THE FUNDAMENTAL FLAWS OF "VARIANCE ANALYSIS"

This paper reflects my observations about the usefulness of standard
cost calculation and variance analysis for a reporting period based on
the comparison of production valued at standard versus actual bookings
to the relevant accounts.

There are at any time errors included in the "creation" of the std cost
for an individual finished product "i" :

1) StdCOSTi = MATERIALi + COSTi

a) MATERIALi = BOMi * PURCHASE_PRICEi

BOM denotes the information behind our bill of materials which is
basically
- material or component spec and
- quantity

The error in our BOM's is in the range of 5%, the error in the purchase
price is in the range of 2%. Therefore the error estimation for the
material portion is 5% + 2% = 7%
Please note that the measurement of the accuracy of a BOMi already
allows for a certain "window" in which the BOMi must be in order to be
considered "correct". So the 7% are the lower end of the actual
error in MATERIALi accuracy.

b) COSTi = CYCLE_TIMEi * RATEi * 1/n

The error in the cycle time count is usually more than 5%.
The measurement of the accuracy of a CYCLE_TIMEi also allows for a
certain "window" in which it must be in order to be considered
"correct". So the 5% are definitely at the lower end of the actual
error.

In the std cost model RATEi = cost_j / HOURSj

Lets assume that we are somehow able to allocate the cost to the
departments with an error of +/- 5% I think this would be a pretty good
job of the controller and the operations manager if they stayed within
that limit.

I'm sure that the estimation of the billable hours for this cost center
is within +/-20%, maybe its only +/-15%. For the individual part it's
probably worse. This is by far the highest contributor to the error in
the standard cost calculation.
Who is responsible for doing the forecast (=billable houres) ? Sales.
Who get's the beating for the variances (=the errors) ? Operations !

Anyway: the error in RATEj = 5%(cost_j) + 15%(HOURSj) = 20% minimum.

Then the error in COSTi = 5%(CYCLE_TIMEi) + 20%(RATEj) = 25%

2) If we assume that material accounts for roughly 50% of our typical StdCOS
then the error in the info about the piece part cost of our products is

ERROR_StdCOS = 0.5 * 7% + 0.5 * 25% = 16% !!!

3) Now one may ask : doe the errors for individual parts "i" average out
when we compute the sum of all parts produced in a reporting period ?

Due to statistical rules the errors MAY average out if we sum up part or
all of the part numbers into a "financial report".

a) if the errors average out then the StdCOS is a useless information.
By chance the sum of individual computations which hold
a 16% error gave a value which is identical to the cost recorded into
our accounts.

b) if it does not average out then the StdCOS are a useless information.

The conclusion : StdCOS is a mediocre information. Variances are built
into the budget right from the start. Achieving zero or close to zero
variances is what I call pure luck or more likely "financial engineering".

A correct interpretation of the reported data is the following : "the
standard COS for the reporting period are x (as an average). They may
well be within +/-16% around this value x".

What happens to any operations manager when he has up to 16% variances

4) The decision making problem.

Why do we have std COST ? Because we have to make decisions.

We need to base our decisions on sound data/information however.
As I have explained above the error in the data we have is significant.
Therefore any conclusions deriving from these data is guesswork at
best.

A professional approach would be to establish a szenario model of the
decision problem with at least three calculations :
- one based on the mean "x"
- one based on x-16%
- one based on x+16%
I am quite sure that these szenarios will result in conflicting
conclusions/decisions.

Material variances are OK taking into account that the error is 7%
minimum.
Direct labor variances might be discussed but may lead to wrong
conclusions or wrong decission making. The portion of direct
labour for businesses in industrialized countries should be below 10%
(otherwise there is a problem with competitiveness). So there is not
much to gain here anyway.
For overhead cost I suggest to monitor cost budgets per cost center
only which is not new, really.

Probably the best answer is to switch to "throughput accounting" as
proposed by Dr. E. Goldratt et al.

Hans Peter Staber
2001-08-04