Sam handed Peter a computer printout and asked, “If the yields are so high, why is my efficiency so low?”

Peter studied the report for a moment and then nodded. “Let me show you what’s going on,” he said as he picked up a marker and drew a diagram (see Figure 1). “This process has 10 separate steps,” Peter began. “Each step has a yield of about 90 percent. This is the unit yield for that process step.”

“Right,” Sam interjected. “And all of them are about 90 percent, so the average yield for the whole process should be about 90 percent.”

“Yes, but that isn’t the number you need if you’re trying to determine the final yield for the process,” Peter responded. “Final yield is the proportion of defect-free units out of the final process step relative to what you started with at the first process step.”

Sam nodded. “Yeah, but even though the average yield is nearly 90 percent, our final yield is nowhere near that high.”

Peter turned back to the board. “Here’s a mathematical model of what happens when all process steps have the same unit yield.” He wrote an equation:

Yoverall = (Ystep)number of steps

“The unit yield at every step is about 0.9, but you have to multiply the step unit yields together to get the final unit yield. You can’t just average them,” Peter explained. “Think of a simple two-stage process. You start 100 units at the first step and 90 pass. These 90 start the second step and 90 percent of them pass, leaving 81. The average unit yield is 90 percent, but the final unit yield is only 81 percent.”

“So for our 10-step process,” Sam began.

Peter punched his calculator keys. “0.9 raised to the 10th power is about 0.35. So 35 percent is your predicted final yield.”

“And that’s pretty close to what we’re getting,” Sam said.

Peter knew that misunderstandings on yields lead to a variety of poor management decisions. He was pleased that Sam had asked for clarification. But, Peter knew, Sam still didn’t know the whole picture. Six sigma requires an entirely different mental model of yields.

“That’s not all,” Peter said. “So far we’ve been talking about unit yields. That’s the customary way of doing it around here, but there’s a better way.”

“Unit yields often have very little to do with costs,” Peter continued. “Who knows how we got those 350 good units? Maybe they were reworked several times. There can be a lot of cost hidden in the numbers. If you want an accurate picture of process performance, use rolled throughput yields.”

Peter sketched another picture on the board (see Figure 2).

igure 2: Unit Yields vs. Rolled-Throughput Yield “Let’s assume that we have two lines making the same product. If we only look at unit yields, they look much different. One process has a 50-percent yield, the other a 90-percent yield. But assume that each unit had 10 critical-to-quality characteristics. If we look at characteristics, we see that both have produced five defects in 100 defect opportunities. In terms of the ability to produce defect-free quality characteristics, they’re actually the same.”

“So if it costs \$100 to fix a defect, the two processes have about the same rework cost, even though the unit yields would make the first process look a lot better,” Sam replied, nodding.

“This is exactly why we use rolled throughput yields in six sigma,” Peter responded. “They correlate much more closely with labor, cycle time, rework costs and other important management metrics.”

Sam frowned. “That means that our efficiency reports are worse than useless–they’re misleading!”

Peter smiled.

“Thanks, Peter!” Sam exclaimed. “I think you’re just the man to head a project to fix them!”

Yields: A Glossary

Yield, First-time Yield (unit-based)–the number of units that pass a particular inspection compared to the total number of units that pass through that point in the process.

Final Yield (unit-based)–the number of units that pass the last step in a series of steps in a process compared to the number of units the entire process started with.

Throughput Yield (defect-based)–the probability that all defect opportunities produced at a particular step in the process will conform to their respective performance standards.

Rolled Throughput Yield (defect-based)–the probability of being able to pass a unit of product or service through the entire process defect-free.

Normalized Yield (defect-based)–the geometric average throughput yield one would expect at any given step in the process. Analogous to the “typical” yield. For a k -step process, the normalized yield would be the kth root of the rolled throughput yield. A note of caution: This metric can be misleading if the throughput yields of the process steps vary a great deal.

