The Older Then Dirt potting soil company uses a machine to fill 500-ounce bags of enriched potting soil. The industry group has set limits on what can be called a 500-ounce bag: a 500-ounce bag of dirt must weigh at least 486 ounces and not more than 514 ounces. The company wants to operate its process at a minimum process capability of 1.10.

a) The specification limits have not changed. Suppose that the mean of the process is now 502 ounces with a standard deviation (σ) of 2 ounces. What is the range (upper and lower limits) on the mean of the process to maintain a Cpk of 1.10 or greater?

b) Suppose that the company is now operating the process with a mean of 504 ounces and a standard deviation (σ) of 4 ounces. Is the company currently capable of meeting the industry group’s specification standards if the company’s minimum Cpk is 1.10? Explain. If it is not, explain if it is due to a drifting of the mean or too much variability. Explain.

c) Now suppose that the company is operating the process with a mean of 503 and continues to use a process capability of 1.10 or greater. What is the maximum acceptable value of the standard deviation (σ) to ensure that the process capability is at least 1.10?

d) Suppose that the company can maintain an average weight of 504 ounces and a standard deviation (σ) of 4 ounces. The company does not believe it can improve on these values. The company wants to see if the industry group would be willing to adjust its spec limits rather than keep them at 486 and 514 so that Older then Dirt can meet the minimum Cpk of 1.10. What should the company tell the industry group that the spec limits need to be to achieve a Cpk of 1.10 or greater? Why?