4. Subgroup analysis. 1. Generate a moving mean control chart. 2. Generate a moving range control chart. 3. Generate a mean control chart for WAFER. 4. Generate a sd control chart for WAFER. 5. Generate a mean control chart for CASSETTE. 6. Generate a sd control chart for CASSETTE. 7. Generate an analysis of variance. This is not currently implemented in DATAPLOT for nested datasets. 8. Generate a mean control chart using lot-to-lot variation. 1. The moving mean plot shows a large number of out-of- control points. 2. The moving range plot shows a large number of out-of- control points. 3. The mean control chart shows a large number of out-of- control points. 4. The sd control chart shows no out-of-control points. 5. The mean control chart shows a large number of out-of- control points. 6. The sd control chart shows no out-of-control points. 7. The analysis of variance and components of variance calculations show that cassette to cassette variation is 54% of the total and site to site variation is 36% of the total. 8. The mean control chart shows one point that is on the boundary of being out of control. 6.6.1.5. Work This Example Yourself http://www.itl.nist.gov/div898/handbook/pmc/section6/pmc615.htm (3 of 3) [5/1/2006 10:35:54 AM] 6. Process or Product Monitoring and Control 6.6. Case Studies in Process Monitoring 6.6.2.Aerosol Particle Size Box-Jenkins Modeling of Aerosol Particle Size This case study illustrates the use of Box-Jenkins modeling with aerosol particle size data. Background and Data1. Model Identification2. Model Estimation3. Model Validation4. Work This Example Yourself5. 6.6.2. Aerosol Particle Size http://www.itl.nist.gov/div898/handbook/pmc/section6/pmc62.htm [5/1/2006 10:35:54 AM] 6. Process or Product Monitoring and Control 6.6. Case Studies in Process Monitoring 6.6.2. Aerosol Particle Size 6.6.2.1.Background and Data Data Source The source of the data for this case study is Antuan Negiz who analyzed these data while he was a post-doc in the NIST Statistical Engineering Division from the Illinois Institute of Technology. Data Collection These data were collected from an aerosol mini-spray dryer device. The purpose of this device is to convert a slurry stream into deposited particles in a drying chamber. The device injects the slurry at high speed. The slurry is pulverized as it enters the drying chamber when it comes into contact with a hot gas stream at low humidity. The liquid contained in the pulverized slurry particles is vaporized, then transferred to the hot gas stream leaving behind dried small-sized particles. The response variable is particle size, which is collected equidistant in time. There are a variety of associated variables that may affect the injection process itself and hence the size and quality of the deposited particles. For this case study, we restrict our analysis to the response variable. Applications Such deposition process operations have many applications from powdered laundry detergents at one extreme to ceramic molding at an important other extreme. In ceramic molding, the distribution and homogeneity of the particle sizes are particularly important because after the molds are baked and cured, the properties of the final molded ceramic product is strongly affected by the intermediate uniformity of the base ceramic particles, which in turn is directly reflective of the quality of the initial atomization process in the aerosol injection device. 6.6.2.1. Background and Data http://www.itl.nist.gov/div898/handbook/pmc/section6/pmc621.htm (1 of 14) [5/1/2006 10:35:55 AM] Aerosol Particle Size Dynamic Modeling and Control The data set consists of particle sizes collected over time. The basic distributional properties of this process are of interest in terms of distributional shape, constancy of size, and variation in size. In addition, this time series may be examined for autocorrelation structure to determine a prediction model of particle size as a function of time such a model is frequently autoregressive in nature. Such a high-quality prediction equation would be essential as a first step in developing a predictor-corrective recursive feedback mechanism which would serve as the core in developing and implementing real-time dynamic corrective algorithms. The net effect of such algorthms is, of course, a particle size distribution that is much less variable, much more stable in nature, and of much higher quality. All of this results in final ceramic mold products that are more uniform and predictable across a wide range of important performance characteristics. For the purposes of this case study, we restrict the analysis to determining