How to correctly calculate the Quality Factor for OEE

Most people assume that the quality factor for Overall Equipment Effectiveness (OEE) is determined by simply calculating the yield of good parts from the total parts produced.  Unfortunately, this logic does not hold true when calculating the quality factor beyond the individual part or process.

We will show you how to correctly calculate the Quality factor and determine a truly weighted result that is consistent with the definition of Overall Equipment Effectiveness.  Although OEE itself does not have a unit of measure, it is based on the effective use of time.

The Quality Factor Defined

Although OEE itself is expressed as a percentage, all of the individual OEE factors are based on time.  Yes, even the quality factor:

The quality factor measures the percentage of time that was used to make or manufacture an acceptable quality product at rate or standard.

We have witnessed too many organizations that attempt to immediately convert the Quality Factor into a Cost of Non-Quality, Parts / Million (PPM), or other type of metric.  This is not the intent of the quality factor from an overall equipment effectiveness perspective.  Again, OEE measures effective use of time.

While it is not our intent to delve into a cost of non-quality discussion, we agree that understanding the cost drivers is in the best interests of the company to minimize losses.  This includes any investment that must be made to improve OEE.

We would also encourage you to download a copy of our Excel spreadsheets (see the BOX file on the sidebar).  There are no charges or fees for downloading these files and we request that these products remain available as such.  Now, let’s move on to the Quality Factor.

Where did the time go?

By definition, OEE is used to determine how effectively the time for a given machine, process, or resource is used:

• Availability:  Planned (Scheduled) versus Unplanned downtime
• Performance:  Standard versus Actual cycle time

All of the OEE factors pertain to time.  From our definition above, the factors are independent of people (labour) required, parts produced, defective product, or the value of these items.  However, when we review many OEE templates, and more specifically the quality factor calculation, the time element is lost.

The true Quality Factor formula

The simple yield calculation works for a single process or part number but not for multiple machines or part numbers.  A simple example will demonstrate the correct way to calculate the Quality factor for a single part.  We will expand on this simple example as we go along.  Click here to download your free copy of the spreadsheet used in this post.

Note:  We are using the standard rate for the Quality time calculations as the Availability and Performance factors already account for downtime and cycle time losses respectively.  Quality is based on the pure standard rate or cycle time only.

EXAMPLE:  Machine A – Production Summary

 Part Number Rate / Minute Total Produced Defective Quantity Yield % Quantity 1 2 800 10 98.75% Totals ——- 800 10 98.75% Averages 2 800 10 98.75%

As we can see from the table above, machine A produces part number 1 at a standard rate of 2 parts / minute.  A total of 800 parts are produced of which 10 are defective and scrapped.  The simple yield formula will correctly calculate the Quality factor as:

Quality Yield = (800 – 10) / 800 = 790 / 800 = 98.75%

From an OEE perspective, however, our interest is not how many parts were scrapped, but rather, how much machine or process time did we lose by making them.  From our example, 10 defective parts results in a loss of 5 minutes:

Lost Time = 10 parts / (2 parts / minute) = 5 minutes

The quality factor actually tells us how effectively the time was used to make good or acceptable parts.  From our example, the time required to make ALL parts at the standard rate is 400 minutes (800 parts / 2 parts / minute = 400).  Our Quality factor can easily be calculated as follows:

• = 400 – 5
• = 395 minutes

Total Time (All Parts) = 400 minutes

Quality Factor = Value Added Time / Total Time
= 395 / 400
= 98.75%

Although the results in this case are the same, the method is uniquely different.  Since this is based on a single machine, the cycle times are cancelled in the formula as shown below:

= (800 – 10) / 2 parts per minute / (800 / 2 parts per minute)

The YIELD pitfall revealed:

Our calculation method becomes relevant when we start looking at the production of different parts running through the same machine or process.  The easiest way to demonstrate this is by extending our first example.

Let’s assume we are also using machine A to produce two additional part numbers.  The production data is summarized in the table below as follows:

EXAMPLE:  Machine A – Production Summary

 Part Number Rate / Minute Total Produced Defective Quantity Yield % Quantity 1 2 800 10 98.75% 2 8 1600 160 90.00% 3 1 800 20 97.50% Totals ——- 3200 190 94.06% Averages 4 1067 63 95.42%

If we calculate the Quality factor for machine A, the simple yield formula will provide a misleading result.  Note that we’ve provided the process yield factor for each line item part number as we have already determined that the ime factors cancel for individual parts.

The average Yield % from the table above is 95.42%.  We will demonstrate that this result is also incorrect.  Remember, we’re interested in the percent of total time used to make a quality product (also known as Value Added Time).

The real question is, “What is the overall Quality factor for machine A?”  The simple yield formula would suggest the following:

Simple Yield Quality Factor = (3200 – 190) / 3200 = 3010/ 3200 = 94.06%

This percentage is misleading and – as we will demonstrate – the WRONG result.

