By: Samah Tout and Bing LiuTeam Potassium Sigma

Nov. 20,2007

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 threestandard deviations of the mean

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(XGA), average range(RA), average

standard deviation(SA) are calculated

◦ n<15: use Table A to find the constants A2, A3, etc.

X-Bar chart◦ Grand average as the centerline

R-chart◦ Average range as the centerline

S-chart◦ Average standard deviation as the centerline

Given:

◦ Number of data points within each subset, n = 4 Need to Find

◦ Calculate XGA, RA, and SA

◦ 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

X-Bar limits◦ UCL= XGA + A2 RA= 1.04

◦ LCL= XGA - A2 RA= 0.96