Inspection of parts produced. A new inspection scheme for determining if parts produced meet customer satisfaction was evaluated in Quality Engineering (Vol. 31, 2019). For a particular part, the customer requirement is that the measured quality value exceeds 644 units. To monitor the new inspection system, data were collected for parts sampled from the production line, one each hour for 48 consecutive hours. Each part was inspected by three different operators and the three measured quality values averaged. The average of the 48 sample means was reported as x = 672.8. The overall standard deviation of the sampled quality values was reported as s = 11.7. Assume that these values reflect an inspection scheme that is “in control.”

a. Find the center line for an x-chart.

b. Find the upper and lower control limits for an x-chart. [Hint: Use an estimate of sx, where n = 3.]

c. In a future inspection, assume the three operators’ quality measurements are 620, 645, and 615 units. Should these results be cause for concern? Explain.