Various quality metrics serve the measurement and evaluation of manufacturing processes from quality and
efficiency standpoint. Being part of an efficient production chain, quality is as important as time. Among several quality related indicators,
the most useful yield metrics are the FPY (First Pass Yield) and the RTY (Roll Throughput Yield).
Both of them represent the chance of manufacturing products that meet the specification the first time,
without being scrapped, reworked, or retested, however there is a slight difference between the two of them (see later).
Running a manufacturing process with high FPY or RTY means proper production performance, less waste
(e.g. scrap, rework), and by this high efficiency.
The basics of yield metrics starts with FTY (First Time Yield), which is the simplest yield metric. Simplicity
itself is not a problem, but FTY has a major disadvantage. It does not take rework / retest into account.
FTY = (entering units - scrapped units) / total entering units
Let’s take an example of a manufacturing chain with 3 processes. 100 units enter the first process, 2
units need to be scrapped, and 8 pieces have to be reworked. As FTY does not take rework into account, the FTY of our first process will be
98%, even though we generated a lot of "waste", by reworking 8% of the entering quantity.
Calculation of FTY (Source: qMindset.com)
Based on this analogy, our overall FTY calculation will look like this:
FTY1 is (100 entered - 2 scrapped) / 100 entered = 0.9800
FTY2 is (98 entered - 5 scrapped) / 98 entered = 0.9489
FTY3 is (93 entered - 10 scrapped) / 93 entered = 0.8924
Overall (rolled) First Time Yield = FTY1 * FTY2 * FTY3
Overall FTY = 0.9800 * 0.9489 * 0.8924 = 0.8298 = 83%
In order to handle auxiliary and unproductive processes, the next metric considers rework / retest, etc.
a waste. First Pass Yield (FPY) calculates with the number of passing units without rework. Based on that, the formulae is the following:
FPY = (entering units – scrapped - reworked units) / entering units
Calculation of FPY (Source: qMindset.com)
Having the same process chain, our calculation will be the following:
FPY1 = (100 entered – 2 scrapped - 8 reworked) / 100 entered = 0.9000
FPY2 = (98 entered – 5 scrapped - 10 reworked) / 98 entered = 0.8469
FPY3 = (93 entered – 10 scrapped - 5 reworked) / 93 entered = 0.8387
Overall (rolled) First Pass Yield = FPY1 * FPY2 * FPY3
Overall FPY = 0.9000 * 0.8469 * 0.8387 = 0.6392 = 64%
Although the process chain has produced 83 units that are in specification, FPY shows a much worse result
compared to the calculation of FTY (64% vs 83%). The 64% value of the FPY in the example tells us, that one unit out of three products can be
expected to be scrapped or reworked.
However FPY takes auxiliary processes into account, there is a bit more improved yield metric, which is
the Rolled Throughput Yield (RTY). RTY represents the probability of producing good units the first time, so what is the chance that a product
goes through the whole process chain defect free.
RTY = (entering units – number of all defects) / entering units
RTY not only considers rework, retest or any other issue, but improves the theory further, by taking defect
distribution into account. It calculates with the number of defects. Why is it so important?
Calculation of RTY (Source: qMindset.com)
Let’s assume you have 100 units, that enter a process, and the number of passing units is still 100, after
99 pieces pass first time, and one is reworked. In such a case the First Time Yield is 100%, as the passing quantity is equal to the entering
quantity. First Pass Yield reflects the one piece that has been reworked, so FPY is 99%. As seen on the chart, RTY is even better to represent
quality, by calculating 3 defects, resulting an RTY of 97%. Note: in quality and Lean Six Sigma
literature, RTY is often given as the product of the FPY of each process, but it is only true, if there is only 1 defect on each failed unit. In
case of a part has more failure modes, it much more erodes the Rolled Throughput Yield, than the First Pass Yield.
Rolled Throughput Yield provides the rate, how capable the process is (with how much chance) to produce a
defect-free unit. The following chart shows the different yield calculations for each method in the same situation. As we see, FTY calculates only
with scrap, FPY takes rework into account, while RTY counts in all defects, giving the most strict result.
Comparison of the yield metrics (Source: qMindset.com)