# Good and Bad Ways to Calculate the OEE

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:

$\displaystyle OEE = A \cdot P \cdot Q$

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.

$\displaystyle A = \frac{Total Time - Downtime }{Total Time } = \frac{7200 min - 1440 min}{7200 min} = 80 \%$

$\displaystyle P = \frac{(Good Units + Defective Units) \cdot Cycle Time }{Total Time - Downtime } = \frac{(2880 pcs + 240 pcs) \cdot 1,5 \frac{min}{pcs}}{7200 min - 1440 min} = 81.25\%$

$\displaystyle Q = \frac{Good Units }{Good Units + Defective Units} = \frac{2880 pcs }{2880 pcs + 240 pcs} =92.31\%$

Hence the overall OEE according to the APQ formula is:

$\displaystyle OEE = A \cdot P \cdot Q = 80 \% \cdot 81.25\% \cdot 92.31\% = 60.0\%$

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

$\displaystyle OEE = \frac{Good Units }{\frac{Total Time }{Cycle Time }} = \frac{2880 pcs }{\frac{7200 min}{1,5 \frac{min}{pcs}}} = \frac{2880 pcs }{4800 pcs }= 60.00\%$

## 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.

$\displaystyle OEE = \frac{Good Units \cdot Cycle Time }{Total Time } = \frac{2880 pcs \cdot1,5 \frac{min}{pcs }}{7200 min} = \frac{4320 min }{7200 min } = 60.00\%$

## 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.

$\displaystyle OEE = \frac{Total Time - Downtime }{Total Time } \cdot \frac{(Good Units + Defective Units) \cdot Cycle Time }{Total Time - Downtime } \cdot \frac{Good Units }{Good Units + Defective Units}$

Rearranging this gives us:

$\displaystyle OEE = \frac{Total Time - Downtime }{Total Time - Downtime } \cdot \frac{Good Units + Defective Units }{Good Units + Defective Units} \cdot \frac{Good Units \cdot Cycle Time}{Total Time }$

Many of the terms cancel out easily, which leaves us with

$\displaystyle OEE = \frac{Good Units \cdot Cycle Time}{Total Time }$

which is exactly the formula we had for the Easy Way by Time above.

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.

$\displaystyle Availability Losses= \frac{Downtime }{Total Time } = \frac{1440 min}{7200 min} = 20\%$

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:

$\displaystyle Availability Losses= \frac{\frac {Downtime } {Cycle Time}}{\frac {Total Time } {Cycle Time}} = \frac{\frac{1440 min}{ 1,5 \frac {min}{pcs}}}{\frac{7200 min }{ 1,5 \frac {min}{pcs}}} = 20\%$

The availability losses and the availability rate together give exactly 100%.

$\displaystyle Availability Losses + Availability Rate = 20 \% + 80 \% = 100\%$

### 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:

$\displaystyle Quality Losses= \frac{Defective Parts \cdot Cycle Time}{Total Time } = \frac{240 pcs \cdot 1,5 \frac {min}{pcs}}{7200 min} = 5\%$

The calculation by lost quantity is equally simple and gives the same number:

$\displaystyle Quality Losses= \frac{Defective Parts}{\frac {Total Time }{ Cycle Time} } = \frac{240 pcs}{\frac {7200 min}{ 1,5 \frac {min}{pcs}} } = 5\%$

However, the quality losses and the quality rate are no longer complimentary.

$\displaystyle Quality Losses + Quality Rate = 5 \% + 92.31 \% = 97.31 \% \neq 100\%$

### 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%.

$\displaystyle Speed Losses = 100 \% - Availability Losses - Quality Losses - OEE = 100 \% - 20 \% - 5\% - 60\% = 15 \%$

Again, the speed losses and the performance efficiency are no longer complimentary.

$\displaystyle Speed Losses + Performance Efficiency = 15 \% + 81.25 \% = 96.25 \% \neq 100\%$

## 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 OeeValueValueA×P×Q = OEE
Availability Losses20%80%Availability Rate
Speed Losses15%81.25%Performance Efficiency
Quality Losses5%92.39%Quality Rate
OEE60%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%

$\displaystyle OEE= Availability Rate \cdot Performance Efficiency \cdot Quality Rate$

$\displaystyle OEE + Availability Losses + Speed Losses + Quality Losses = 100 \%$

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!

