# Statistical Quality Control Questions and Answers – Time-Weighted – EWMA Control Chart – 4

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This set of Statistical Quality Control Multiple Choice Questions & Answers (MCQs) focuses on “Time-Weighted – EWMA Control Chart – 4”.

1. What is the initial S in EWMS stand for?
a) Severity error
b) Signal error
c) Square error
d) Simple error

Explanation: The EWMS charts were used to monitor the variability in the process. They are variants of EWMA chart. EWMS stands for Exponentially Weighted Mean Square error.

2. Who were the first people to introduce the EWMA charts to monitor process standard deviation?
a) McGregor and Harris
b) Harris and Roberts
c) Crowder and Roberts
d) Harris and Roberts

Explanation: It was Macgregor, and Harris (1993), who were the first people to identify the importance of EWMA charts to monitor process std deviation. They recommended using EWMS charts to do so.

3. What is the value of EWMS?
a) $$S_i^2= λ(x_i-μ)^2-(1-λ) S_{i-1}^2$$
b) $$S_i^2= λ(x_i-μ)^2-(1+λ) S_{i-1}^2$$
c) $$S_i^2= λ(x_i-μ)^2+(1-λ) S_{i-1}^2$$
d) $$S_i^2= λ(x_i-μ)^2+(1+λ) S_{i-1}^2$$

Explanation: EWMS is defined as the exponentially weighted mean square error. It is expressed as,$$S_i^2= λ(x_i-μ)^2+(1-λ) S_{i-1}^2$$

4. “Si22” has an approximate __________ distribution.
a) Normal
b) Lognormal
c) Exponential
d) Chi-square

Explanation: If the observations in EWMS are independent and normally distributed, then Si22 will have an approximate chi-square distribution, with v=(2-λ)/λ degrees of freedom.

5. EWRMS chart plots __________ on the control chart.
a) Exponentially weighted root moving square error
b) Exponentially weighted root mean square error
c) Exponentially weighted root mean signal error
d) Exponentially weighted root moving signal error

Explanation: If we have a target value for the mean, and if we want to monitor process standard deviation, we use the EWRMS charts which use Exponentially Weighted Root Mean Square error.

6. EWRMS charts have the upper limit of ____________
a) UCL=$$σ_0 \sqrt{\frac{χ_{v,\frac{α}{2}}^2}{v}}$$
b) UCL=$$\frac{σ_0}{2} \sqrt{\frac{χ_{v,\frac{α}{2}}^2}{v}}$$
c) UCL=$$σ_0 \sqrt{\frac{χ_{v,\frac{α}{2}}^2}{2v}}$$
d) UCL=$$\sqrt{\frac{χ_{v,\frac{α}{2}}^2}{v}}$$

Explanation: The EWRMS chart is plotted by obtaining the value of Exponentially Weighted Root Mean Square error, which has an approximate chi-square distribution. It has an upper limit of,
UCL=$$σ_0 \sqrt{\frac{χ_{v,\frac{α}{2}}^2}{v}}$$

7. What is the lower limit of the EWRMS chart?
a) LCL=$$3σ_0 \sqrt{\frac{χ_{v,1-\frac{α}{2}}^2}{v}}$$
b) LCL=$$σ_0 \sqrt{\frac{χ_{v,1-\frac{α}{2}}^2}{2v}}$$
c) LCL=$$σ_0 \sqrt{\frac{χ_{v,1-\frac{α}{2}}^2}{v}}$$
d) LCL=$$\frac{σ_0}{2} \sqrt{\frac{χ_{v,1-\frac{α}{2}}^2}{v}}$$

Explanation: We know that the EWRMS chart has an approximate chi-square distribution when the observations are independent and normally distributed. So LCL of the EWRMS chart will be,
LCL=$$σ_0 \sqrt{\frac{χ_{v,1-\frac{α}{2}}^2}{v}}$$

8. EWRMS chart is sensitive to _____________
a) Process mean only
b) Process standard deviation only
c) Neither process mean nor standard deviation
d) Both, process mean and standard deviation

Explanation: EWRMS chart is constructed to monitor the process standard deviation. But this also, is considered that the process mean is also a factor affecting the EWRMS chart. So EWRMS chart is sensitive to both, the process mean and the standard deviation.

9. EWMV is ____________
a) Exponentially weighted mean variability
b) Exponentially weighted moving variance
c) Exponentially weighted mean variance
d) Exponentially weighted moving variability

Explanation: EWMV is the exponentially weighted moving variance. It is a term derived from the EWRMS and it is used in measuring variability of the process with EWMA charts.

