# Statistical Quality Control Questions and Answers – Time-Weighted – Cumulative Sum Control Chart – 1

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This set of Statistical Quality Control Multiple Choice Questions & Answers (MCQs) focuses on “Time-Weighted – Cumulative Sum Control Chart – 1”.

1. Cusum control charts were originated in ____________
a) 1950s
b) 1960s
c) 1920s
d) 1980s

Explanation: The emphasis on more and more variability reduction, yield enhancement and process improvement, forced people to create new process monitoring techniques. Cusum charts were originated due to the same reason in 1950s.

2. Which of the control charts are used in phase I application of SPC?
a) Shewhart control charts
b) Cusum control charts
c) Both, Shewhart control charts and Cusum control charts
d) Neither one of the Shewhart control charts or the Cusum control charts

Explanation: Shewhart control charts are used for preliminary process monitoring, so the Shewhart control charts are used in the phase I implementation of SPC.

3. Which of these is not one of the phenomenons likely to occur while the phase I application of SPC?
a) Process likely to be out of control
b) Process changing its state continuously between in-control and out-of-control
c) Experiencing assignable causes
d) Large shifts in the monitored parameters

Explanation: Shewhart control charts are used in phase I implementation of the SPC, where process is likely to be out-of-control, and experiencing assignable causes, which may result in large shifts in the monitored parameters.

4. Which of these is a disadvantage of Shewhart control charts?
a) Can be for both attributes and variables
b) Gives process information
c) Using only the information about the last sample observations
d) Uses every information about the process

Explanation: The major disadvantage of a Shewhart control chart is that, it uses only the information about the process contained in the last sample observation, and it ignores the information given by the entire sequence of points.

5. Shewhart control charts are insensitive to ________ process shifts.
a) Small (<1.5σ)
b) Medium (1.5 σ<shift<3 σ)
c) Big (>6 σ)
d) Very Big

Explanation: As the Shewhart control charts ignore the information about the entire sequence of the points, it ignores the small process shifts, say on the order of 1.5σ or less.

6. Which of these is a reason why the Shewhart control charts are not used in phase II application of SPC?
a) Because they can count larger shifts in process
b) Because they can analyze information about the last sample observation
c) Because they become insensitive to lower order process shifts
d) Because they are impractical

Explanation: Shewhart control charts are insensitive towards small process shifts. As the process shifts in the phase II application are of very less order, Shewhart control charts are not generally used for phase II application of SPC.

7. Which of these can be applied to Shewhart control charts to enhance their performance in the phase II application of the SPC?
a) Control limits
b) Mean of the process
c) Standard deviation of the process
d) Warning limits

Explanation: To enhance the performance of the Shewhart control charts in the phase II application of the SPC, we can use the warning limits and other sensitizing rules with the Shewhart control charts.

8. What is the effect of warning limits and other sensitizing rules over the average run length of the process?
a) Increase
b) Decrease
c) Remains same
d) Does not change the ARL

Explanation: The warning limits and the other sensitizing rules are used to improve the performance of Shewhart control charts, to get better results in the Phase II applications of the SPC. But it also decreases the ARL of the process.

9. Which of the error types are likely to occur when the warning limits are used with Shewhart control charts the phase II of SPC?
a) Type I
b) Type II
c) Type I and Type II
d) Type III

Explanation: As ARL of the process reduces, due to the use of warning limits with the Shewhart control charts, we conclude a process out-of-control when it is actually in-control, which is actually type I error.

10. What is the full form of the Cusum control charts?
a) Curetted sum control charts
b) Corrected sum control charts
c) Compressive sum control charts
d) Cumulative sum control charts

Explanation: The Cusum chart is an alternative of the Shewhart control charts. Its full name is cumulative sum control chart, which is used in the place of the Shewhart control charts with warning limits.

11. In which phase of SPC are the Cusum control charts are used?
a) Phase I
b) Phase II
c) Both, phase I and II
d) Neither in phase I nor in phase II

Explanation: The Cusum control charts, or the cumulative control charts were originated due to the degraded performance of Shewhart control charts in the phase II of SPC. So they are used in the phase II only.

12. What is the value of the quantity plotter on the Cusum charts?
a) $$C_i=\sum_{j=1}^i (\bar{x}_j-μ)$$
b) $$C_i=\sum_{j=1}^i (\bar{x}_j+2μ)$$
c) $$C_i=\sum_{j=1}^i (\bar{x}_j-2μ)$$
d) $$C_i=\sum_{j=1}^i (\bar{x}_j+μ)$$

Explanation: Cusum control charts are plotted instead of Shewhart control charts in phase II applications of SPC. The quantity plotted on the charts is written as,
$$C_i=\sum_{j=1}^i (\bar{x}_j-μ)$$

13. What is the name of the quantity plotted Cion Cusum charts?
a) Cumulative sum from ith sample
b) Cumulative sum to ith sample
c) Cumulative sum to and ith sample
d) Cumulative sum from and ith sample

Explanation: The quantity plotted on the Cusum charts or the cumulative sum control charts is Ci. It is called, Cumulative sum to and ith sample.

14. Shewhart control charts are better for phase II applications than the Cusum charts.
a) True
b) False

Explanation: As Shewhart control charts fail to detect small shifts in process in phase II of SPC, Cusum charts are better in the detection of small shifts in process.

15. Type I possibility in the phase II application of the Shewhart control charts with warning limits.
a) True
b) False 