This set of Tricky Statistical Quality Control Questions and Answers focuses on “Time-Weighted – EWMA Control Chart – 3”.

1. The largest standard deviation of the sample mean from the target, not leading to an immediate out-of-control signal, is called _______________ of a control chart.

a) ARL

b) UCL

c) Signal resolution

d) Signal resistance

View Answer

Explanation: Signal Resistance is a very important property of any control chart. It is defined as the maximum standard deviation of the sample mean from the target or in-control value, not leading to an immediate out-of-control signal.

2. For a Shewhart control chart, what is the value of SR?

a) Z_{α/2}

b) 2

c) L

d) 2L

View Answer

Explanation: The value of SR is the maximum standard deviation of mean off-target without any out-of-control signal. This is L for the Shewhart control chart, i.e.

SR(x)=L

Where L is the multiplier used to obtain the control limits.

3. Which of these is a having a constant SR?

a) A x chart

b) A Cusum chart

c) An EWMA chart

d) Every control chart

View Answer

Explanation: The Shewhart control charts have the signal resistance value equal to the multiplier used to obtain the control limit, which is constant. As a x chart is also a Shewhart control chart, so for this also, “ SR=constant”.

4. Which of these is not having a constant SR value?

a) c-chart

b) R-chart

c) p-chart

d) EWMA chart

View Answer

Explanation: We know that only Shewhart control chart have the SR value equal to constant. As EWMA chart is not a Shewhart chart, it does not have a constant SR value.

5. What is the value of SR for an EWMA chart?

a) SR(EWMA)=\(\frac{L\sqrt{\frac{λ}{2-λ}}+(λ-1)w}{λ}\)

b) SR(EWMA)=\(\frac{L\sqrt{\frac{λ}{2-λ}}-(1-λ)w}{λ}\)

c) SR(EWMA)=\(\frac{L\sqrt{\frac{λ}{2-λ}}-(λ-1)w}{λ}\)

d) SR(EWMA)=\(\frac{L\sqrt{\frac{λ}{2-λ}}+(1-λ)w}{λ}\)

View Answer

Explanation: We have derived an equation of an EWMA chart SR which includes the value of the EWMA statistic. The SR is given by,

SR(EWMA)=\(\frac{L\sqrt{\frac{λ}{2-λ}}-(1-λ)w}{λ}\)

6. What is the value of the term “w” called in the SR value of a EWMA chart?

a) First EWMA value

b) Last EWMA value

c) Value of EWMA statistic

d) Weight average

View Answer

Explanation: The SR value of EWMA chart is given by,

SR(EWMA)=\(\frac{L\sqrt{\frac{λ}{2-λ}}-(1-λ)w}{λ}\)

Here, w is called the value of EWMA statistic.

7. Which of these is the maximum value of the SR averaged over all values of EWMA statistic?

a) \(SR_{max} (EWMA)=L \frac{(2-λ)}{λ}\)

b) \(SR_{max}(EWMA)=L\sqrt{\frac{(2-λ)}{λ}}\)

c) \(SR_{max} (EWMA)=L+\sqrt{\frac{(2-λ)}{λ}}\)

d) \(SR_{max} (EWMA)=L-\sqrt{\frac{(2-λ)}{λ}}\)

View Answer

Explanation: If the chart has asymptotic limits, then the maximum value of the signal resistance averaged over all values of EWMA statistic is,

\(SR_{max}(EWMA)=L\sqrt{\frac{(2-λ)}{λ}}\)

8. Small values of λ gives ______ values of the SR (EWMA).

a) Larger

b) Lower

c) Equal

d) Both, larger and smaller

View Answer

Explanation: As we know that,

SR(EWMA)=\(\frac{L\sqrt{\frac{λ}{2-λ}}-(1-λ)w}{λ}\)

We get the inference that, SR(EWMA)∝1/λ, so SR(EWMA) will be larger for smaller values of λ.

9. Which of these methods can be used to counteract the signal resistance in case of small values of λ with EWMA charts?

a) To use a cusum chart paralleled

b) To use a Shewhart control chart paralleled

c) To just wait for EWMA chart to be plotted till 50 observations

d) To increase the value of process mean target

View Answer

Explanation: To counteract the signal resistance’s higher value in the case of low λ value, we use the Shewhart control charts in conjunction with an EWMA chart.

10. Who were the first persons to recommend the use of Shewhart control charts with the EWMA charts with low values of λ?

a) Woodall and Mahmoud

b) Woodall and Roberts

c) Roberts and Mahmoud

d) Roberts and Crowder

View Answer

Explanation: Woodall and Mahmoud (2005) recommended to always use a Shewhart control chart with a EWMA chart (especially when λ is small), as one way to counteract the signal resistance’s high value.

11. Which of these is not an advantage of using a Shewhart control chart with the EWMA chart?

a) Detection of larger process shifts

b) ARL adjustment

c) Counteraction to the high signal resistance value

d) No defects

View Answer

Explanation: We know that Shewhart control charts are used with the EWMA control charts. They provide advantages like easy ARL adjustment, counteraction to high signal resistance value, and detection of larger process shifts, without lowering the ability to find lower process shifts.

12. Which of these is not an advantage of low value of λ in the case of EWMA charts?

a) Good ARL performance

b) Insensitivity to the normality of the data

c) Good ability to detect the larger process shifts

d) Easy detection of small process shifts

View Answer

Explanation: Low values of λ are quite helpful in finding small process shifts, good AR performance, and in increasing the insensitivity of the EWMA charts to the normality of the data. They don’t give the charts ability to detect the larger process shifts.

13. In the case of Shewhart charts, if the data is not according to the normal distribution, the actual in-control ARL (ARL_{0}) will be ____________ the expected value.

a) Considerably higher than

b) Considerably lower than

c) Equal to

d) Almost equal to

View Answer

Explanation: It is experimentally determined that if the process data does not follow the normal distribution, then the Shewhart control charts ARL value will be quite less than the value expected based on the normality assumption.

14. The signal resistance value depends on the value chosen for λ.

a) True

b) False

View Answer

Explanation: We know that,

SR(EWMA)=\(\frac{L\sqrt{\frac{λ}{2-λ}}-(1-λ)w}{λ}\)

Here the value of L and w are constants. So the value of SR (EWMA) depends only on the value of the λ.

15. The EWMA charts are recommended for phase II applications as it is totally a nonparametric procedure.

a) True

b) False

View Answer

Explanation: We know that the variation in ARL, which is caused by the non-normality of data, is very low in the case of low λ with the EWMA charts. So they are recommended for phase II applications as it is a perfectly nonparametric (distribution-free) procedure.

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