In response to a recent fuel economy bill passed by the U.S. Senate raising the average fleet-wide gas mileage to 35 miles per gallon by the year 2020, Victor Puente, the chief operating officer of an up-and-coming auto-maker was put in charge to evaluate the quality output of a flexible engine assembly line. The production process was subject to several modifications after a number of changes were made to existing engine designs in order to increase fuel efficiency. Victor currently has a team of 6- specialists (called black belts) in the organization to help him carry out this task. You are the master black belt reporting directly to Victor. After carefully designing the rational sub-groups in a test, you have received the gas mileage ratings of 25 engine groups, each of size 5, for analysis. The numbers are given in the Excel sheet. 

a) Your first order of business is to determine the X-bar and R for each sample. You would also like to compute X-barbar and R-bar. What do those numbers look like? 

b) Construct X-bar and R charts to deduce whether the process is in control.

 

Group		X1	X2	X3	X4	X5		n	d2	D3	D4
1		34.951	35.043	34.889	34.931	34.862		5	2.326	0	2.115
2		34.916	34.920	35.014	35.061	35.060
3		35.092	35.139	35.033	34.885	34.967
4		35.251	35.064	34.982	34.826	35.023
5		35.255	34.778	34.890	35.010	35.068
6		34.895	35.033	34.749	34.998	34.699
7		34.955	34.979	35.119	35.156	35.065
8		34.991	34.992	34.846	34.982	35.022
9		34.802	35.007	35.086	34.989	34.975
10		34.867	34.830	34.928	35.050	35.027
11		34.894	34.936	35.053	34.898	35.069
12		34.781	34.926	35.078	35.015	34.993
13		34.930	35.210	34.910	34.866	35.014
14		35.016	35.105	35.007	34.988	34.772
15		35.181	35.006	35.033	35.089	35.208
16		34.961	35.087	34.986	34.787	35.018
17		35.063	34.890	35.005	34.992	35.049
18		35.023	35.054	35.003	35.063	34.909
19		35.132	34.773	35.056	35.022	34.950
20		35.085	34.858	35.037	34.939	35.099
21		35.134	34.942	35.108	35.061	34.834
22		35.141	34.957	35.044	34.955	35.065
23		35.044	34.967	34.896	35.006	35.102
24		34.978	34.820	35.113	35.000	34.893
25		34.877	34.925	35.011	35.069	35.094