The specification for a plastic handle calls for a length of 6.0 inches ± 0.5 inches (5.5 to 6.5 inches). The process is known to operate at a mean thickness of 6.1 inches. The minimum acceptable process capability is 2.0. The standard deviation (σ) of the process is currently 0.08 inches.
a) Can the company meet the customer's specification requirements at this time? If it cannot, explain if it is due to a drifting of the mean or too much variability.
b) Suppose that the mean of the process has now shifted to 6.2 inches. What is the maximum standard deviation (σ) of this process if the company wants to ensure that it can maintain a C_{pk} of 2.0?
c) The specification limits have not changed. Suppose that the mean of the process has now shifted to 5.9 inches with a standard deviation (σ) of 0.05. What is the range (upper and lower limits) on the mean of the process to maintain a C_{pk }of 2.0 or greater?