What methods are there for determining the root cause behind a drop in business performance? My question is best explained with a very simple example...

There are two Widget Factories (A and B).

Each factory has an output ($y_X$) given by the product of number_of_workers ($N_X$) and avg_production_rate_per_worker ($r_X$):

$$y_X = N_X \cdot r_X$$

where $X$ refers to the factory, and the total output is:

$$y = y_\mathrm{A} + y_\mathrm{B}$$

From week 1 to week 2, the total output decreases from 1,000 to 500.

Is there a way of determining the root metrics/dimensions behind this drop? i.e., has $y$ gone down due to $N_\mathrm{A}$, or $N_\mathrm{B}$, or $r_\mathrm{A}$, etc.?

I have data in the following form:

                 Number of  Avg. Production   Total
Week   Factory   Workers    Rate per Worker   Output
1      A         10         10/week           100 
2      A         15         10/week           150
...    ...       ...        ...               ...
1      B         10         10/week           100
2      B          5         15/week            75
  • $\begingroup$ For example, a drop in $y$ may be due to a: 1) local change - a single metric in one factory decreasing, e.g.: a) a bout of flu meaning many staff are off sick (reduces number_of_workers), b) automated production line breaks meaning production has to be done manually (reduces avg_production_rate) 2) global change - a single metric over both factories decreasing, e.g.: a) a national holiday meaning more staff off due to annual leave (reduces number_of_workers) or b) a new company-wide QA process meaning more checks are added (reduces avg_production_rate) $\endgroup$
    – Ben
    Jul 26 at 11:22
  • $\begingroup$ Any ideas? Can Sensitivity Analysis help? Can I change data to logs and use Structured Equation Modelling? $\endgroup$
    – Ben
    Jul 26 at 12:56
  • $\begingroup$ Graph models perhaps? $\endgroup$
    – Ben
    Jul 26 at 13:28

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