ASSIGNMENT #11.

1. For the following problems, use the formulas in the chapter flow diagram to find the upper and lower control limits for the process mean and process range. You should use an ordinary calculator or the computer calculator (or Excel) to make the calculations. Assume that none of the samples had sample means or ranges that were out of control.

(a) A process measuring the shaft diameter had 30 samples of size 5 items taken with the following results:

Find :

ANS: x-dlb.bar (the average of the 30 averages) = 30.75/30 = 1.025

R-bar (the average of the 30 ranges) = 0.419/30 = .014

UCL (x-bar) = x-dlb.bar + A2R-bar = 1.025 + (.58)(.014) = 1.03312

Note: The value for A2 comes from the table on page 78 for samples of size 5.

LCL (x-bar) = 1.025 (.58)(.014) = 1.01688

UCLR = D4R-bar = 2.11*.014 = .02954 where D4 comes from page 78.

LCLR = D3R-bar = 0 * .014 = 0

Now that youve seen how these are done and checked your answers, you should be able to do the example below.

2. A process measuring the width of a metal plate had 25 samples of size 3 taken with the following results:

Find:

3. Given the following table of values from 5 samples, find the sample mean and range for each sample. Then, find the control limits for the range chart and for the x-bar chart.

Sample	X1	X2	X3	X4	x-bar	R
1	7	5	5	6
2	6	9	7	7
3	5	6	5	7
4	8	6	5	8
5	6	7	7	9

Find:

Based on the R chart values and the five individual R values in the table above, is the R chart in control? ____________ Yes or No?

Based on the x-bar chart values and the five individual x-bar values in the table, is the x-bar chart in control? ________________ Yes or no?