Fujiyama Electronics Inc. has had difficulties with circuit boards purchased from an outside supplier. Unacceptable variability occurs between two drilled holes that are supposed to be 5 cm apart on the circuit boards. Thirty samples of four boards each were taken from shipments from the supplier. The data obtained can be found on a worksheet in Files: “Fujiyama_Electronics_Sample_Data.xlsx”.

		Observations
Sample		1	2	3	4
1		4.92	4.26	4.94	4.29
2		4.65	5.54	5	5.42
3		5.77	5.26	4.76	4.79
4		6.25	4.88	5.66	4.44
5		5.27	5.41	6.02	4.91
6		5.22	5.38	5.08	4.65
7		5.47	4.68	4.56	4.7
8		5.71	4.54	4.17	4.87
9		5.24	5.58	4.72	5.41
10		4.42	5.18	4.79	4.73
11		5.14	4.26	4.71	5.48
12		4.92	5.78	5.5	5.05
13		5.79	3.83	4.3	4.78
14		4.92	4.8	4.75	5.59
15		5.68	5.74	4.65	5.2
16		5.43	4.81	5.27	4.96
17		4.79	6.04	4.47	5.18
18		4.43	5.08	3.69	6.43
19		6.35	5.95	6.29	5.89
20		5.03	4.66	5.25	4.46
21		6.32	6.09	5.57	5.91
22		4.3	5.47	4.27

Complete and answer the following questions.

1. Calculate X-bar-bar, R-bar, and associated control limits using the data in the table above.
2. Create x̄ and R (average and range) control charts from the data in the table above.
3. Discuss notable out-of-control conditions displayed in the completed x̄ and R (average and range) control charts. Only consider points outside the control limits. Do not consider runs, set of points within certain zones, and so forth.
4. If the conditions you note could be defined as assignable conditions, and they are removed from the process, then what will happen to the X-bar and R control chart?
5. Remove the data related to the out-of-control points you observed from the original data, and recalculate new X-bar-bar, R-bar, and associated control limits.
6. Create new X-bar and R (average and range) control charts from your updated data.