1. 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:
Sample 1 | 2 | 3 | 4
1 | 0.594 | 0.622 | 0.598 | 0.590
2 | 0.587 | 0.611 | 0.597 | 0.613
3 | 0.571 | 0.580 | 0.595 | 0.602
4 | 0.610 | 0.615 | 0.585 | 0.578
5 | 0.580 | 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 in ± 0.050 and the population standard deviation is 0.013 in. What is the Process Capability Index? The Process Capability Ratio?
Your answers are on the attached Excel spreadsheet, along with these explanations:
a. Since we are told to "use the data to determine control limits for an R- and an x-bar chart", we have to average the measurements of each of the six samples and find the range of each of the six. This is at the top of columns F and I, respectively. We then find the separate control limits based on three anti-biasing constants in cells A12 thru A14 and resulting in the limits at the top of columns G-H and J-K, respectively. I am using commonly ...
Answers are on the attached Excel spreadsheet, along with detailed explanations. Excel functions are used to find the grand average and ranges. Also in Excel, a chart is made along with calculating Process Capability Index Cp.