# Statistical Quality Control Questions and Answers – Attribute Charts – Control Charts for Nonconformities (Defects) – 1

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This set of Statistical Quality Control Multiple Choice Questions & Answers (MCQs) focuses on “Attribute Charts – Control Charts for Nonconformities (Defects) – 1”.

1. The event of a specification not satisfied at one point of a product, is called ____________
a) Nonconformity
b) Non-defectiveness
c) Un-specification
d) Non-specification

Explanation: Each event, in which a specification is not satisfied or an error occurs in approaching the specification value, is called nonconformity or a defect.

2. A nonconforming item has at least ____________ conformities.
a) 4
b) 3
c) 1
d) 2

Explanation: A nonconforming item is defined as the item or product, which has at least one defect. It is necessary that a nonconforming item has one or more than one defects.

3. The c-control chart is plotted for _____________
a) Fraction nonconforming
b) Number of nonconformities per unit
c) Number of defects observed
d) Deviation from median of the defects in samples

Explanation: The c-control chart is based on the total number of nonconformities in a product unit of a process output. So a c-chart is also called control chart for nonconformities.

4. Which of these is an assumption made for designing a control chart for noncorformities?
a) Normal Distribution
b) Poisson Distribution
c) Lognormal Distribution
d) Weibull Distribution

Explanation: The control charts for nonconformities, make an assumption that the sample taken is well modeled by the Poisson distribution. This is a necessary assumption to deal with these control charts.

5. Which of these is not an assumption of the c-chart?
a) Number of potential locations for nonconformities should be large
b) Probability of occurrence of nonconformities should be small
c) Probability of occurrence of nonconformities should be variable
d) Probability of occurrence of nonconformities should be constant

Explanation: The assumption of Poisson distribution of nonconformities in the samples of constant size, for c-charts, makes it necessary that, number of potential locations for nonconformities should be large, and the probability of occurrence of nonconformities should be small and constant.

6. What will be the value of the 3-sigma Upper control limit for the c chart when standard is given?
a) UCL = c + 3√c
b) UCL = c – √c
c) UCL = c + √c
d) UCL = c + 2√c

Explanation: The 3 – sigma upper control limit for the c-chart is expressed algebraically by
UCL = c + √c.

7. The center line for the control chart for nonconformities is representing the value equal c, which is ____________
a) The total number of nonconformities
b) The average number of conformities in a preliminary sample
c) The total number of nonconforming products
d) The total number of conforming products

Explanation: If there is no standard given for the c-chart, the center line represents the estimation of standard, c which is equal to the average number of nonconformities in a preliminary sample.

8. When there is no standard given, the value of LCL for the c-chart is given by ___________
a) LCL=$$\bar{c}-3\sqrt{\bar{c}}$$
b) LCL=$$\bar{c}+2\sqrt{\bar{c}}$$
c) LCL=$$\bar{c}-2\sqrt{\bar{c}}$$
d) LCL=$$\bar{c}+3\sqrt{\bar{c}}$$

Explanation: When there is no standard given for the number of conformities (c), for the c chart, the lower control limit is given by,
LCL=$$\bar{c}+3\sqrt{\bar{c}}$$

9. If the average number of nonconformities in a preliminary sample of a process is 19.67, which of these represents the value of UCL for a c-chart for this process output?
a) 19.67
b) 6.37
c) 32.97
d) 25.77

Explanation: The UCL for the c-chart is given by,
UCL=$$\bar{c}-3\sqrt{\bar{c}}$$
Now UCL=32.97.

10. For c=13.11, what will be the value of LCL for the c-chart?
a) 23.97
b) 10.86
c) 8.84
d) 2.24

Explanation: The LCL for c-chart is expressed by
LCL=$$\bar{c}+3\sqrt{\bar{c}}$$
Putting c=13.11, we get LCL for the control chart for nonconformities = 2.24.

11. With c-chart, which of these is used to analyze nonconformity data?
a) X bar charts
b) R charts
c) Cause and Effect diagram
d) Tolerance Diagram

Explanation: The c-chart is usually used to analyze the nonconformity data to get more information about the process state. Cause and effect diagram are also a good way to analyze nonconformity data.

12. The control chart used to inspect the process state by using the average number of nonconformities per unit data, is called _______________
a) u-chart
b) c-chart
c) p-chart
d) R-chart

Explanation: The control chart, which uses the average number of nonconformities per unit data to analyze the process state, is generally termed as the Control chart for Average number of Nonconformities per Unit.

13. If xi=total number of nonconformities in a sample of ni inspection units, and there are N samples of different sample size, and x varies according to a Poisson distribution, what will be the value of center line of the u-chart?
a) $$\bar{u} = \frac{\sum_{i=1}^N \frac{2x_i}{n_i}}{N}$$
b) $$\bar{u} = \frac{\sum_{i=1}^N \frac{x_i}{2n_i}}{2N}$$
c) $$\bar{u} = \frac{\sum_{i=1}^N \frac{x_i}{n_i}}{N}$$
d) $$\bar{u} = \frac{\sum_{i=1}^N \frac{x_i}{n_i}}{2N}$$

Explanation: As u-chart uses the value of the average number of nonconformities per unit, the center line of the u-chart is given by,
$$\bar{u} = \frac{\sum_{i=1}^N \frac{x_i}{n_i}}{N}$$

14. For a control chart for nonconformities, the sample size can only be 1.
a) True
b) False

Explanation: For a control chart for nonconformities, sample size can be greater than 1. This increases the area of opportunity for the occurrence of nonconformities. This can be used to obtain a positive lower control limit also.

15. The sample for the control chart for nonconformities is assumed to have, a variable sample size, and the sample conformities distributed according to Normal distribution.
a) True
b) False

Explanation: The control charts for nonconformities, usually assume that the occurrence of nonconformities in samples of constant size, is well modeled by the Poisson distribution.

16. Count rate of a defect is defined as _____________
a) Defects per unit
b) Average number of defects per unit
c) Total number of nonconformities
d) Occurrence of n defects in N number of units