12. An R chart is used to monitor the variation in the weights of packages of chocolate chip cookies produced by a large national producer of baked goods. An analyst has collected a baseline of 200 observations to construct the chart. Suppose the com- puted value of R is 3.825. a. If subgroups of size six are to be used, compute the value of three-sigma limits for this chart. b. If an X chart based on three-sigma limits is used, what is the difference between the UCL and LCL?

Do part A

Arana is a company that produces homemade Rotini pasta. They use statistical process control to monitor the manufacturing process. The company collects five samples, each containing six packs of pasta. Below is the sample data, but the standard deviation of the process output is unknown. If an R chart is created using three-sigma limits (i.e., z = 3) to monitor the variability of products, what would be the upper control limit for this R chart? Sample 1 Sample 2 Sample 3 Pack 1 452.3 451.6 448.6 Sample 4 454.7 Sample 5 448.9 7.614 9.328 11.653 13.427 Pack 2 452.8 451.2 455.6 451.7 453.4 Pack 3 456 454.6 456.5 451 456.7 Pack 4 457.2 455.3 451.9 452.6 456.3 Pack 5 457.8 452.2 455.6 454.7 452.4 Pack 6 451.8 451.9 448.3 458.4 456

6-9. A process that produces computer chips has a mean of .04 defective chip and a standard deviation of .003 chip. The allowable variation is from .03 to .05 defective. (a) Compute the capability index for the process (b) Is the process capable?