A local brewery and bottling plant wants to keep track of the bottle filling equipment's performance accuracy carefully. Bottles are to be filled with exactly 8-oz of drinks. If a bottle is over-filled, it results in waste of the drink (since distributors are only paying for 8-oz) and also higher transportation costs. Under-filling will alienate distributors and could open up the brewery to legal problems. 

Following is data from the bottling equipment where 5 samples of bottles filled were pulled

every hour and measured for actual quantity filled.

Hour	X-bar	R	Hour	X-bar	R
1	8.05	.20	6	8.06	.37
2	8.03	.25	7	7.98	.46
3	7.96	.62	8	8.09	.21
4	7.97	.58	9	7.94	.35
5	8.03	.71	10	8.01	.29

 

a. Draw a (X, R)-chart with 3σ limits. 

b. Comment on the brewery's bottling equipment's performance