Question

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	4
1	0.617	0.582	0.602	0.610
2	0.596	0.606	0.615	0.574
3	0.591	0.594	0.580	0.593
4	0.613	0.616	0.613	0.591
5	0.622	00.596	0.604	0.619
6	0.578	0.571	0.575	0.595

Factors for calculating​ three-sigma limits for the

x​-chart

and​ R-chart

Size of Sample​ (n)	Factor for UCL and LCL for x overbarx​-chart ​(Upper A 2A2​)	Factor for LCL for​ R-Chart ​(Upper D 3D3​)	Factor for UCL for​ R-Chart ​(Upper D 4D4​)
2	1.880	0	3.267
3	1.023	0	2.575
4	0.729	0	2.282
5	0.577	0	2.115
6	0.483	0	2.004
7	0.419	0.076	1.924
8	0.373	0.136	1.864
9	0.337	0.184	1.816
10	0.308	0.223	1.777

Suppose that the specification for the bottle neck diameter is 0.600 ±0.050 in. and the population standard deviation is 0.011 in.

a. What is the process capability​ index?

The C pk is ___?____

Round to two decimal points.

Answer 1

# SAMPLE	1	2	3	4	AVERAGE
1	0.617	0.582	0.602	0.61	0.603
2	0.596	0.606	0.615	0.574	0.598
3	0.591	0.594	0.58	0.593	0.59
4	0.613	0.616	0.613	0.591	0.608
5	0.622	0.596	0.604	0.619	0.61
6	0.578	0.571	0.575	0.595	0.58
AVERAGE					0.598

UPPER LIMIT = 0.65

LOWER LIMIT = 0.55

MEAN = 0.598

STDEV = 0.011

PROCESS CAPABILITY INDEX = MIN(UPPER LIMIT - MEAN / 3 * STDEV, MEAN - LOWER LIMIT / 3 * STDEV)

PROCESS CAPABILITY INDEX = MIN((0.65 - 0.598) / 3 * 0.011), (0.598 - 0.55) / 3 * 0.011)

PROCESS CAPABILITY INDEX = MIN(1.5758, 1.4545)

PROCESS CAPABILITY INDEX = 1.45

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