The following summary should be read first. This article is a direct response to
Roehm, H., A. L. Weinstein, and J. F. Castellano. 2000. Management control
systems: How SPC enhances budgeting and standard costing. Management
Accounting Quarterly (Fall): 34-40. (Summary).
In order to understand the purpose of Holmes and Hurley’s article, one must
first have a general understanding of the Roehm, Weinstein and Castellano
article (Hereafter referred to as the RWC article for brevity’s sake).In the RWC article, the authors’ purpose is to show the effect of
statistical process control (SPC) when evaluating a standard against an actual
result.In that article, the authors
applied an SPC technique, an X-Moving Range Chart, to test the stability of
productivity data for J&J Inc.’s widget production.
The RWC article concludes that their process is “in control” and stable when
it produces 55 widgets per hour with 40 workers.The
data they used in their analysis included the daily units (the total number of
widgets produced per day) for two different shifts of employees.Holmes and Hurley’s article (Hereafter referred to as H&H for
brevity) examine this same fictitious example of J&J Inc.’s widget
production, but come to a new conclusion about what constitutes being “in
control” or stable.H&H
believe that there is no significant statistical difference between the
production levels of the two shifts from the RWC example.They assert that keeping the shift information separate distracts us when
analyzing the data for stability.
Therefore, H&H combined the two shifts of data into one set.They created their own X-Moving Range Chart for total daily production.Their chart looked like this:
H&H point out that all the data points
are within the control limits, as the RWC article asserts, but that there are
unusual patterns that could not be seen among the data before the two shifts
were combined. These unusual patterns in the data imply that the process is in
fact NOT stable.Nonrandom events
have occurred, despite the fact that all the data points are within the control
limits.Looking carefully at the above
figure, one can see that discernable patterns do in fact exist.Thus, there must be one or more assignable or controllable causes within
the production environment of J&J, Inc.The
discernable patterns include the following:The
last eight days of the production were below the average value of 110, and the
previous seven days were all above the average.This
indicates that the process is NOT stable.(Recall
that the RWC article indicated 55 hours as the mean; because the two shifts have
been combined, one would expect the mean to double in size.For this reason, the mean on the above figure is 110 instead of 55).
H&H computed the probability that there
could be a pattern of seven consecutive points above the average, followed by a
pattern of eight consecutive points below the average, from a random process.The probability that this could happen was less than 0.008.Based on this extremely low probability, H&H conclude that nonrandom
events must have caused these patterns.They
suggest that the management of J&J, Inc. should investigate the reasons for
the unusually high and low production levels for these two back-to-back periods.Possible causes could be different raw materials, different work teams,
different products, etc.But the most
important thing is to determine the causes and capitalize on this knowledge.
To further support their assertion that the process is unstable, H&H use
another statistical tool to illustrate their point.The 7-Point Moving Average of the Daily Production can be seen below:
This figure illustrates that the daily production level has actually been on a
downhill slope.Thus, the process must not
be in control, and RWC’s recommendation that the standard should be 60 instead
of 55 is probably not the best idea.
Conclusion
In conclusion, H&H do not believe that the
control process for the fictitious data indicates process stability.Rather, the reasons for the up and down averages in production for the
third and fourth weeks should be sought.
In turn, however, RWC got the chance to respond to H&H’s article as well.They had the opportunity to assert that they were right in NOT combining
the data of the two shifts.They
referenced Wheeler (an expert on SPC), when stating that it was the right thing
to keep these two subgroups separate.According
to Wheeler, “If there is any possibility that two things may differ, make sure
that they are in different subgroups…The control chart looks for differences
between subgroups.It uses the variation
within the subgroups to define how much variation to ignore in this quest.Therefore, by minimizing the variation within each subgroup and
maximizing the opportunity for variation from subgroup to subgroup, one will get
useful and sensitive control charts.”
RWC made a valid point in continuing to defend their position.They asserted:“Special
cause variation could develop for one shift but not another.If we were to combine the shifts into a single data point, we might not
detect this special cause variation and miss an opportunity to improve the
process in the future.”
Finally, the two groups of authors agree that
statistical process control
tools should be used by managerial accountants.But
they disagree on the interpretation of the SPC data! Our
questions in class related to whether the two shifts should be combined (See the
RWC summary).