an appropriate Box-Jenkins model of the particle size. Case study data 115.36539 114.63150 114.63150 116.09940 116.34400 116.09940 116.34400 116.83331 116.34400 116.83331 117.32260 117.07800 117.32260 117.32260 117.81200 117.56730 118.30130 117.81200 118.30130 117.81200 118.30130 118.30130 118.54590 118.30130 117.07800 116.09940 6.6.2.1. Background and Data http://www.itl.nist.gov/div898/handbook/pmc/section6/pmc621.htm (2 of 14) [5/1/2006 10:35:55 AM] 118.30130 118.79060 118.05661 118.30130 118.54590 118.30130 118.54590 118.05661 118.30130 118.54590 118.30130 118.30130 118.30130 118.30130 118.05661 118.30130 117.81200 118.30130 117.32260 117.32260 117.56730 117.81200 117.56730 117.81200 117.81200 117.32260 116.34400 116.58870 116.83331 116.58870 116.83331 116.83331 117.32260 116.34400 116.09940 115.61010 115.61010 115.61010 115.36539 115.12080 115.61010 115.85471 115.36539 115.36539 115.36539 115.12080 6.6.2.1. Background and Data http://www.itl.nist.gov/div898/handbook/pmc/section6/pmc621.htm (3 of 14) [5/1/2006 10:35:55 AM] 114.87611 114.87611 115.12080 114.87611 114.87611 114.63150 114.63150 114.14220 114.38680 114.14220 114.63150 114.87611 114.38680 114.87611 114.63150 114.14220 114.14220 113.89750 114.14220 113.89750 113.65289 113.65289 113.40820 113.40820 112.91890 113.40820 112.91890 113.40820 113.89750 113.40820 113.65289 113.89750 113.65289 113.65289 113.89750 113.65289 113.16360 114.14220 114.38680 113.65289 113.89750 113.89750 113.40820 113.65289 113.89750 113.65289 6.6.2.1. Background and Data http://www.itl.nist.gov/div898/handbook/pmc/section6/pmc621.htm (4 of 14) [5/1/2006 10:35:55 AM] 113.65289 114.14220 114.38680 114.63150 115.61010 115.12080 114.63150 114.38680 113.65289 113.40820 113.40820 113.16360 113.16360 113.16360 113.16360 113.16360 112.42960 113.40820 113.40820 113.16360 113.16360 113.16360 113.16360 111.20631 112.67420 112.91890 112.67420 112.91890 113.16360 112.91890 112.67420 112.91890 112.67420 112.91890 113.16360 112.67420 112.67420 112.91890 113.16360 112.67420 112.91890 111.20631 113.40820 112.91890 112.67420 113.16360 6.6.2.1. Background and Data http://www.itl.nist.gov/div898/handbook/pmc/section6/pmc621.htm (5 of 14) [5/1/2006 10:35:55 AM] 113.65289 113.40820 114.14220 114.87611 114.87611 116.09940 116.34400 116.58870 116.09940 116.34400 116.83331 117.07800 117.07800 116.58870 116.83331 116.58870 116.34400 116.83331 116.83331 117.07800 116.58870 116.58870 117.32260 116.83331 118.79060 116.83331 117.07800 116.58870 116.83331 116.34400 116.58870 116.34400 116.34400 116.34400 116.09940 116.09940 116.34400 115.85471 115.85471 115.85471 115.61010 115.61010 115.61010 115.36539 115.12080 115.61010 6.6.2.1. Background and Data http://www.itl.nist.gov/div898/handbook/pmc/section6/pmc621.htm (6 of 14) [5/1/2006 10:35:55 AM] 115.85471 115.12080 115.12080 114.87611 114.87611 114.38680 114.14220 114.14220 114.38680 114.14220 114.38680 114.38680 114.38680 114.38680 114.38680 114.14220 113.89750 114.14220 113.65289 113.16360 112.91890 112.67420 112.42960 112.42960 112.42960 112.18491 112.18491 112.42960 112.18491 112.42960 111.69560 112.42960 112.42960 111.69560 111.94030 112.18491 112.18491 112.18491 111.94030 111.69560 111.94030 111.94030 112.42960 112.18491 112.18491 111.94030 6.6.2.1. Background and Data http://www.itl.nist.gov/div898/handbook/pmc/section6/pmc621.htm (7 of 14) [5/1/2006 10:35:55 AM] 112.18491 112.18491 111.20631 111.69560 111.69560 111.69560 111.94030 111.94030 112.18491 111.69560 112.18491 111.94030 111.69560 112.18491 110.96170 111.69560 111.20631 111.20631 111.45100 110.22771 109.98310 110.22771 110.71700 110.22771 111.20631 111.45100 111.69560 112.18491 112.18491 112.18491 112.42960 112.67420 112.18491 112.42960 112.18491 112.91890 112.18491 112.42960 111.20631 112.42960 112.42960 112.42960 112.42960 113.16360 112.18491 112.91890 6.6.2.1. Background and Data http://www.itl.nist.gov/div898/handbook/pmc/section6/pmc621.htm (8 of 14) [5/1/2006 10:35:55 AM] [...]