solution

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	0.611	0.620	0.606	0.572
2	0.586	0.615	0.573	0.602
3	0.575	0.596	0.596	0.597
4	0.588	0.617	0.613	0.605
5	0.605	0.612	0.578	0.603
6	0.599	0.622	0.620	0.608

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?.)

Size of Sample? (n)	Factor for UCL and LCL for x?-chart ?(A2?)	Factor for LCL for?R-Chart ?(D3?)	Factor for UCL for?R-Chart ?(D4?)
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