Calculating the True Weighted Quality Factor

Let’s take the table from above and expand on it to reflect our TIME based calculations.  We will calculate the time required to produce all parts (Total Time) and the time lost to produce defective parts (Lost Time).  Remember, these times are calculated at the standard cycle time or rate.  The resulting table appears below:

EXAMPLE:  Machine A – Production Summary

 Part Number Rate / Minute Total Produced Total Time Defective Quantity Lost Time Yield % Time 1 2 800 400 10 5 98.75% 2 8 1600 200 160 20 90.00% 3 1 800 800 20 20 97.50% Totals ——- 3200 1400 190 45 96.79% Averages 4 1067 467 63 15 95.42%

From this table, we can quickly calculate the true weighted quality factor as follows:

Quality Factor = Value Added Time / Total Time
= (1400 – 45) / 1400
= 1355 / 1400
= 96.79 %

Putting it ALL together

From the discussion above, we have combined the results into the table below:

EXAMPLE:  Machine A – Production Summary

 Part Number Rate / Minute Total Produced Total Time Defective Quantity Lost Time Yield % Quantity Yield % Time Delta 1 2 800 400 10 5 98.75% 98.75% 0.00% 2 8 1600 200 160 20 90.00% 90.00% 0.00% 3 1 800 800 20 20 97.50% 97.50% 0.00% Totals ——- 3200 1400 190 45 94.06% 96.79% 2.72% Averages 4 1067 467 63 15 95.42% 95.42% 0.00%

The true weighted quality factor can be found in the Yield % Time column (96.79%).  This result fits the true definition of Overall Equipment Effectiveness.

The table also shows that the differences between the methods can lead to a significant variance between the results (96.79% – 94.06% = 2.72%):

• = 94.06% (Simple)
• = 95.42% (Average)
• = 96.79 % (Weighted)

We can quickly prove which answer is correct quite easily.  Referring to the table below, the only factor that resulted in the correct time calculations is the Yield Time % factor (96.79%).  The table shows that the true Value Added Time or Earned Time is 1355 minutes and the total time lost due to defective parts is 45 minutes.  Exactly what we expected to find based on our earlier calculations.

 Quality Factor – Validation Table – All Times are in minutes Method “Yield %” Total Time Earned Lost Time Delta Time Yield Quantity % 94.06% 1400 1316.9 83.1 38.1 Average Yield % 95.42% 1400 1335.8 64.2 19.2 Yield Time % 96.79% 1400 1355.0 45.0 0.0

What does all this mean in terms of time?  The results shown in this table clearly demonstrate that a seemingly small delta of 2.72% between the different methods of calculating the Quality Factor can be significant in terms of time.  The Delta time indicated in the table is the difference between the calculated lost time for Method and the actually calculated lost time of 45 minutes.

If this machine was actually scheduled to run 450 minutes per shift on 2 shifts the results would be even more dramatic over the course of a year.  Assuming the machine is loaded with the same part mix and there are 240 working days per year:

Annual Working Time = 240 * 450 * 2 = 216,000 minutes

The following table summarizes the results on an annualized basis:

 Quality Factor – Annualized Results – All Times are in minutes Method “Yield %” Total Time Earned Lost Time Delta Time Yield Quantity % 94.06% 216,000 203,169.6 12,830.4 5896.8 Average Yield % 95.42% 216,000 206,107.2 9892.8 2959.2 Yield Time % 96.79% 216,000 209,066.4 6933.6 0.0

The “Yield Quantity %” method indicates the actual lost time that could be incurred annually is 12830.4 minutes (28.51 shifts).  Relative to our “Yield Time %” method, this is overstated by 5896.8 minutes, the equivalent of just over 13 shifts.  Similarly, the “Average Yield %” method indicates a total lost time of 9892.8 minutes (21.98 shifts).  Relative to our “Yield Time %” method, this is overstated by 2959.2 minutes or approximately 6.6 shifts.  This further exemplifies the need to understand the correct way to calculate the Quality Factor.

Let’s continue to re-affirm the validity of our calculation method.

Individually Weighted Quality Factors

We will now show you how to calculate the individually weighted quality factors for each part number or line item.  The weighted “time based” quality factor is calculated using the following formula for each line item part number:

Weighted Line Item = (Value Added Time)
Total Time for All Parts

Where, Value Added Time = Total Time – Lost Time

We have simplified the table from our example to show the time related factors only.  The table showing the time weighted quality factors from our example is as follows:

 Part Number Rate / Minute Total Produced Total Time Defective Quantity Lost Time Yield % Time Weighted % Yield Time 1 2 800 400 10 5 98.75% 28.21% 2 8 1600 200 160 20 90.00% 12.86% 3 1 800 800 20 20 97.50% 55.71% Totals 3200 1400 190 45 96.79% 96.79% Averages 4 1067 467 63 15 95.42%

As we can see from the table, the sum of the “Weighted % Yield Time” percentages is the same as the “Yield % Time”.  The time based formula is once again validated.  We will now take this table one step further to reveal where the real opportunities are to improve the Quality Factor and Overall Equipment Effectiveness.

