There are different ways to calculate an OEE. I know of at least three different ways. However, some of them are easier and more practical than others.
Maybe you have seen a formula similar to OEE = A x P x Q. I see this formula often, but for me it is a very impractical way to calculate the OEE. Let me show you why by comparing the three different ways to calculate an OEE.
Example Data
Throughout this post I will be using examples. To calculate an OEE, we need a few data points. Our example process will be as follows:
- Total Time: Total time the process is scheduled to work, 5 days with 24 hours each or a total of 7200 minutes
- Downtime: Machine stopped for whatever reason: 1440 minutes
- Cycle Time: Needed to produce one unit: 1.5 minutes/unit
- Good Units: Total number of good parts produced during the 5 days: 2880 pieces
- Defective Units: Total number of defective parts produced during the 5 days: 240 pieces
The Impractical Formula
In literature you sometimes find the following formula for the OEE:
\[ OEE = A \cdot P \cdot Q \]where
- A is the availability rate, the ratio of the time the machine is running vs. the total time in consideration.
- P is the performance efficiency. This is calculated based on the ideal time needed to produce the parts (including defective parts) divided by the total running time of the process.
- Q is the quality rate. This is simply the number of good parts divided by the total number of good and bad parts produced.
A, P, and Q for our example are calculated below.
\[ A = \frac{Total Time – Downtime }{Total Time } = \frac{7200 min – 1440 min}{7200 min} = 80 \%\] \[P = \frac{(Good Units + Defective Units) \cdot Cycle Time }{Total Time – Downtime } = \frac{(2880 pcs + 240 pcs) \cdot 1,5 \frac{min}{pcs}}{7200 min – 1440 min} = 81.25\%\] \[Q = \frac{Good Units }{Good Units + Defective Units} = \frac{2880 pcs }{2880 pcs + 240 pcs} =92.31\%\]Hence the overall OEE according to the APQ formula is:
\[ OEE = A \cdot P \cdot Q = 80 \% \cdot 81.25\% \cdot 92.31\% = 60.0\%\]You can already see that this is quite a bit of work to calculate.
The Easy OEE by Pieces
If you need only the OEE, there are much easier ways to calculate it. One is by using the ratio of good parts produced vs. the number of parts that could have been produced. Hence
\[ OEE = \frac{Good Units }{\frac{Total Time }{Cycle Time }} = \frac{2880 pcs }{\frac{7200 min}{1,5 \frac{min}{pcs}}} = \frac{2880 pcs }{4800 pcs }= 60.00\%\]The Easy OEE by Time
Above we calculated the OEE by dividing the good units by the total number of units that could have been produced. You can calculate the OEE similarly by using time. You divide the duration that you would have needed at a minimum by the time you actually needed.
\[ OEE = \frac{Good Units \cdot Cycle Time }{Total Time } = \frac{2880 pcs \cdot1,5 \frac{min}{pcs }}{7200 min} = \frac{4320 min }{7200 min } = 60.00\%\]Why A x P x Q is bad
Much More Complex
It is easy to see that the calculation through pieces or through the time is much easier and simpler. The A x P x Q approach is much more complex, and hence has a much higher likelihood of mistakes. The formula is error prone not only because there are more calculation steps, but also because you have to always pay attention when you use the total time, or only the time the machine is actually running, when to use all parts, and when to use only the good parts, and so on. I find it very confusing (but admittedly I used the other way much more frequently).
Same Result
Additionally, if we put the entire complex formula together, we can easily cancel out many terms.
\[OEE = \frac{Total Time – Downtime }{Total Time } \cdot \frac{(Good Units + Defective Units) \cdot Cycle Time }{Total Time – Downtime }\cdot\] \[\cdot \frac{Good Units }{Good Units + Defective Units} \]Rearranging this gives us:
\[ OEE = \frac{Total Time – Downtime }{Total Time – Downtime } \cdot \frac{Good Units + Defective Units }{Good Units + Defective Units} \cdot \frac{Good Units \cdot Cycle Time}{Total Time } \]Many of the terms cancel out easily, which leaves us with
\[ OEE = \frac{Good Units \cdot Cycle Time}{Total Time } \]which is exactly the formula we had for the Easy Way by Time above.
