Instructions: Be sure to show all calculations and final answers for each of the
ID: 428093 • Letter: I
Question
Instructions: Be sure to show all calculations and final answers for each of the following problems. Use the control limit factors table from your book to compute your answers. A production process, sampled 30 times with a sample size of 8, gave these X and R values: X 28.5 and R-1.6 1) a Calculate the UCL and LCL for the X and R charts for this process. After the control charts were created, nine samples of the item, produced these results for X :28.55, 28.65, 29.00, 28.72, 28.9, 28.4, 28.5, 28.65, and 28.95. Is the process in or out of control? Explain why or why not. b) Does the following set of sample results for X indicate that the process is in control or out of control: 28.01,28.8,28.1, 28.9,28.01, and 29.01? Explain why or why not. c)Explanation / Answer
For sample size N = 8
A2 = 0.373
D4 = 1.864
D3 = 0.136
X double bar = 28.5
R bar = 1.6
Ans a)
For X bar chart?
UCL = X double bar + A2 *R bar = 28.5 + 0.373* 1.6 = 29.0968
LCL = X double bar - A2 *R bar? = 28.5 - 0.373* 1.6? = 27.9032
For R chart?
UCL = D4* Rbar = 1.864 * 1.6 = 2.9824
LCL = D3* Rbar? = 0.136 * 1.6 = ?0.2176
Ans b)
All the values of X bar,i.e. 28.55, 28.65, 29.00, 28.72, 28.9, 28.4, 28.5, 28.65, 28.95 are within the upper and lower control limits for X bar. Hence the process is in control and no corrective measures need to be taken.
Ans c)
The following values of X bar, 28.01, 28.8, 28.1, 28.9, 28.1 and 29.01 are again within the upper and lower control limits for X bar. Hence the process is in control and no corrective measures need to be taken.