part B-

b. Suppose that the specification for the bottle neck diameter is 0.600 +/- 0.050 population standard deviations is 0.013in. What is the process capability index? The process capability ratio? *round to two decimal places

Cpk=

Cp=

part C-

c. If the firm is seeking four-sigma quality, is the process of capable of producing the bottle neck?

Factors for calculating three-sigma limits for the x-chart and R-chart Size of Sample Factor for UCL and LCL Factor for LCL for Factor for UCL for (n) for X-chart (A2) R-Chart (D3) R-Chart (14) 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 3 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 4 1 0.579 0.588 0.578 0.601 2 0.587 0.572 0.584 0.608 3 0.591 0.608 0.574 0.576 4 0.623 0.590 0.578 0.604 5 0.583 0.624 0.615 0.581 6 0.590 0.606 0.589 0.608 Click the icon to view the table of factors for calculating three-sigma limits for the x-chart and R-chart. Assume that only these six samples are sufficient, and use the data to determine control limits for an R-and an x-chart. Compute the range R and the sample mean x for each sample. (Enter your responses rounded to three decimal places.) 1 4 Sample 1 2 3 4 5 0.579 0.587 0.591 0.623 0.583 Bottle 2 3 0.588 0.578 0.572 0.584 0.608 0.574 0.590 0.578 0.624 0.615 0.606 0.589 0.601 0.608 0.576 0.604 0.581 R 0.023 0.036 0.034 0.045 x 0.587 0.588 0.587 0.599 6 0.590 0.608