2. Eng. Mgt. 385 Statistical Process Control Stephen A. Raper Chapter 3 Continued

3. Shewharts Bowl Experiment Read, reread, and read again the detail of Shewharts Bowl Experiment Demonstrates that the larger the sample taken from the universe, it is more likely that the average of the samples will be close to the process average Averages of the samples themselves will form a frequency distribution

4. Shewharts Bowl Experiment The average of such a frequency distribution of xbar values tends to be near “mu” , the average of the universe The spread of the distribution of the xbar values depends on the spread of the universe but also on the sample size “n”.

5. Shewharts Bowl Experiment The larger the value of n, the less the spread of the xbar values The standard deviation of the distribution of xbar values will be  divided by the square root of n Even if the universe is nonnormal, statistical theory says that the expected frequency distribution of the xbar values also will be normal

6. Shewharts Bowl Experiment Relationship between sbar—subgroup sample standard deviations, and the universe standard deviation:  = sbar/c 4 Relationship between rbar –grand range of samples and the universe standard deviation:  = rbar/d 2

7. Program Completed Program Completed University of Missouri-Rolla Copyright 2001 Curators of University of Missouri