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117

Economic Control Chart

Notation Used in the Model

Input Variablcs
A =	exponential parameter (mean = \lA)
A =	number of standard deviations slip when out of control
PO, PI =	proportion of nonconforming items produced when in and
	out of control
E =	time to sample and chart one item
TO =	expected search time when false alarm
T\ =	expected time to discover the assignable cause
T2 =	expected time to repair the process
Sl =	1 if production continues during searches; 0 otherwise
dl =	1 if production continues during repair; 0 otherwise
Co =	ąuality cost/hour while producing in control
Cl =	ąuality cost/hour while producing out of control (> Co)
Y =	cost per false alarm
W =	cost to locate and repair the assignable cause
a =	fixed cost per sample
b =	cost per unit sampled
Output and Calculated Yariables
C =	expected cost per hour
* n,n =	sample size and its optimal value
h,h* =	time between samples (hours) and its optimal value
	control limit and its optimal value
</,</* =	acceptance value for sampling by attributes and its optimal
	value
5 =	expected number of samples taken while the process is in
	control
=	e^_/Łfy( 1 - e^-^)
r =	expected time of occurrence of the assignable cause, within
	a sampling interval
=	[1 - (1 + 1 - e^_>^)] or, equivalently, HA - hs