This set of Statistical Quality Control Multiple Choice Questions & Answers (MCQs) focuses on “The 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.
Explanation: EWMS is defined as the exponentially weighted mean square error. It is expressed as,
4. “Si2/σ2” has an approximate ____ distribution.
Explanation: If the observations in EWMS are independent and normally distributed, then Si2/σ2 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.
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,
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,
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.
Explanation: The EWMV is said to be the exponentially weighted moving average. It is expressed by the following expression,
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,
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,
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.
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.
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?
c) EWMA chart
Explanation: The EWMA charts have both monitoring, and the 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.
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.
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,
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