# First pass yield

First pass yield (FPY), also known as throughput yield (TPY), is defined as the number of units coming out of a process divided by the number of units going into that process over a specified period of time. Only good units with no rework are counted as coming out of an individual process.

Also related, "first time yield" (FTY) is simply the number of good units produced divided by the number of total units going into the process. First time yield considers only what went into a process step and what went out, while FPY adds the consideration of rework.

Consider the following:

You have a process that is divided into four sub-processes: A, B, C and D. Assume that you have 100 units entering process A. To calculate first time yield (FTY) you would:

1. Calculate the yield (number out of step/number into step) of each step.
2. Multiply these together.

For Example:

(# units leaving the process as good parts) / (# parts put into the process) = FTY

• 100 units enter A and 90 leave as good parts. The FTY for process A is 90/100 = .9000
• 90 units go into B and 80 leave as good parts. The FTY for process B is 80/90 = .8889
• 80 units go into C and 75 leave as good parts. The FTY for C is 75/80 = .9375
• 75 units got into D and 70 leave as good parts. The FTY for D is 70/75 = .9333

The total first time yield is equal to FTYofA * FTYofB * FTYofC * FTYofD or .9000 * .8889 * .9375 * .9333 = .7000.

You can also get the total process yield for the entire process by simply dividing the number of good units produced by the number going in to the start of the process. In this case, 70/100 = .70 or 70% yield.

The same example using first pass yield (FPY) would take into account rework:

(# units leaving process A as good parts with no rework) / (# units put into the process)

• 100 units enter process A, 5 were reworked, and 90 leave as good parts. The FPY for process A is (90-5)/100 = 85/100 = .8500
• 90 units go into process B, 0 are reworked, and 80 leave as good parts. The FPY for process B is (80-0)/90 = 80/90 = .8889
• 80 units go into process C, 10 are reworked, and 75 leave as good parts. The FPY for process C is (75-10)/80 = 65/80 = .8125
• 75 units go into process D, 8 are reworked, and 70 leave as good parts. The FPY for process D is (70-8)/75 = 62/75 = .8267

The first pass yield of the set of processes is equal to FPYofA * FPYofB * FPYofC * FPYofD = .8500 * .8889 * .8125 * .8267 = .5075

Notice that the number of units going into each next process does not change from the original example, as that number of good units did, indeed, enter the next process. Yet the number of FTY units of each process counts only those that made it through the process as good parts that needed no rework to be good parts. The calculation of FPY, first pass yield, shows how good the overall set of processes is at producing good overall output without having to rework units.

# Throughput Yield (TPY)

### Also called First Pass Yield

Throughput Yield (TPY) is the number of acceptable pieces at the end of the end of a process divided by the number of starting pieces excluding scrap and rework (meaning they are a part of the calculation).

Rework IS a part of the TPY calculation. Use the process map as a guide for evaluating each individual process.

TPY is used to only to measure a single process.

Sometimes only raw material is available at the start so it may be necessary to convert the raw material to expected pieces that it should make, or use a unit of weight at the start and weight out at the end to calculate final yield.

The unit of measure must be the same for the numerator and denominator throughout the calculation. Calculation (assuming all rework only takes one time to correct):

Process 1 TPY:

40 of the 50 pieces that entered Process 1 went through Process 1 correctly the first time.

Therefore Process 1 TPY = 40 / 50 = 80.0%

Process 2 TPY:

34 of the 46 pieces that entered into Process 2 went through Process 2 correctly the first time through.

Therefore Process 2 TPY = 34 / 46 = 73.9%

Process 3 TPY:

37 of the 46 pieces that entered Process 3 went through Process 3 correctly the first time.

Therefore Process 3 TPY = 37/46 = 80.4%

Process 2 has the lowest throughput yield but not necessarily the most costs. If a scrapped piece in Process 3 has significantly more cost then Process 3 it may still be in the team’s best interest to improve. The later the process is downstream the more cost are accumulated in the piece or part.

