Question

4 Aspen Plastics produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machine 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 0.592 0.588 0.590 0.617 2 0.598 0.587 0.580 0.585 3 0.613 0.594 0.615 0.589 0.608 0.610 0.623 0.623 5 0.572 0.623 0.572 0.585 0.582 0.580 0.581 0.576 4 6 Click the icon to view the table of factors for calculating three-sigma limits for the x-chart and R-chart. Suppose that the specification for the bottle neck diameter is 0.600 +0.050 in, and the population standard deviation is 0.013 in. a. What is the process capability index? The Cpk is (Enter your response rounded to two decimal places.)

Answer 1

# SAMPLE	1	2	3	4	AVERAGE
1	0.592	0.588	0.59	0.617	0.5968
2	0.598	0.587	0.58	0.585	0.5875
3	0.613	0.594	0.615	0.589	0.6028
4	0.608	0.61	0.623	0.623	0.616
5	0.572	0.623	0.572	0.585	0.588
6	0.582	0.58	0.581	0.576	0.5798
GRAND AVERAGE					0.5952

GRAND MEAN = 0.595

UPPER SPECIFICATION = 0.65

LOWER SPECIFICATION = 0.55

PROCESS MEAN = 0.595

STANDARD DEVIATION = 0.013

Cpk = MINIMUM((UPPER SPECIFICATION - MEAN) / 3 * STANDARD DEVIATION), (MEAN - LOWER SPECIFICATION) / 3 * STANDARD DEVIATION)

Cpk = MINIMUM((0.65 - 0.595) / 3 * 0.013), (0.595 - 0.55) / 3 * 0.013)

Cpk = MINIMUM(1.4103, 1.1538)

Cpk = 1.15

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