6. Process or Product Monitoring and Control
6.6. Case Studies in Process Monitoring
6.6.2. Aerosol Particle Size

6.6.2.5.

Work This Example Yourself

View Dataplot Macro for this Case Study

This page allows you to repeat the analysis outlined in the case study description on the previous page using Dataplot . It is required that you have already downloaded and installed Dataplot and configured your browser. to run Dataplot. Output from each analysis step below will be displayed in one or more of the Dataplot windows. The four main windows are the Output Window, the Graphics window, the Command History window, and the data sheet window. Across the top of the main windows there are menus for executing Dataplot commands. Across the bottom is a command entry window where commands can be typed in.

Data Analysis Steps	Results and Conclusions
Click on the links below to start Dataplot and run this case study yourself. Each step may use results from previous steps, so please be patient. Wait until the software verifies that the current step is complete before clicking on the next step.	The links in this column will connect you with more detailed information about each analysis step from the case study description.
1. Invoke Dataplot and read data. 1. Read in the data.	1. You have read one column of numbers into Dataplot, variable Y.
2. Model identification plots 1. Run sequence plot of Y. 2. Autocorrelation plot of Y. 3. Run sequence plot of the differenced data of Y. 4. Autocorrelation plot of the differenced data of Y. 5. Partial autocorrelation plot of the differenced data of Y.	1. The run sequence plot shows that the data show strong and positive autocorrelation. 2. The autocorrelation plot indicates significant autocorrelation and that the data are not stationary. 3. The run sequence plot shows that the differenced data appear to be stationary and do not exhibit seasonality. 4. The autocorrelation plot of the differenced data suggests an ARIMA(0,1,1) model may be appropriate. 5. The partial autocorrelation plot suggests an ARIMA(2,1,0) model may be appropriate.
3. Estimate the model. 1. ARIMA(2,1,0) fit of Y. 2. ARIMA(0,1,1) fit of Y.	1. The ARMA fit generates parameter estimates for the ARIMA(2,1,0) model. 2. The ARMA fit generates parameter estimates for the ARIMA(0,1,1) model.
4. Model validation. 1. Generate a 4-plot of the residuals from the ARIMA(2,1,0) model. 2. Generate an autocorrelation plot of the residuals from the ARIMA(2,1,0) model. 3. Perform a Ljung-Box test of randomness for the residuals from the ARIMA(2,1,0) model. 4. Generate a 4-plot of the residuals from the ARIMA(0,1,1) model. 5. Generate an autocorrelation plot of the residuals from the ARIMA(0,1,1) model. 6. Perform a Ljung-Box test of randomness for the residuals from the ARIMA(0,1,1) model.	1. The 4-plot shows that the assumptions for the residuals are satisfied. 2. The autocorrelation plot of the residuals indicates that the residuals are random. 3. The Ljung-Box test indicates that the residuals are random. 4. The 4-plot shows that the assumptions for the residuals are satisfied. 5. The autocorrelation plot of the residuals indicates that the residuals are random. 6. The Ljung-Box test indicates that the residuals are not random at the 95% level, but are random at the 99% level.