What about the Losses?
Your OEE is below 100% due to losses. These losses are typically grouped in availability losses, speed losses, and quality losses. To know how big your losses are will help you with actually improving the system.
With the A x P x Q formula, you get something that at least sounds similar – the availability rate, performance efficiency, and quality rate. I think breaking down the OEE in these three terms is the reason the calculation is done the way it is in the first place. However, I still think it is impractical.
You could hope that the corresponding terms sum up to 100%. Unfortunately they do not! Only the availability rate and the availability losses together give 100%, but the speed loss is not complementary to the performance efficiency, and the quality rate is again not complementary to the quality losses. They are completely different numbers! Let’s do the math.
Availability Losses and Availability Rate
The availability losses are the part of the losses that you lose due to stopped machines. This is usually calculated by time, since the total time and the stops are usually given as times.
\[Availability Losses= \frac{Downtime }{Total Time } = \frac{1440 min}{7200 min} = 20\%\]It is also possible to calculate this through the number of parts, but since this usually involves more math, the above way is easier. In any case, the losses are the same. Below, for reference, is the marginally more complex calculation using the number of parts:
\[ Availability Losses= \frac{\frac {Downtime } {Cycle Time}}{\frac {Total Time } {Cycle Time}} = \frac{\frac{1440 min}{ 1,5 \frac {min}{pcs}}}{\frac{7200 min }{ 1,5 \frac {min}{pcs}}} = 20\%\]The availability losses and the availability rate together give exactly 100%.
\[Availability Losses + Availability Rate = 20 \% + 80 \% = 100\% \]Quality Losses and Quality Rate
The quality losses is the time lost due to defective parts. This can also be done either by calculating through the time or through the quantity. Let’s do the calculation by lost time first:
\[ Quality Losses= \frac{Defective Parts \cdot Cycle Time}{Total Time } = \frac{240 pcs \cdot 1,5 \frac {min}{pcs}}{7200 min} = 5\%\]The calculation by lost quantity is equally simple and gives the same number:
\[ Quality Losses= \frac{Defective Parts}{\frac {Total Time }{ Cycle Time} } = \frac{240 pcs}{\frac {7200 min}{ 1,5 \frac {min}{pcs}} } = 5\%\]However, the quality losses and the quality rate are no longer complimentary.
\[ Quality Losses + Quality Rate = 5 \% + 92.31 \% = 97.31 \% \neq 100\% \]Speed Losses and Performance Efficiency
Finally, the speed losses. I kept these losses for last, as the speed losses are simply the remainder to 100%.
Again, the speed losses and the performance efficiency are no longer complimentary.
\[ Speed Losses + Performance Efficiency = 15 \% + 81.25 \% = 96.25 \% \neq 100\% \]Overview of Losses
Here’s a quick overview of the different values, and it is easy to see that they differ. The different losses or efficiencies are not complementary (except for availability).
| Easy Oee | Value | Value | A×P×Q = OEE |
|---|---|---|---|
| Availability Losses | 20% | 80% | Availability Rate |
| Speed Losses | 15% | 81.25% | Performance Efficiency |
| Quality Losses | 5% | 92.39% | Quality Rate |
| OEE | 60% | 60% | OEE |
In fact, they must differ. After all, the A x P x Q formula is a multiplication, and the other one sums up to 100%
\[ OEE= Availability Rate \cdot Performance Efficiency \cdot Quality Rate\] \[ OEE + Availability Losses + Speed Losses + Quality Losses = 100 \%\]For me, it is quite obvious that summing up the losses has significant benefits. It is easier to see which part of the losses contributes how much to the total losses. This also makes it much easier to estimate how much a system will improve based on different improvement actions. Below is a simple waterfall bar chart showing which part of the losses contributes how much to the overall OEE losses.
Regarding the product in the A x P x Q formula, however, I fail to see any benefit. Hence my recommendation: Do not use the A x P x Q formula! If you know of any reasons, please enlighten me. Until then I will continue to advise you to avoid the A x P x Q formula, and instead use one of the two easy ways described above. Now, go out and organize your industry!
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