# Statistical Quality Control Questions and Answers – Time-Weighted – Cumulative Sum Control Chart – 2

This set of Statistical Quality Control Multiple Choice Questions & Answers (MCQs) focuses on “Time-Weighted – Cumulative Sum Control Chart – 2”.

1. Which of these is a reason, why the Cusum charts are better than the Shewhart control charts?
a) Because they are having information about only one sample
b) Because the quantity plotted on the Shewhart control charts is variable
c) Because the quantity plotted on the Cusum chart contains information about more than one sample
d) Because the quantity plotted on the Cusum control charts is containing information about a single sample

Explanation: The quantity plotted in the Cusum charts, contains more information as it contains information about more than one samples (Ci cumulative sum to and including an ith sample).

2. Which charts are particularly more effective for sample size one?
a) p-charts
b) c-charts
c) X bar and s charts
d) Cusum charts

Explanation: Because of the reason that Cusum control charts can detect small process shifts easily, and they contain information about more than one sample, they are better used for sample size=1.

3. Which charts are more effective for the chemical and process industries?
a) p-charts
b) c-charts
c) X bar and s charts
d) Cusum charts

Explanation: Cusum charts are more effective when the rational subgrouping with sample size 1 concept is used. As chemical and process industries use the concept of rational subgrouping with sample size 1, Cusum charts are more productive in them.

4. The processes where discrete part manufacturing is done, which charts are better?
a) p-charts
b) c-charts
c) Cusum charts
d) X bar and R charts

Explanation: The process where discrete part manufacturing is done, the sample size is usually 1. As the Cusum charts are better and more effective than Shewhart control charts when it comes to sample size 1, they are used in the mentioned situations.

5. Which of these control charts will have a better performance in the discrete part manufacturing assembly, where automatic measurement of each part is done?
a) X bar charts
b) Cusum charts
c) u-charts
d) c-charts

Explanation: As automatic measurement of each part is indicating a sample size of 1 unit, the Cusum charts are used for the processes of such type. The reason behind it being that, they are effective for the industries having a sample size, mostly 1.
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6. Cumulative control charts were first presented by ____________
a) Shewhart
b) ASQC
c) ASQ
d) Page

Explanation: The initial proposal for the use of the cumulative sum control charts, was first introduced by Page in the year of 1954. Then the improvements and the use of the charts started in the industries.

7. If the mean changes to a higher value, what will be the effect on the cumulative sum?
a) Decrease
b) Increase
c) Can decrease or increase
d) Can’t be predicted.

Explanation: If the value of the mean of the process shifts to a higher value i.e. a positive drift, we note form the formula of Cusum,
$$C_i=\sum_{j=1}^i (\bar{x}_i-μ)$$
That it will introduce a positive drift in the cumulative sum too.

8. If the value of the cumulative sum shifts to a lower value what is likely to be the reason for it?
a) The decrease in the value of the mean
b) The increase in the value of the mean
c) No change in the value of mean
d) Decrement in the value of the standard deviation

Explanation: It is noted while operating on the Cusum chart that, whenever there is a downward drop in the process mean, there is a negative drop in the value of the cumulative sum.

9. How are the changes in the conditions of the process, known using the Cusum charts?
a) By the change in Cusum value
b) By the change in the sample standard deviation
c) By plotting a s chart first
d) By plotting an R chart first

Explanation: As a positive drift, and a negative drift in the Cusum or cumulative sum value indicates a shifting of mean in positive or negative direction respectively, we can sense the shifting of mean continuously by checking the Cusum value, and hence the process state.

10. A significant trend upwards in the process cumulative sum chart indicates ____________
a) Shifting of mean in the positive direction
b) Shifting of mean in the negative direction
c) No shift in the process condition
d) No shift in the mean

Explanation: A significant trend developed in the Cusum chart due to the positive drift of the Cusum value, points toward the positive shift of the mean of the process. An assignable cause is present in this case.

11. Which of these conditions don’t describe an assignable cause in the process?
a) A positive shift in the Cusum value
b) A negative shift in the Cusum value
c) Random change in Cusum value
d) Continuous upward drift of Cusum value after a continuous downward drift in the Cusum value

Explanation: A random change in the Cusum value indicates that the mean is shifting randomly. This indicates an in-control process condition, of the process for which the Cusum chart is made for.

12. Which of these is another form of the cumulative sum value plotted on the cumulative sum chart?
a) $$C_i=(x_i-μ)+\sum_{j=1}^{i-1} (x_j+μ)$$
b) $$C_i=(x_i-μ)+C_{i-1}$$
c) $$C_i=(x_i-μ)+\sum_{j=1}^{i-1} (x_j+2μ)$$
d) $$C_i=(x_i-μ)-C_{i-1}$$

Explanation: As we know,
$$C_i=\sum_{j=1}^i (\bar{x}_j-μ_0)$$
This can be written as,
$$C_i=(x_i-μ)+\sum_{j=1}^{i-1}(x_j-μ)=(x_i-μ)+C_{i-1}$$

13. If the value of xi=9.29, and Ci-1=-2.56, what will be the value of the cumulative sum for this sample, if the value of μ0=10?
a) -3.27
b) -5.13
c) 3.27
d) 5.13

Explanation: We know that,
Ci=(xi-μ)+Ci-1
Putting the values from the question, we get,
Ci=-3.27

14. Upward or downward shifts in the Cusum value, directly indicate changes in process condition.
a) True
b) False

Explanation: As we know, the upward and downward shifts in the Cusum values are caused due to process mean shift, and the process mean shift indicates a shift in the process condition, hence, the shifts in the Cusum values directly indicates changes in process condition.

15. A change of process mean changes the value of Ci>Ci-1, so we can say that the process mean has shifted upwards.
a) True
b) False

Explanation: As the positive shift in the process mean indicates a positive drift in the Cusum chart, we can say that, the inequality Ci>Ci-1 indicates the upward shift of the process mean too.

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