# Statistical Quality Control Questions and Answers – Control Charting Techniques – Control Charts for Multiple-Stream Processes – 2

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This set of Statistical Quality Control Multiple Choice Questions & Answers (MCQs) focuses on “Control Charting Techniques – Control Charts for Multiple-Stream Processes – 2”.

1. The upper control limits for the GCC will be ____________ for the x̅ chart.
a) UCL=$$\bar{\bar{x}}+A_2 \overline{R}$$
b) UCL=$$\bar{\bar{x}}-A_2 R$$
c) UCL=$$\bar{\bar{x}}-A_2 \overline{R}$$
d) UCL=$$\bar{\bar{x}}+A_2 R$$

Explanation: The GCC are used to control the multiple stream processes. These control charts are having the upper control limits as,
UCL=$$\bar{\bar{x}}+A_2 \overline{R}$$

2. What is the value of the difference between the UCL and the LCL of x̅ chart of the GCC?
a) 1
b) 0
c) 3A2 R
d) 2A2 R

Explanation: As we know that the control limits for the GCC are,
UCL=$$\bar{\bar{x}}+A_2 \overline{R}$$; LCL=$$\bar{\bar{x}}-A_2 \overline{R}$$
So the difference between the control limits of GCC will be 2A2 R

3. What is the value of the UCL of the R chart constructed for the GCC?
a) UCL = D4 R
b) UCL = D3 R
c) UCL = R ̅+ D3 R
d) UCL = R ̅+ D4 R

Explanation: The GCC is prepared with the same way as the simple x and R charts are constructed for individual process streams. The value of the UCL of the R chart of the GCC is,
UCL=D4 R

4. What is the ratio of the UCL to LCL of the same GCC R chart?
a) UCL/LCL=D2/D3
b) UCL/LCL=D3/D4
c) UCL/LCL=D4/D3
d) UCL/LCL=D4/D2

Explanation: We know that the values of the control limits of the R chart for the GCC are,
UCL=D4 R ;LCL=D3 R
So their ratio will be,
UCL/LCL=D4/D3.

5. If the sample size is 4, what will be the value of the upper control limit of the GCC R chart?
a) UCL=2.672R̅
b) UCL=2.282R̅
c) UCL=2.114R̅
d) UCL=2.574R̅

Explanation: We know that, for sample size= 4, the value of D4=2.282. So putting it into the equation of the UCL of R chart of the GCC gives,
UCL=2.282R

6. What will be the value of the LCL of the x chart of the GCC when the value of x =12, and the value of R̅= 0.1 and sample size = 4?
a) 12.0729
b) 12.9271
c) 11.9271
d) 11.0729

Explanation: We know that, for n=4, A2=0.0729 Putting the above data into the equation of the UCL of the x̅ chart of GCC, we get,
UCL=12.0729.

7. When the subgroup size is 4 for any process samples, what will be the value of the R chart LCL of the GCC?
a) 5
b) 1
c) 0
d) 2

Explanation: We know that for n=4, D3 has the value of zero. Putting it into the equation of the LCL of the R chart for the GCC, gives us, LCL=0.

8. In GCC we plot ___________ means observed at any time period.
a) Only the maximum
b) Only the minimum
c) Mean of the
d) Both, the maximum and the minimum

Explanation: When the GCC are used to control the process, we plot only the largest and the smallest of the s means observed at any time period on the x̅ chart. If they lie inside the control limits, so will others do.

9. ___________ range will be plotted on the R chart of the GCC.
a) Maximum
b) Minimum
c) Both the maximum and the minimum
d) Neither the maximum nor the minimum

Explanation: Only the largest range is plotted on the range chart because if it will exceed the control limits, there is a possibility that other ranges will also do the same. The lower limit of the Range chart is mostly zero.

10. Each plotted point on the GCC is identified by __________
a) The mean value of the stream
b) The stream that produced it
c) The standard deviation of the stream
d) The variance of the stream

Explanation: The maximum and minimum means are plotted on the x̅ chart, and only the maximum range is plotted on the range chart while using the GCC. Each point on the GCC is identified by the stream that produced it.

11. A MSP is out of control if a point on the GCC exceeds __________
a) 3-sigma limit
b) 2-sigma limit
c) 1.5-sigma limit
d) 1-sigma limit

Explanation: The GCC is used to control the MSP or the multiple stream processes. The data from the different streams is plotted on it, if any point on the GCC exceeds a 3-sigma limit, the process is out of control.

12. What is the value of the one sided in-control ARL for the GCC?
a) $$ARL(1)_0=\frac{s^r}{s-1}$$
b) $$ARL(1)_0=\frac{s^r-1}{s-1}$$
c) $$ARL(1)_0=\frac{s^{2r}-1}{s+1}$$
d) $$ARL(1)_0=\frac{s^r+1}{s+1}$$

Explanation: If a process has s streams and r is the consecutive times a particular stream has given largest value, the one sided in-control ARL will be,
$$ARL(1)_0=\frac{s^r-1}{s-1}$$

13. If there are 6 streams of a MSP, and one of the streams has given 4 consecutive times the largest value, what will be the value of the one sided in-control ARL for this event?
a) 200
b) 400
c) 259
d) 421

Explanation: Given: s=6, r=4. We know that,
$$ARL(1)_0=\frac{s^r-1}{s-1}$$
By putting the values, we get, ARL(1)0=259.

14. Runs tests can be applied on the GCC.
a) True
b) False

Explanation: Runs tests cannot be applied on the GCC for any MSP, as the conventional run tests were not developed to test averages or ranges that are the extremes of a group of averages or ranges.

15. If the number of times a particular stream gives the maximum value of average or range for the GCC, increases, the value of one sided in-control ARL for that event will increase.
a) True
b) False

Explanation: As we know that,
$$ARL(1)_0=\frac{s^r-1}{s-1}$$
As the value of r increases, the value of ARL(1)0 also increases.

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