AGENDA Statistical Process Control Basics Review Quiz Homework Statistical Process Control Basics Almost all process have built in variability SPC charts monitor different measures of variablity over a period of time HMS, shifts, days, etc Compares current performance to historical performance Many different types of SPC charts X bar of a sample, S of a sample, R of a sample By analyzing the data patterns, non-random variability problems can be detected and corrected Chart Components Central Line Average measured value Upper Control Limit CL + three standard deviations from the CL Lower Control Limit CL – three standard deviations from the CL Other Limits + and – one standard deviation from the CL + and – two standard deviations from the CL Chart Components Chart Components for X bar Chart Minimum of 20 historical periods Take a sample of n=5 for each period Calculate the sample average for each period CL The grand mean of the sample average for the 20 periods UCL CL plus 3 times the sample std of the 20 sample means LCL CL minus 3 times the sample std of the 20 sample means X BAR CHART Make ball bearings for car wheels Data was collected over 20 days to create an X bar Chart X bar was calculated for each day’s sample The grand mean or x bar bar was 10.00 mm The std of the x bars was 0.03 mm X BAR Chart X Bar Bar of 10 mm USING THE SPC CHART Each period, we collect a sample of size n N is typically 5 Calculate summary statistics for the sample X bar Standard deviation or range Plot the summary statistic Observe the plot for behavior patterns that would exhibit out of control behavior needing examination REVIEW With linear regression we want to determine the relationship between independent and dependent variables Use the least squares method to determine a prediction line Normal equations Intercept Slope coefficient Determine the suitability of the equation R squared T tests for the intercept and the slope NORMAL EQUATIONS PROCEDURE Sum the X, xy, x2 Insert the summations into the normal equations Solve for the A intercept B slope coefficent Predict the value of the dependent variable by inserting the independent value in the prediction equation HOMEWORK 11.6 both by hand and using Excel