Inspection and
control charting
687
An economic comparison of
inspection and control
charting using simulation
James D.T. Tannock
Department of Manufacturing Engineering and Operations
Management, University of Nottingham, Nottingham, UK
Introduction
Statistical quality control (SQC) charts are widely used to establish and
maintain statistical control of critical outputs from manufacturing and other
complex processes where variation arises from a wide range of sources. A
number of SQC chart types are available, although the most important remain
those referred to as Shewhart charts, after their inventor. They may be used
with both attribute (discrete) and variable (continuous) data, and consist of
time-series graphs, representing the results of periodic sampling and
assessment of some critical quality characteristic from the output of the
process.
A variety of methods are used to calculate control limits, which are limits of
variation set for sample data relating to a quality characteristic, beyond which
control action such as process adjustment or repair should be taken. Limits
based on actual process performance (called process capability limits) are most
frequently used, calculated on the basis of a number of initial samples assessed
once the process is believed to be stable and capable. Process capability refers to
the ability of the process to produce individual items within the design
specification limits for the quality characteristic in question.
The control limits are calculated such that common-cause variation natural
to the process will only result in sample data points plotting beyond them at a
known probability. Such control limits operate as an ongoing statistical test of
the hypothesis “the process has not changed” – that is no assignable or special
cause has caused a difference to occur in the process output. Unfortunately,
correct placement of control limits is not always achieved using the standard
methods. Indeed Alwan and Roberts[1] have shown that a majority of “expert”
control chart applications found in textbooks and training materials suffers
from misplaced control limits owing to the use of data violating the basic
theoretical assumptions on which control charts are based.
Even if the control limits are correctly placed, the design of control charts is
not a trivial task. The designer must decide on parameters such as sub-group
size, frequency of sampling and which (if any) additional alarm rules to use.
Although practical guidelines are available, it is probable that most users of
control charts are not in a position to attempt the optimization of chart
International Journal of Quality
& Reliability Management,
Vol. 14 No. 7, 1997, pp. 687-699,
© MCB University Press, 0265-671X
Received April 1996
Revised September
1996