Building Cost Function 3D Benchmarks to Improve the Economic Statistical Design of Control Charts

Table 1

Definitions of elements of the cost function.

	Probability of failure of a process at the end of an interval .
	Probability of the error Type I: false positive detection of the out-of-control state.
	Probability of the error Type II: false negative detection of the out-of-control state.
	Point of time within where the process changes from the in-control state to the out-of-control state.
	Time associated with finding an assignable cause of failure when there is a false positive detection of the out-of-control state.
	Time associated with finding an assignable cause of failure and restoring the process to an in-control state.
	Sampling cost: constant () and variable () cost.
	In-control state production cost per hour.
	Out-of-control state production cost per hour: .
	Cost of a false positive detection of the out-of-control state.
	Cost associated with finding an assignable cause of failure and restoring the process to an in-control state.