A large manufacturing firm is concerned about lost production: that is, production capability that was not utilised for a variety of reasons. One of the causes of such lost production has been identified as employees taking time off work because of illness. Last year the firm estimated that around 53000 units of production were lost each week due to this cause, with a standard deviation of 4800. The Personnel Department has decided to monitor, on a weekly basis, a small sample of 15 employees on the production line in terms of their attendance at work and to translate this into a weekly production loss figure for the company. For the first eight weeks the results are as follows:
Estimated lost production (000 units)
Week 1 50.3 Week 2 53.9 Week 3 55.6 Week 4 51.2 Week 5 51.0 Week 6 50.9 Week 7 48.7 Week 8 49.3

(a) Using this information construct a control chart for Personnel to use.

(b) Draft a short report outlining the potential for using control charts on a regular basis in this context.

(c) Explain what is meant by Type I and Type II errors in this context.