This set of Statistical Quality Control Questions & Answers for Exams focuses on “The Cumulative Sum Control Chart – 5”.

1. What are the graphical displays of tabular cusum called?

a) Cusum regular charts

b) Cusum regulated display

c) Cusum level display

d) Cusum status charts

View Answer

Explanation: it is useful to present a graphical display for the tabular cusum. These charts are sometimes called the cusum status charts.

2. Which of these is a correct statement for cusum status charts?

a) A plot between C_{i}^{+} or C_{i}^{–} and the sample number

b) A plot between the C_{i}^{+} or C_{i}^{–} and the sample mean

c) A plot between the C_{i}^{+} or C_{i}^{–} and the sample variance

d) A plot between the C_{i}^{+} or C_{i}^{–} and the sample standard deviation

View Answer

Explanation: Cusum status charts are constructed by plotting C

_{i}

^{+}or C

_{i}

^{–}versus the sample number. These are used to get an quick information about the process from the displayed chart.

3. Each vertical bar in cusum status chart represents _____

a) The value of C_{i}^{+} and C_{i}^{–}

b) The value of C_{i}^{–}

c) The value of C_{i}^{+}

d) Neither the value of C_{i}^{+} nor C_{i}^{–}

View Answer

Explanation: Cusum status charts are the charts made to represent the cusum data on a graphical display, where each vertical bar in the cusum status charts, represents the value of C

_{i}

^{+}and C

_{i}

^{–}.

4. What is analogous to the control limits as in Shewhart control charts, in the cusum status charts?

a) The reference value

b) The allowance value

c) The value of the decision intervals

d) The value of C_{i}^{+} and C_{i}^{–}

View Answer

Explanation: The value of the decision interval H can be used as the control limits in the cusum charts as in the Shewhart charts. This gives us an indication about when the process is out-of-control.

5. In the Minitab version of the cusum control charts, which of these is used?

View Answer

Explanation: The Minitab version of the tabular cusum charts uses the negative of C

_{i}

^{–}i.e. it uses the following expression for C

_{i}

^{–},

.

6. Which of these is true for the Minitab version of tabular cusum charts?

View Answer

Explanation: The Minitab version of the tabular cusum uses the negative expression for the C

_{i}

^{–}, so the value of C

_{i}

^{–}always remains less than or equal to zero.

7. Which of these steps, is not carried out when the process becomes out-of-control when using the cusum control charts?

a) Search for an assignable cause

b) Taking corrective action

c) Restarting the control chart from zero

d) Continuing the control chart

View Answer

Explanation: When an out-of-control situation is encountered while using the cusum control charts, we use the same procedure, used as in the Shewhart control charts. First, identifying the assignable cause, then second, taking corrective action, and then restarting the control chart from zero.

8. Which of these control charts may accurately tell when the assignable cause has occurred?

a) Cusum control charts

b) p-charts

c) c-charts

d) x bar and s charts

View Answer

Explanation: As the pattern changes in the cusums due to an assignable cause, the changed pattern gets recorded in all the next cusums. So, we can identify from which cusum, the pattern changed, and hence the assignable cause location can be known.

9. Which of these can be used to calculate the estimate of mean of the process in the case of the tabular cusums when C_{i}^{+} > H?

View Answer

Explanation: In cases when a manipulative variable is required to take an out-of-control process back to target valueμ

_{0}, we use the new process mean estimate, which is written as,

10. Which of these following expressions can be used to calculate the estimate of mean of the process in the case of the tabular cusums when C_{i}^{–} > H?

View Answer

Explanation: The cases when there is a need to estimate the changed process mean, the expression of new process mean estimate is written as,

11. What of these can be used as the decision interval for the tabular cusum charts?

a) 2σ

b) 1σ

c) 5σ

d) 4σ

View Answer

Explanation: It is a generalized rule that, the decision intervals should always be five times of the standard deviations of the process.

12. What is the expression for the two sided cusum ARL?

View Answer

Explanation: The expression for the ARL of the two sided cusum from the ARLs of the two one sided statistics, is written as,

It is used to estimate the average time till an out-of-control signal comes from the cusum chart.

13. Which of these is an expression for Siegmund’s approximation?

View Answer

Explanation: The Siegmund’s approximation is used to evaluate the average run length for the cusum charts. It is expressed as,

14. The value of K and H should be determined according to the ARL required for the corresponding cusum chart.

a) True

b) False

View Answer

Explanation: ARL value tells about the time until the next out-of-control signal. So it is also an estimate to predict the type I error possibility. Hence, K and H values should be determined according to the ARL required.

15. The desired ARL is obtained by using the Siegmund’s approximation.

a) True

b) False

View Answer

Explanation: A desired ARL predicts the probability of occurrence of a type I error. This ARL is obtained by using the Siegmund’s approximation.

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