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Aspen Plastics produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machne and measures the outside diameter of the bottle neck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimensions (in.) from the last six samples are
BOTTLE
Sample
1
2
3
4
1
0.594
0.622
0.598
0.59
2
0.587
0.611
0.597
0.613
3
0.571
0.58
0.595
0.602
4
0.61
0.615
0.585
0.578
5
0.58
0.624
0.618
0.614
6
0.585
0.593
0.607
0.569
a. Assume that only these six samples are sufficient, and use the data to determine control limits for an R- and an x-bar-chart.
b. Suppose that the specification for the bottle neck diameter is 0.600 +/- 0.050 and the population standard deviation is 0.013 in. What is the Process Capability index? The Process Capability Ratio?
c. If the firm is seeking four-sigma performance, is the process capable of producing the bottle?
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