# Statistical Quality Control Questions and Answers – Time-Weighted – Cumulative Sum Control Chart – 6

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This set of Statistical Quality Control Multiple Choice Questions & Answers (MCQs) focuses on “Time-Weighted – Cumulative Sum Control Chart – 6”.

1. What is the standardized value used for xi in the standardized cusum chart?
a) $$y_i=\frac{x_i-μ_0}{3σ}$$
b) $$y_i=\frac{x_i-μ_0}{σ}$$
c) $$y_i=\frac{x_i-μ_0}{2σ}$$
d) $$y_i=\frac{x_i-μ_0}{6σ}$$

Explanation: Many users of the cusum prefer to standardize the variable xi, before performing the calculations. The standardized value of the variable is,
$$y_i=\frac{x_i-μ_0}{σ}$$

2. What is the value of one sided upper cusum of the standardized cusum chart?
a) $$C_i^+=max⁡\left\{0,y_i-k+C_{i-1}^+\right\}$$
b) $$C_i^+=max⁡\left\{0,y_i+k+C_{i-1}^+\right\}$$
c) $$C_i^+=min⁡\left\{0,y_i+k+C_{i-1}^+\right\}$$
d) $$C_i^+=min\left\{0,y_i-k+C_{i-1}^+\right\}$$

Explanation: The standardized cusum chart uses the standardized value of variable xi, i.e. yi, so the value of the one-sided upper cusum of the standardized cusum chart will be,
$$C_i^+=max⁡\left\{0,y_i-k+C_{i-1}^+\right\}$$

3. What is the value of the one-sided lower cusum of the standardized cusum chart?
a) $$C_i^+=max⁡\left\{0,-y_i-k+C_{i-1}^+\right\}$$
b) $$C_i^-=max⁡\left\{0,y_i-k+C_{i-1}^-\right\}$$
c) $$C_i^-=max⁡\left\{0,-y_i-k+C_{i-1}^-\right\}$$
d) $$C_i^+=max⁡\left\{0,-y_i-k+C_{i-1}^-\right\}$$

Explanation: The standardized cusum uses the different variable to calculate the upper and lower cusums. The lower cusum of the standardized cusum chart is expressed as,
$$C_i^-=max⁡\left\{0,-y_i-k+C_{i-1}^-\right\}$$

4. Which of these is an advantage of the standardized cusum chart?
a) There can be same means chosen for different processes
b) There can be same standard deviations chosen for different processes
c) The choices of k and h parameters are not scale dependent
d) No variability at all

Explanation: As in the standardized cusum charts, many charts can now have the same values of k and h, and because of the fact that the choice of k and h is dependent over the value of process standard deviation in normal cusum, the standardized cusum has k and h not scale dependent or σ dependent.

5. Combined Cusum-Shewhart procedure is applied _____________
a) On-line control
b) On-line measure
c) Off-line control
d) On-line measure

Explanation: As Combined Cusum-Shewhart procedure is used while using the cusum charts to detect the large process shifts while keeping the process continued, this is called an on-line control.

6. To apply Shewhart-cusum combined procedure, the Shewhart control limits should be applied almost _________ standard deviation from the center.
a) 2
b) 1
c) 1.5
d) 3.5

Explanation: Combined Cusum-Shewhart procedure is an on-line control method. It is used to detect larger process shifts. The Shewhart control limits in the procedure are put approx. 3.5 standard deviations away from center.

7. What is the full form of FIR feature in the cusum charts?
a) First initial response
b) Fast initial response
c) First initiation response
d) Free initial response

Explanation: The cusum control charts sensitivity at the process start-up is improved by the means of the FIR feature of the cusum charts. It means the Fast Initial Response.

8. What is the meaning of the 50% headstart?
a) The value of C0 equal to H/2
b) The value of C0+ equal to H/2
c) Both the values of C0+ and C0 equal to H/2
d) Both the values of C0+ and C0 lesser than H/2

Explanation: The FIR feature of the cusum charts essentially sets the starting values of both, the values of C0+ and C0 equal to typically, H/2. This is called 50% headstart.

9. What is the standardized variable value for the cusum charts from Hawkins?
a) $$v_i=\frac{\sqrt{|y_i|}-0.822}{0.349}$$
b) $$v_i=\frac{\sqrt{|y_i|}-0.822}{0.500}$$
c) $$v_i=\frac{3\sqrt{|y_i|}-0.822}{0.349}$$
d) $$v_i=\frac{2\sqrt{|y_i|}-0.822}{0.349}$$

Explanation: Hawkins presented a new standardized variable vi to be used in the standardized cusum chart. It had a value equal to,
$$v_i=\frac{\sqrt{|y_i|}-0.822}{0.349}$$

10. The standardized variable vi was subjected to vary more with respect to ____________ than process mean.
a) Sample mean
b) Sample variance
c) Process variance
d) Process standard deviation

Explanation: Hawkins had presented the std. variable vi to construct a cusum chart, which could possibly monitor process variability, by the variation of the variance of the process.

11. The two-sided standardized scale, i.e. standard deviation cusums will have its upper cusum value equal to ___________
a) $$S_i^+=max⁡⁡\left\{0,v_i-k+S_{i-1}^+\right\}$$
b) $$S_i^+=max⁡\left\{0,v_i+k-S_{i-1}^+\right\}$$
c) $$S_i^+=max⁡\left\{0,v_i-k-S_{i-1}^-\right\}$$
d) $$S_i^+=max⁡\left\{0,v_i-k+S_{i-1}^-\right\}$$

Explanation: The two-sided standardized scale cusums was first presented by Hawkins. This has the upper cusum value equal to,
$$S_i^+=max⁡⁡\left\{0,v_i-k+S_{i-1}^+\right\}$$

12. What is the value of lower cusum in the standardized scale cusum chart for process variability?
a) $$S_i^+=max⁡\left\{0,v_i-k+S_{i-1}^+\right\}$$
b) $$S_i^-=max⁡\left\{0,v_i-k+S_{i-1}^+\right\}$$
c) $$S_i^-=max⁡\left\{0,-v_i-k+S_{i-1}^-\right\}$$
d) $$S_i^+=max⁡\left\{0,-v_i-k+S_{i-1}^+\right\}$$

Explanation: The value of the lower cusum used in the standardized scale cusum chart, used for monitoring the process variability, is having the negative value of what was used in the normal cusum. This is written as,
$$S_i^-=max⁡\left\{0,-v_i-k+S_{i-1}^-\right\}$$

13. The values of Si+ or Si at the starting are ____ if the FIR feature is not used.
a) 1
b) H
c) H/2
d) 0

Explanation: The values of Si+ or Si are H/2 mostly when the fast initial response feature is used. When it is not used the values of them become zero.

14. Only two-sided cusums are useful all over the industries.
a) True
b) False

Explanation: There are situations in which only a single one-sided cusum procedure is useful. For example, in the chemical process industry, where viscosity of a liquid can be allowed to drop below one value but should not increase rapidly. So this increase is monitored in the upper cusum.

15. Some cusums can have different sensitivity of the lower cusum than the upper cusum.
a) True
b) False 