index iii) u + 3 $$\sqrt {\overline {u} /n}$$

a) p-iii, q-ii, r-i
b) p-ii, q-i, r-iii
c) p-i, q-iii, r-ii
d) p-i, q-ii, r-iii

Explanation: The criterion for matching is formula and UCL. They are matched as follows:

 C chart c + 3 √c U chart $$\frac {USL-LSL}{6\sigma }$$ Capability index u + 3 $$\sqrt {\overline {u} /n}$$

2. Calculate the process capability index (CP) considering the specification limits as 20 ± 0.05 mm and standard deviation as 0.25 mm.
a) 0.0667
b) 0.667
c) 0.0067
d) 0.6067

Explanation:
We know that,
Capability index, CP = $$\frac {USL-LSL}{6\sigma }$$
Given that,
USL = 20 + 0.05 = 20.05 mm
LSL = 20 – 0.05 = 19.95 mm
σ = 0.25 mm
CP = $$\frac {20.05-19.95}{6 \times 0.25}$$ = 0.0667

3. Process capability compares the output of an in-control process to the specification limits by using capability indices.
a) True
b) False

Explanation: Process capability measures the output of a process and compares it to the customer specification limits. Thus, it can be said that the process capability compares the output of an in-control process to the specification limits by using capability indices.

4. Process capability analysis finds out whether the process is fundamentally capable of meeting the specified tolerance limits.
a) True
b) False

Explanation: Process capability is defined as the ratio of total specification tolerance to the process capability i.e., it compares the output of a process to the given specification limits. Hence, the above statement is true.

5. Find the upper specification limit (USL) of a process when its capability index is 0.134. Take LSL as 10.5 and Standard deviation as 0.498. Consider the units in mm.
a) 100.8
b) 10.9
c) 1.09
d) 0.109

Explanation: Given that,
LSL = 10.5 mm
σ = 0.498 mm
CP = 0.134
We know that,
Capability index, CP = $$\frac {USL-LSL}{6\sigma }$$
USL = (CP × 6σ) + LSL = 0.134 × 2.986 + 10.5 = 10.9 mm.

6. Process capability index (CP) indicates the process of potential performance by relating the natural process spread to the specification spread.
a) True
b) False

Explanation: Process capability index symbolically denoted as CP indicates the process of potential performance by relating the natural process spread to the specification spread. Hence, the above statement is true.

7. Process capability cannot be considered as comparing ‘voice of the process’ with ‘voice of the customer’.
a) True
b) False

Explanation: Process capability compares the output of an in-control process to the specification limits by using capability indices. Hence, it can be regarded as comparing the ‘voice of the process’ with ‘voice of the customer’.

8. The specifications of a hollow spindle is defined as 20 ± 0.05 mm. Calculate the total specification tolerance.
a) 0.10
b) 0.01
c) 0.011
d) 0.001

Explanation: Given that,
Specifications of a hollow spindle = 20 ± 0.05 mm
Total specification tolerance = Upper specification tolerance (USL) – Lower specification tolerance (LSL) = 20.05 – 19.95 = 0.1 mm

9. Match the following.

p) CP > 1                                          i) Process is capable of meeting the specifications
q) CP < 1                                          ii) Process is not capable of meeting the specifications
r) CP = 1                                           iii) Process is just meeting the specifications


a) p – ii, q – i, r – iii
b) p – iii, q – ii, r – i
c) p – iii, q –i, r – ii
d) p – i, q – ii, r – iii

Explanation: The criterion for matching is the interpretation of the process capability index (CP).
They are to be matched as follows:
CP > 1 – Process is capable of meeting the specifications
CP < 1 – Process is not capable of meeting the specifications
CP = 1 – Process is just meeting the specifications

10. Which of the following is true for the figure shown below?

a) The process is very much capable and centered
b) The process is just capable
c) Process is centered
d) The process is not centered

Explanation: The above figure depicts that the process is very much capable and centered because both CP and CPK are greater than 1.

11. Which of the following figure represents the process that is just capable, but does not conform to specifications?
a)

b)

c)

d)

Explanation: It is stated that the process that is just capable, but does not conform to specifications.
For a process to be just capable, CP should be 1. Similarly, for a process to not to conform to the specification, CPK should be less than 1. Hence, the below figure represents the process

12. Match the following.

 p) i) Process is just capable and just conforms to specifications. It is also centered. q) ii) Process is just capable and it does not conform to specifications. r) iii) Process is not capable of meeting the specifications. It is also centered. s) iv) Process is not capable of meeting the specifications.

a) p – i, q – ii, r – iii, s – iv
b) p – ii, q – i, r – iii, s – iv
c) p – i, q – ii, r – iv, s – iii
d) p – i, q – iii, r – ii, s – iv

Explanation: Criterion for matching is the process capability index. It is explained below-

 CP < 1 The process is not capable of meeting the specifications CP = 1 The process is just capable of meeting the specifications CP > 1 The process is capable of meeting the specifications

13. Match the following.

p) CP = CPK                       i) Process is centered
q) CPK > 1                         ii) Process confirms the specifications
r) CPK < 1                          iii) Process does not conform to specifications
s) CPK = 1                          iv) Process just conforms to specifications


a) p – i, q – ii, r – iii, s – iv
b) p – ii, q – i, r – iii, s – iv
c) p – i, q – ii, r – iv, s – iii
d) p – i, q – iii, r – ii, s – iv

Explanation: Criterion for matching is the interpretation of CPK. They are matched as follows:
p) CP = CPK – Process is centered
q) CPK > 1 – Process confirms the specifications
r) CPK < 1 – Process does not conform to specifications
s) CPK = 1 – Process just conforms to specifications

Sanfoundry Global Education & Learning Series – Industrial Engineering.

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