A health care facility is monitoring daily expenditures for a certain diagnosis-related group (DRG). Individual observations are selected. After 50 samples, the average and standard deviation of daily expenditures (in hundreds of dollars) are estimated to be 15 and 2, respectively.
(a) Find the 3σ control limits.
(b) Suppose that Rules 1 and 2 are used simultaneously for the detection of out-of control conditions. Assuming independence of the rules, what is the overall probability of a type I error? Explain the meaning of a type I error in this context.
(c) What is the ARL using Rule 1?
(d) Suppose that the average daily expenditures for the same DRG increases to $1750. What is the chance of detecting this shift by the second sample drawn after the shift using Rule 1?