### Abstract:

In production processes, there are two types of
variations that affect production quality - - variations
produced by chance causes and variations produced by
assignable causes. One of the main instruments in quality
control used to control quality by distinguishing between
variations produced by chance causes and a real process
change is the control chart. Each type of control chart
has advantages and disadvantages in a specified situation.
For example, some control charts fail to detect small
shifts, while the others are ineffective to detect large
shifts in process mean.
In this study, three types of control charts, namely,
X[bar], cumulative sum, and geometric moving average control
charts were compared on an economic basis. A simulation
model was developed to simulate the control chart
functions in a typical production process. The simulation was executed in BASIC on an IBM PC/XT. Before comparison,
each control chart was matched so that all the control
charts have the same characteristics when the process
operates in-control for a certain period of time. The
effects of the type of control chart, sample size,
sampling interval, and the magnitude of shift in process
mean on profit per hour were observed and analyzed using
Analysis of Variance (ANOVA).
The results show that, in general, the cumulative sum
control chart has advantage over the other two types of
control charts when shift of small magnitude of about 0.5σ
is present. X[bar]-control chart is ineffective to detect
small shifts; however, its effectiveness increases
sharply as the magnitude of shift increases to values of
1.5σ or beyond. Geometric moving average control chart
gives best results at intermediate shift levels of about
l.0σ.
Of the three sample sizes (3, 4 and 5) used in this
study, sample size of five yields the highest profit per
hour. However, too large a sample size may result in a
decrease of profit per hour if the testing causes the
destruction of items and the cost of sampling per item is
very high.
Small sampling interval of one hour yields the
highest profit per hour among three sampling intervals (1,
2 and 4 hours) used in this study. Too small sampling interval could yield lower profit per hour if the
increased cost of more frequent sampling, more
investigations caused by false alarms, and more frequent
shut down of the production process exceeds the savings
from early detection of the shift, particularly, when the
cost of sampling, the cost of searching for an assignable
cause, and the income per hour of production are very
high.