## 15 thoughts on “Good and Bad Ways to Calculate the OEE”

1. Steve Milner says:

‘Performance’ is a vague word. ‘Utilisation’ clearer, and embraces factors such as not filling every pocket, or operators absent, parts missing etc.

2. Hi Christoph,

I go even thurther!
I more or less eliminated the OEE- approach out of my lean toolkit. If we already have this kind of discussions between us, how can we expect to get the OEE- thinking/ understanding into our shop floor people. As we need to manage the shop floor and want the involvement of the operators, I started already a few years ago to track unplanned downtime, which is very simple to understand and measure.
If you look into OEEs of most pieces of equipment, unplanned downtime is the major equipment loss anyway, second being usually scrap/ rework (which is usually separated measured anyway). This two things usually create already more than enough problem solving activity.
So let us focus on that these 2 first, before we talk about speed losses.
Furthermore, OEE is a metric which supports the local optima appoach, which as we know is only really improtant, if we speak about a bottleneck process.

Regards
Dirk

3. Great review of OEE here and the components. I have authored the same equations in eVSM software so it can ask the lean practitioner for the components like changeover times, downtime, scrap etc.. directly and calculate the OEE as above.

OR, if OEE numbers are available directly they can type them in.

OR if they know the number of good parts, they can input it this way.

Goal is to take the information that is easily available, as you say and without tedious calculations on the users part.

One of the most useful outputs of all this is a Cycle Time/Takt Time chart that shows each of the losses to scale so you can understand the impact on capacity and in light of the demand. With scrap there is the rolling effect of having to make more parts upstream and this should be reflected on the plot also.

Look forward to the next blog. Really enjoy these.

4. Hi Steve, in the above context Performance Efficiency are the equivalent of speed losses, whereas missing material would be availability and defective parts quality. In any case, I don’t like the Performance Efficiency anyway. Cheers, Chris

5. Hi Dirk, I think the OEE can be very useful to improve a particular machine, but I do not like the shotgun approach to measure the OEE everywhere either. As for your approach, in my experience speed losses are often the largest loss groups, and also a group that you usually cannot measure directly. Downtime and scrap only would miss a big piece of the losses – although this is usually a hard to improve piece. Cheers, Chris

6. Hi Dilesh, many thanks 🙂 . Cycle Time / Takt time is very useful, it is also the same as the OEE. Cheers, Chris.

7. In my past experience I spent hours and hours in collecting data to calculate OEE!

What a waste!

First: Why and where I need OEE?

Second: Use the approach you proposed is fast and effective.

At the gemba please! Then OEE.

Great Chris.

8. Availability and utilization are not supposed to be the same thing. The availability of a resource is the probability that you can use it when you need it; it’s utilization, the fraction of the total time that you use it. A pen that always works whenever you need to jot down dome notes has 100% availability; if you use it 1 hour every day, it’s utilization is about 4%.

Confusing the two in OEE calculations makes using all machines all the time appear to be high performance.

More generally, if you want to make any use of OEEs, you need to break them down into their factors, and you might as well focus directly on them: availability, speed losses, and quality losses. Like unit cost, OEE is an overly aggregated metric, whose use can easily do more harm than good.

9. Hi Michel, I always like your clarity and precision in using words 🙂

10. Ricardo Mejía says:

How do you change the formula if they have different cycle time ?

11. Hi Ricardo, if you rparts have different cycle time, then you would have to calculate by time. e.g. if you make 2000 parts A and 5000 Parts B in an 8 hour shift, then your perfect time would be 2000 x Cycle time A plus 5000 x cycle time B. The OEE would be this perfect time divided by the 8 hours (make sure the units match). The quality losses are calculated similarly using the individual cycle times. Speed losses and availability losses remain unchanged.
Hope this helps,

Chris