Question

PS: Kindly solve with in MS WORD

Eight samples (m=8) of size (n = 5) have been collected from a manufacturing process that is in statistical control, and the dimension of interest has been measured for each part. It is desired to determine the values of the center, LCL, and UCL for ̅ and R charts. The calculated ̅ values (units are in mm) are 2.004, 1.993, 2.008, 1.929, 1.999, 2.001, 1.995 and 2.002. The calculated R values (mm) are 0.015, 0.021, 0.020, 0.023, 0.013, 0.024, 0.014 and 0.011. Als,o plot the control chart. Comment on your answer.

Answer 1

The given data is

Sample No.	Xbar	R
1	2.004	0.015
2	1.993	0.021
3	2.008	0.02
4	1.929	0.023
5	1.999	0.013
6	2.001	0.024
7	1.995	0.014
8	2.002	0.011
Total	15.931	0.141

For n=5, The tabulated value of A₂ = 0.58, D₃ = 0 and D₄ = 2.11

Chart

R Chart

From the X bar Chart, it is clear that process average is out of control since the point corresponding to 3rd and 4th sample lie outside the control limits

From R Chart, since all the sample ranges fall within the control limits, this a\chart shows that process variability is in control.