... using the autocorrelation plot Autocorrelation Plot Interpretation of the Autocorrelation Plot The autocorrelation plot has a 95% confidence band, which is constructed based on the assumption that the process is a moving average process The autocorrelation plot shows that the sample autocorrelations are very strong and positive and decay very slowly The autocorrelation plot indicates that the process is... Identification 6 Process or Product Monitoring and Control 6.6 Case Studies in Process Monitoring 6.6.2 Aerosol Particle Size 6.6.2.2 Model Identification Check for Stationarity, Outliers, Seasonality The first step in the analysis is to generate a run sequence plot of the response variable A run sequence plot can indicate stationarity (i.e., constant location and scale), the presence of outliers, and seasonal... Model Identification Akaike Information Criterion (AIC and AICC) Information-based criteria, such as the AIC or AICC (see Brockwell and Davis (2002), pp 171-174), can be used to automate the choice of an appropriate model When available, the AIC or AICC can be a useful tool for model identification Many software programs for time series analysis will generate the AIC or AICC for a broad range of models... support this feature However, based on the plots in this section, we will examine the ARIMA(2,1,0) and ARIMA(0,1,1) models in detail Note that whatever method is used for model identification, model diagnostics should be performed on the selected model http://www.itl.nist.gov/div898/handbook/pmc/section6/pmc622.htm (5 of 5) [5/1/2006 10:35:56 AM] 6.6.2.3 Model Estimation 6 Process or Product Monitoring. .. Monitoring and Control 6.6 Case Studies in Process Monitoring 6.6.2 Aerosol Particle Size 6.6.2.3 Model Estimation Dataplot ARMA Output for the AR(2) Model Based on the differenced data, Dataplot generated the following estimation output for the AR(2) model: ############################################################# # NONLINEAR LEAST SQUARES ESTIMATION FOR THE PARAMETERS OF # # AN ARIMA MODEL USING BACKFORECASTS... Differenced Data Interpretation of the Partial Autocorrelation Plot of the Differenced Data The partial autocorrelation plot of the differenced data with 95% confidence bands shows that only the partial autocorrelations of the first and second lag are significant This suggests an AR(2) model for the differenced data http://www.itl.nist.gov/div898/handbook/pmc/section6/pmc622.htm (4 of 5) [5/1/2006 10:35:56... data or fitting some type of trend curve We would then attempt to fit a Box-Jenkins model to the differenced data or to the residuals after fitting a trend curve Although Box-Jenkins models can estimate seasonal components, the analyst needs to specify the seasonal period (for example, 12 for monthly data) Seasonal components are common for economic time series They are less common for engineering and. .. differenced data less autocorrelated than the original data The next step is to examine the sample autocorrelations of the differenced data Autocorrelation Plot of the Differenced Data http://www.itl.nist.gov/div898/handbook/pmc/section6/pmc622.htm (3 of 5) [5/1/2006 10:35:56 AM] 6.6.2.2 Model Identification Interpretation of the Autocorrelation Plot of the Differenced Data The autocorrelation plot of the... confidence band shows that only the autocorrelation at lag 1 is significant The autocorrelation plot together with run sequence of the differenced data suggest that the differenced data are stationary Based on the autocorrelation plot, an MA(1) model is suggested for the differenced data To examine other possible models, we produce the partial autocorrelation plot of the differenced data Partial Autocorrelation... ############################################################# SUMMARY OF INITIAL CONDITIONS -MODEL SPECIFICATION FACTOR 1 (P 2 D 1 Q) 0 S 1 DEFAULT SCALING USED FOR ALL PARAMETERS ##STEP SIZE FOR ######PARAMETER ##APPROXIMATING #################PARAMETER DESCRIPTION #####DERIVATIVE INDEX #########TYPE ##ORDER ##FIXED ##########(STP) 1 AR (FACTOR 1) 0.77167549E-06 2 AR (FACTOR 1) 0.77168311E-06 3 MU 0.80630875E-06 STARTING VALUES ##########(PAR) . AM] 115.85471 116.34400 116.34400 115.85471 116.58870 116.34400 115.61010 115.85471 115.61010 115.85471 115.12080 115.61010 115.61010 115.85471 115.61010 115.36539 114. 87611 114. 87611 114. 63150 114. 87611 115.12080 114. 63150 114. 87611 115.12080 114. 63150 114. 38680 114. 38680 114. 87611 114. 63150 114. 63150 114. 63150 114. 63150 114. 63150 114. 14220 113.65289 113.65289 113.89750 113.65289 113.40820 113.40820 113.89750 113.89750 113.89750 113.65289 113.65289 113.89750 6.6.2.1 Background and Data http://www.itl.nist.gov/div898/handbook/pmc/section6/pmc621.htm (14 of 14) [5/1/2006 10:35:55 AM] 6. Process or Product Monitoring and Control 6.6. Case Studies in Process Monitoring 6.6.2 AM] 114. 87611 114. 87611 115.12080 114. 87611 114. 87611 114. 63150 114. 63150 114. 14220 114. 38680 114. 14220 114. 63150 114. 87611 114. 38680 114. 87611 114. 63150 114. 14220 114. 14220 113.89750 114. 14220 113.89750 113.65289 113.65289 113.40820 113.40820 112.91890 113.40820 112.91890 113.40820 113.89750 113.40820 113.65289 113.89750 113.65289 113.65289 113.89750 113.65289 113.16360 114. 14220 114. 38680 113.65289 113.89750 113.89750 113.40820 113.65289 113.89750 113.65289 6.6.2.1.