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

1. What is the full form of E in the EWMA chart?

a) Exponentially

b) Experimentally

c) Exactly

d) Estimated

View Answer

Explanation: The EWMA charts are a better alternative to the Shewhart control charts. The full form of E in the EWMA chart is exponentially.

2. What is the full form of EWMA?

a) Exponentially weighted moving average

b) Exponentially weighted measured approximate

c) Exponentially weighted moving approximate

d) Exponentially weighted measured average

View Answer

Explanation: The EWMA charts were developed after the cusum charts. They have a full form of Exponentially Weighted Moving Average charts.

3. EWMA charts are better than Shewhart control charts in detecting the ___________ shifts.

a) Large process

b) Medium process

c) Small process

d) Every process

View Answer

Explanation: EWMA charts and Cusum charts are used instead of the Shewhart control charts as the capability of these charts to find small process shifts, is greater than the Shewhart control charts’ capability.

4. Which of these is not an advantage of EWMA control charts?

a) Almost equivalent performance to the cusum charts

b) Easier set up than cusum charts

c) Easier to operate than cusum charts

d) Intricacy is a little higher than cusum charts

View Answer

Explanation: The EWMA control charts are the control charts, which have almost equivalent performance to the cusum charts, and in some ways, they are easier to set up and operate.

5. Who did first introduce the EWMA charts?

a) Lucas (1990)

b) Saccucci (1990)

c) Roberts (1959)

d) Crowder (1987a, 1989)

View Answer

Explanation: The EWMA charts, which are also called the Exponentially Weighted Moving Average charts, were first introduced in the year of 1990 by Roberts. It was a revolutionary step towards process control.

6. What is the correct expression for the EWMA?

a) z_{i} = λx_{i} + (1-λ) z_{i-1}

b) z_{i} = λx_{i} – (1-λ) z_{i-1}

c) z_{i} = λx_{i} + (1-λ) z_{i+1}

d) z_{i} = λx_{i} + (1+λ) z_{i-1}

View Answer

Explanation: The EWMA charts use the exponentially weighted moving average as the quantity plotted. The EWMA used is expressed as,

z

_{i}= λx

_{i}+ (1-λ) z

_{i-1}.

7. Which of these is correct for λ in EWMA expression?

a) 0 > λ

b) 1 < λ

c) 1 ≤ λ

d) 0 < λ ≤ 1

View Answer

Explanation: The EWMA expression is written as,

z

_{i}= λx

_{i}+ (1-λ) z

_{i-1}

Where λ is a constant, and it is having a value, 0 < λ ≤ 1.

8. What is the starting value of the EWMA?

a) Zero

b) Process target mean

c) Process target variance

d) Process target standard deviation

View Answer

Explanation: The starting value of the exponentially weighted moving averages is z

_{0}and its starting value is equal to the process target (mean). So,

z

_{0}= μ

_{0}.

9. Which of these is another name of EWMA charts?

a) GMA charts

b) AMA charts

c) EMA charts

d) RMA charts

View Answer

Explanation: Because of the fact, that the weights decline geometrically when connected by a smooth curve, EWMA charts are also called the GMA charts.

10. GMA stands for ___________

a) Geosum moved average

b) Geometric Moving average

c) Geometrically moved average

d) Geocentric moving average

View Answer

Explanation: GMA stands for Geometric moving average. It is another name of the EWMA charts because the weights decrease geometrically when connected by a smooth curve.

11. Which of these is the use of the EWMA charts?

a) In time series modeling

b) In Real-time processing

c) In acceptance sampling

d) In designing of experiments

View Answer

Explanation: The EWMA charts are better at forecasting future results and predicting future trends in the control chart. So they are used in time series modeling and in forecasting future process behavior.

12. Which of these is an ideal chart for individual measurements among these all?

a) p-chart

b) Cusum charts

c) EWMA charts

d) x bar and R chart

View Answer

Explanation: Since EWMA can be viewed as a weighted average of all past and current observations, it is very sensitive to the normality assumption. It is therefore an ideal control chart to use with individual observations.

13. If the observations x_{i} are independent random variables with variance σ^{2} then according to the EWMA charts, the variance of z_{i} will be ________________

a) \(\sigma_{zi}^2 = \sigma^2 (\frac{λ}{2-λ})[1+(1+λ)^{2i}]\)

b) \(\sigma_{zi}^2 = \sigma^2 (\frac{λ}{2-λ})[1+(1-λ)^{2i}]\)

c) \(\sigma_{zi}^2 = \sigma^2 (\frac{λ}{2-λ})[1-(1-λ)^{2i}]\)

d) \(\sigma_{zi}^2 = \sigma^2 (\frac{λ}{2+λ})[1-(1-λ)^{2i}]\)

View Answer

Explanation: The variance of the variable z

_{i}when used with EWMA, we get to know that, weights decline geometrically. So the variance becomes,

\(\sigma_{zi}^2 = \sigma^2 (\frac{λ}{2-λ})[1-(1-λ)^{2i}]\)

14. The weights of EWMA charts may also increase.

a) True

b) False

View Answer

Explanation: We know that weights of EWMA charts decline with a geometric pattern. So they are called GMA charts. It makes clear that weights of EWMA charts can never increase.

15. The starting value of the variable z_{i} is always equal to μ_{0}.

a) True

b) False

View Answer

Explanation: The starting value of the variable z

_{i}is mostly taken as μ

_{0}or the target value for mean but, sometimes the average of preliminary data is used as the starting value of EWMA. So that,

z

_{0}= x.

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