Problems for Section 5.4: Statistical Quality Control 1. () Tyler Apiaries sells bees and beekeeping supplies. Bees (including a queen) are shipped in special packages accord- ing to weight. The target weight of a package is 1.4 kg. Historically, Tyler's shipments have weighed on average 1.4 kg, with a standard deviation of 0.15 kg. a. (*) Calculate the process capability ratio, assuming that the lower and upper tolerance limits are 1.1 kg and 1.7 kg, respectively. Is Tyler Apiaries currently able to meet the tolerance limits 99.7% of the time? b. (**) What would the standard deviation have to be for Tyler Apiaries to achieve Six Sigma quality levels with regard to the weight of the bee packages? c. (**) The average bee weighs 0.1 grams. Use this infor- mation to convert the target package weight and tolerance limits into number of bees for Tyler Api- aries. How might the company use this information to better control the package weights? Should Tyler Apiaries think about resetting the tolerance limits? 6. BlueBolt Bottlers has a bottle-filling process with a mean value of 64 ounces and a standard deviation of 8 ounces. a. (**) Suppose that the upper and lower tolerance limits are 71 and 57 ounces, respectively. What is the process capability ratio? What would the standard deviation have to be in order for the process to meet the toler- ance limits 99.7% of the time? b. (***) Now suppose BlueBolt Bottlers makes some pro- cess improvements, thereby lowering the standard deviation of the process to 1.5 ounces, rather than 8 ounces. Using the data in problem 10 and the new standard deviation, calculate the process capability ratio. Is the filling process able to meet the tolerance limits 99.7% of the time? Does the process provide Six Sigma quality levels? Explain. 10. (**) Lazy B Ranch produces leather hides for use in the furniture and automotive upholstery industry. The com- pany has taken 10 samples of nine observations each, measuring the square footage of each hide. Summary data are as follows: MEAN (SQ FT) (n = 9) MINIMUM MAXIMUM 12.7 13.3 13.7 12.6 12.5 131 12.7 12.9 13.2 13.0 13.1 12.9 13.0 13.3 13.5 13.6 13.4 13.5 Use these data to set up control limits for the hides. Why would it be important for the Lazy B Ranch to track this information? Why might it be harder for the Lazy B Ranch to reduce process variability than it would be for a more typical "manufacturer"? 11. An insurance company has an online help service for its customers. Customer queries that take more than 5 min- utes to resolve are categorized as "unsatisfactory experi- ences. To evaluate the quality of its service, the company takes 10 samples of 100 calls each while the process is under control. The resulting p values are as follows: p VALUES (n = 100) 0.08 0.11 0.12 0.06 0.13 0.09 0.16 0.09 0.18 0.15 a. ("") Calculate the p and s, values and set up control limits so that future sample p values should fall within the control limits 99.7% of the time. b. (**) Suppose the insurance company takes four addi- tional samples, yielding the following p values: 0.9. 0.12.0.25, and 0.10. Plot the results and circle all val- ues that suggest that the process is out of control."Is it possible that a sample result could fall outside the con- trol limits due to pure chance? Explain. c. (**) Now suppose that the sample size is actually 50. not 100. Recalculate ihe control limits for the p chart. What happened? Explain