Improving the Quality Factor

The Yield % or the Weighted Time % do not provide any real indication of the contribution of each part number to the overall weighted quality factor.  We can see from the table that part numbers 2 and 3 both resulted in 20 minutes of lost time compared to part number 1 where only 5 minutes were lost.

Since part numbers 2 and 3 resulted in an equivalent loss of time, we would expect that they would also result in an equal contribution to improve the Quality Factor.  To demonstrate this and to appreciate the real improvement opportunity, we added two more columns to our table as shown below – “Weighted % Process Time” and “Yield % Opportunity”:

 Machine A – Weighted Quality Factor – EXAMPLE Part Number Total Time Weighted % Process Time Lost Time Value Added Time Yield % Time Weighted % Yield Time Yield % Opportunity 1 400 28.57% 5 395 98.75% 28.21% 0.36% 2 200 14.29% 20 180 90.00% 12.86% 1.43% 3 800 57.14% 20 780 97.50% 55.71% 1.43% Totals 1400 100.00% 45 1355 96.79% 96.79% 3.21% Averages 467 33.33% 15 452 95.42% 32.26% 1.07%

The weighted process time was calculated by dividing the process time for each part number by the Total Time.  Once again, we can validate our weighted Quality Time by multiplying the “Weighted % Process Time” by the “Yield %” for each line item.

To make sure we understand the calculations involved, let’s work out one of the line items in the table.  For Part Number 1,

• Weighted % Process Time = 400 / 1400 = 28.57%
• (1)  Weighted % Yield Time = 28.57% * 98.75% = 28.21%
• (2)  Weighted % Yield Time = (400 – 5) / 1400 = 28.21 %

Note that we showed two ways to demonstrate the Weighted % Yield Time to once again validate the quality factor calculation method.

The opportunity to improve the OEE for the three part numbers is the difference between the Weighted Process Time and the Weighted Yield Time.  For Part Number 1,

Improvement = 28.57% – 28.21% = 0.36%

Similarly, the improvements for part numbers 2 and 3 are as follows:

• Improvement Part Number 2 = 14.29% – 12.86% = 1.43%
• Improvement Part Number 3 = 57.14% – 55.71% = 1.43%

Three Key Observations

1. First, the results of the calculations are consistent the actual observed down time.
2. Second, although the yields for part numbers 2 and 3 are significantly different, each has the same NET impact to the final OEE result.
3. Third, when add the total “Yield % Opportunity” (3.21%) for all three part numbers to the total “Weighted % Yield Time” (96.79%), the result is 100%.

This last calculation once again demonstrates that the Quality Factor calculation presented here is consistent with the true definition of OEE.

The formula for the Quality Factor is:

Total Time to Produce Good Parts @ Rate / Total Time to Produce ALL Parts @ Rate

One Final Proof

Our method will produce a result that is consistent with the formula OEE = A * P * Q.  Using our example, it is clear that if Availability and Performance are both 100% and the Quality Factor is 96.79%, the final OEE for all parts will also be 96.79%.

Consistent with the definition of OEE, using our example, 96.79% of 1400 minutes is 1355 minutes.  This is the time that was used to make good or acceptable quality parts.  Similarly then, the time lost making all defective parts is 45 minutes (1400 – 1355 = 45).

The Impact to Operations

OEE is typically used by the Operations team for capacity planning, labour planning, and to determine how much time to schedule for a given resource to produce parts.  The above examples clearly demonstrate that even a small delta can have significant capacity, labour, and scheduling implications.  From this perspective it also becomes a relatively simple task to determine the direct labour costs associated with the production of defective parts.

Purchasing, Materials, Scheduling (Lead Times), Inventory (Stock), Finance, and Quality are all affected by inaccurate data and, in this case, OEE calculation errors.  Of course these errors are not just limited to the Quality Factor itself.

There are other significant losses and costs related to quality as well.  It is not our intent to pursue a discussion on the cost of non-quality as we recognize there are many other factors (internal and external) that must be considered to truly understand the real cost of non-quality for activities such as sorting, inspection, scrap (material losses), rework, re-order, machine time, and administration.

In the real world, someone may just be preparing a plan to improve the Quality of parts running on Machine A to reduce excessive labour and material costs.  We can only wonder what method they used to calculate the “savings”.  Inevitably, many companies approve the project and the funding only to realize the savings fell well short of expectations or will never materialize at all.

In Closing

We would contend that the differences in the calculation method presented here and those found elsewhere are significant.  In our example case, the difference is 2.72%.  We demonstrated that this can be significant when annualized over time.  Similarly, the opportunity for improvements using our method is clear and concise.

Now when someone asks you how to calculate the Quality Factor, you can confidently show them how and tell them why.

The example used in this post can also be downloaded from our BOX File on the sidebar or CLICK HERE.  This is offered at no charge and of course will make it easier for you to use for your own applications.

Thank you for visiting – Until Next Time – STAY lean!