1. By: Samah Tout and Bing Liu Team Potassium Sigma Nov. 20,2007

2.  Statistical tool to improve and monitor quality  Detect the presence of variation  A plot of some function of measurements of process vs. time ◦ Data points are compared to UCL and LCL ◦ All points should fall within three standard deviations of the mean

3.  Mean is distributed according to a normal distribution  Measurements are independent of each other  Initial predictions taken when process is stable ◦ Multiple subset of data must be collected ◦ Grand Average(X GA ), average range(R A ), average standard deviation(S A ) are calculated ◦ n<15: use Table A to find the constants A 2, A 3, etc.

4.  X-Bar chart ◦ Grand average as the centerline  R-chart ◦ Average range as the centerline  S-chart ◦ Average standard deviation as the centerline

5.  Given: ◦ Number of data points within each subset, n = 4  Need to Find ◦ Calculate X GA, R A, and S A ◦ Determine UCL and LCL Subset #Value(Kg) 8(experimental)1.02,0.99,1.01,0.99 9(experimental)1.01,0.99,0.97,1.00 10(experimental)1.02,0.98,0.99,1.00 11(experimental)0.98,0.97,1.02,1.03

6.  X-Bar limits ◦ UCL= X GA + A 2 R A = 1.04 ◦ LCL= X GA - A 2 R A = 0.96