question archive Aspen Plastics produces plastic bottles to customer order
Aspen Plastics produces plastic bottles to customer order
Subject:StatisticsPrice:2.87 Bought7
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. Suppose that the specification for the bottle neck diameter is 0.600±0.0500.050 in. and the population standard deviation is 0.0140.014 in. What is the process capability? index?
Bottle Sample 1 2 3 4
1 0.609 0.593 0.61 0.581
2 0.59 0.59 0.599 0.624
3 0.586 0.577 0.619 0.613
4 0.609 0.624 0.592 0.605
5 0.599 0.576 0.607 0.614
6 0.608 0.619 0.622 0.591
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Answer:
USL (Upper Specified Limit) = 0.600+0.05 = 0.65 in
LSL (Lower Specified Limit) = 0.600-0.05 = 0.55 in
Std deviation = 0.014 in
Mean = 0.6034 in
Process Capability Index:
Cpk = min [ ((USL - mean) / (3 * std. dev.)) , ((mean - LSL) / (3 * std. dev.)) ]
= min [ ((0.65- 0.6034) / (3 * 0.014)) , ((0.6034 - 0.55) / (3 * 0.014)) ]
= min [ 0.0466/0.042 , 0.0534/0.042 ]
= min [ 1.109 , 1.271 ] = 1.109