10. What is the value of EWMV?
a) $$S_i^2=λ(x_i-z_i)^2- (1+λ) S_{i-1}^2$$
b) $$S_i^2=λ(x_i-z_i)^2± (1-λ) S_{i-1}^2$$
c) $$S_i^2=λ(x_i-z_i)^2- (1-λ) S_{i-1}^2$$
d) $$S_i^2=λ(x_i-z_i)^2+ (1-λ) S_{i-1}^2$$

Explanation: The EWMV is said to be the exponentially weighted moving average. It is expressed by the following expression,
$$S_i^2=λ(x_i-z_i)^2+ (1-λ) S_{i-1}^2$$

11. What is the upper limit for the EWMA for Poisson data?
a) UCL=$$μ_0+A_U \sqrt{\frac{λμ_0}{2-λ}\big\{1-(1-λ)^{2i}\big\}}$$
b) UCL=$$μ_0-A_U \sqrt{\frac{λμ_0}{2-λ}\big\{1-(1-λ)^{2i}\big\}}$$
c) UCL=$$μ_0-A_L \sqrt{\frac{λμ_0}{2-λ}\big\{1-(1-λ)^{2i}\big\}}$$
d) UCL=$$μ_0+A_L \sqrt{\frac{λμ_0}{2-λ}\big\{1-(1-λ)^{2i}\big\}}$$

Explanation: The EWMA is generally plotted for normal data. It is also said that the EWMA chart with low value of λ is nonparametric. When EWMA is plotted for Poisson data, the UCL is,
UCL=$$μ_0+A_U \sqrt{\frac{λμ_0}{2-λ}\big\{1-(1-λ)^{2i}\big\}}$$

12. LCL for EWMA chart for Poisson distribution is written as ____________
a) LCL=$$μ_0-A_L \sqrt{\frac{λμ_0}{2-λ}\big\{1-(1+λ)^{2i}\big\}}$$
b) LCL=$$μ_0+A_L \sqrt{\frac{λμ_0}{2-λ}\big\{1-(1+λ)^{2i}\big\}}$$
c) LCL=$$μ_0+A_L \sqrt{\frac{λμ_0}{2-λ}\big\{1-(1-λ)^{2i}\big\}}$$
d) LCL=$$μ_0-A_L \sqrt{\frac{λμ_0}{2-λ}\big\{1-(1-λ)^{2i}\big\}}$$

Explanation: EWMA charts are made to monitor the process mean shift. The EWMA chart for Poisson distribution is plotted with an assumption that, the data from the process follows Poisson distribution, It has LCL of,
LCL=$$μ_0-A_L \sqrt{\frac{λμ_0}{2-λ}\big\{1-(1-λ)^{2i}\big\}}$$

13. “AL” in the expression of the LCL of EWMA charts for Poisson distribution, is ______
a) Lower control limit factor
b) Lower allowance factor
c) Life Allowance factor
d) Last Allowance factor

Explanation: The factors AU and AL are included in the expressions of UCL and LCL of the EWMA charts plotted for Poisson data, respectively. They are called upper and lower control limit factors respectively.

14. EWMA recursion is different in the case of the EWMA charts for normal data and EWMA charts for Poisson data.
a) True
b) False

Explanation: The recursion of EWMA is the property of the EWMA statistic. That is why, the EWMA charts show trend due to an assignable cause. This recursion is always same, whether the EWMA charts are plotted for normal data or for the Poisson data.

15. The Poisson EWMA has considerably better ability to detect assignable causes than Shewhart c-chart.
a) True
b) False

Explanation: As Poisson EWMA has a better ability of detecting small process shifts in the phase II applications of SPC, they are also having a better ability to detect assignable causes than Shewhart c-chart.

16. Which of these can be used as a forecast of where the process mean will be at the next time period?
a) p-chart
b) c-chart
c) EWMA chart
d) R-chart

Explanation: The EWMA charts have both monitoring, and forecasting abilities. They can actually predict the position of process mean at the next time period. The statistic, zi is actually a forecast of the value of the process mean at time i+1.

17. The EWMA chart can be used as a basis for a dynamic process-control algorithm.
a) True
b) False

Explanation: Due to the fact that the EWMA charts can both monitor the process, and forecast the process mean in future time, they can be useful in process control. They can also detect small process shifts. So they may be used as the basis of a dynamic process control algorithm.

18. The moving average span w at a time I is defined as ____________
a) $$M_i=\frac{x_i+x_{i-1}+⋯x_{w+1}}{w}$$
b) $$M_i=\frac{x_i+x_{i-1}+⋯x_{w+1}}{i}$$
c) $$M_i=\frac{x_i+x_{i-1}+⋯x_{i-w+1}}{w}$$
d) $$M_i=\frac{x_i+x_{i-1}+⋯x_{i-w+1}}{i}$$

Explanation: The moving average is also a time weighted chart as EWMA charts and the Cusum charts. The moving average chart uses Moving Average span w at time i, which is expressed as,
$$M_i=\frac{x_i+x_{i-1}+⋯x_{i-w+1}}{w}$$

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