# Statistical Quality Control Questions and Answers – Attribute Charts – Control Charts for Fraction Nonconforming – 4

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This set of Statistical Quality Control Multiple Choice Questions & Answers (MCQs) focuses on “Attribute Charts – Control Charts for Fraction Nonconforming – 4”.

1. The standardized control chart has the center line at ____________
a) 1 σ
b) 2 σ
c) Zero
d) -1σ

Explanation: The standardized control chart used for control charts for fraction nonconforming with variable sample size, has its center line at the value zero.

2. To deal with the variable sample size, the standardized chart is used, which has its upper limit at ___________
a) 3
b) -3
c) 1
d) 0

Explanation: The standardized control chart, which has been used over quite some time to handle the situations of variable sample size, has its upper limit at +3.

3. A type II error is also called a ___________
a) α Error
b) δ Error
c) β Error
d) ∅ Error

Explanation: A type II error is concluding a process in-control when it is actually in out-of-control state. A type II error is also called an β error.

4. An OC curve is a display of ___________
a) β Error against defectives in a process output over a limited period of time
b) β Error against time
c) β Error against the process fraction nonconforming
d) Fraction nonconforming against β Error

Explanation: An OC curve or Operation characteristic curve for a p-chart is a graphical representation of β Error against the process fraction nonconforming computed.

5. ARL (Average run length) for the fraction nonconforming control chart, is calculated by ___________
a) ARl=1/β
b) ARL=β/α
c) ARL=1/βn
d) ARL=$$\frac{1}{probability\, of \,sample \,point\, plots\, out\, of\, control}$$

Explanation: The average run lengths for the fraction nonconforming control charts are calculated by the following formula,
ARL=$$\frac{1}{probability\, of \,sample \,point\, plots\, out\, of\, control}$$.

6. If the process is in control, the ARL for the fraction nonconforming chart, is calculated by __________
a) $$ARL_0=\frac{1}{\alpha}$$
b) $$ARL_0=\frac{1}{1-\alpha}$$
c) $$ARL_0=\frac{\beta}{\alpha}$$
d) $$ARL_0=\frac{1}{\alpha \beta}$$

Explanation: The average run length, for the process of Fraction nonconforming control chart for processes in-control, is expressed by,
ARL0=1/α.

7. If the for a fraction nonconforming chart, the probability of a sample point plotting out of control is 0.0531, what will be the ARL for this?
a) 12.31
b) 8.16
c) 18.83
d) 22.78

Explanation: The fraction nonconforming chart which has the probability of a sample point plotting out of control as p, the ARL is given by,
ARL = 1p
Putting p=0.0531, ARL=18.83.

8. If a process is out of control, what will be its ARL for the fraction nonconforming chart?
a) $$ARL_1=\frac{1}{1-β}$$
b) $$ARL_1=\frac{1-β}{1+β}$$
c) $$ARL_1=\frac{1}{1+β}$$
d) $$ARL_1=\frac{1+β}{1-β}$$

Explanation: When the process is out of control, it has possibility of β error. The Average run length for the fraction nonconforming chart of this process, is calculated by following formula,
$$ARL_1=\frac{1}{1-β}$$

9. If type II error probability for a process is 0.8594, its ARL will be ____
a) 8
b) 1
c) 3
d) 7

Explanation: We know,
$$ARL_1=\frac{1}{1-β}$$
We have, β=0.8594, so ARL1≅7

10. We cannot analyze abnormal runs or patterns directly, on p-chart with variable sample size.
a) True
b) False

Explanation: We cannot analyze abnormal runs or patterns directly on p chart with variable sample size. It’s because, the sample nonconforming data can indicate poorer quality for a sample with less defects or variability.

11. The gap between the UCL and LCL is double the gap between either one of them and the Center line, for the standardized chart.
a) True
b) False

Explanation: The Center line for standardized chart is at 0, and UCL and LCL for standardized chart are at ±3 respectively. So the gap between the UCL and LCL is 6, which is double the gap between the gap between either, one of them and the center line, which is 3 units.

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