There is more direct material, direct labor, and/or manufacturing overhead in each process as the part proceeds through its value stream. Process 3 at its initiation has all the costs in Process 2 + the costs of Process 1.

There is another method to calculate TPY for a single process. If the DPU or defects and units are known then: Rework involves many of the 7-wastes and contains the hidden factory opportunity, it is relevant to understand when guiding the team's direction.

Throughput Yield, TPY, and other yield metrics can serve as baseline scores (MEASURE phase) and final scores for Six Sigma projects (CONTROL phase).

The baseline score does not have to be a z-score and often this yield metrics are easier for team and other company employees to relate with and understand.

# Final Yield (FY)

Final Yield represents the acceptable pieces at the end of the process divided by the pieces started. The FY excludes scrap.

In other words, if there are the same amount of pieces at the end as there were at the start (without any being introduced in the middle) then there is perfect 100% final yield. Rework is not a part of the FY calculation. Use the process map as a guide for evaluating each individual process.

FY does not depend on the number of processes involved. It is a high level determination the percentage of good pieces that came out of the entire process compared to the quantity started or that should have been made.

NOTE: Sometimes only raw material is available at the start so it may be necessary to convert the raw material into expected pieces that it should make, or use a unit of weight at the start and weight out at the end for the calculation.

Calculation from above example:

The unit of measure must be the same for the numerator and denominator throughout the calculation.

Process 1 Yield: 46 passed / 50 entered = 92.0%

Process 2 Yield (itself): 46 passed / 46 passed = 100%

Yield AFTER Process 2: 46 passed / 50 entered: 92.0%

Process 3 Yield (itself): 37 passed / 46 entered = 80.4%

Yield AFTER Process 3 (also the same as the final yield of entire process):

37 passed / 50 entered

Final Yield = 74%

Process 3 has the lowest yield and probably the most cost associated since all the material, labor, and overhead costs are already in the pieces from the previous processes.

Final Yield and other yield metrics can serve as baseline scores (Measure Phase) and final scores for Six Sigma projects (Control Phase). The baseline score does not have to be a z-score and often this yield metrics are easier for team and other company employees to relate with and understand.

IF there is known rework and it is significant to your team and company success, then throughput yield and rolled-throughput yield are better metrics.

# Rolled Throughput Yield (RTY)

Rolled Throughput Yield is the probability of the entire process producing zero defects. RTY is more important as a metric to use where the process has excessive rework.

Since this rework involves many of the 7-wastes and contains the hidden factory opportunity, it is relevant to guide the team in the right direction.

RTY is the product of each process’s throughput yield, TPY.

Using the same process as shown in the TPY example: Calculation from above example:

RTY = Process 1 TPY * Process 2 TPY * Process 3 TPY

RTY = 0.800 * 0.739 * 0.804

RTY = 0.475 = 47.5%

There is a 47.5% of the entire process producing zero defects.

RTY and other yield metrics can serve as baseline scores (Measure Phase) and final scores for Six Sigma projects (Control Phase).

The baseline score provided in the MEASURE phase does not have to be a z-score and often the yield metrics are easier for team and other company employees to relate with and understand.

Another formula is shown below to estimate RTY if the defects per unit or defects and units are known: # Normalized Yield (NY)

Normalized Yield (NY) is the average yield per process step. The probability of a unit passing through one process step or opportunity without rework.

Formula: where k equals the number of processes.

A calculation using example from above: Calculation:

Using k = 3

NY = 0.475^(1/3)

NY = 0.780 = 78.0%

There is a 78% chance of a unit passing through one process step without rework.

Another relationship is shown below to obtain the normalized defects per unit. The normalized defects per unit equals 0.2481.

Normalized Yield and other yield metrics can serve as baseline scores (Measure Phase) and final scores for Six Sigma projects (Control Phase).

The baseline score does not have to be a z-score and often these yield metrics are easier for team and other company employees to relate with and understand.