# Question About Rolled Throughput Yield

#### Marlin60

##### Starting to get Involved
I posted this on one of the other forums, but re-posting here in hopes of getting a reply:

Question:

My company builds large, commercial HVAC units. The process map is:

Assembly Station 1
Assembly Station 2
Assembly Station 3
Assembly Station 4
Assembly Station 5
Assembly Station 6
Assembly Station 7
Assembly Station 8
Assembly Station 9
Assembly Station 10
Functional Testing (100% of completed units)
Close

My Quality Technician conducts an AQL sample (12%) in the Assembly Stations. He also conducts end-of-line audits (12%) on completed units.

We currently report the audit results and test results as three separate first-pass yield numbers. What I would like to do is also combine them into a single Rolled Throughput Yield. My question is whether it would be reasonable to do so since some data is sampled and some is 100%?

#### John Predmore

Trusted Information Resource
"all models are wrong. Some are useful" - George Box, famous statistician

Rolled Throughput Yield is a mathematical model of your process yield. I suppose you can combine any yield numbers you choose as long as you choose numbers which are representative of reality. When you state (for example) the inspection yield of functional testing station is 97%, no educated person interprets that test station is 97% every single day of the year. Some days the station will pass 100% and some days 95% or even fewer. The 97% yield is an average figure, or a best guess. Therefore if your total yield figure combines data from sampling and data from actual counts, that is your best practical estimate of reality that you have. If you want full transparency, include a footnote with your results table to reveal the sources, assumptions or tradeoffs used in the calculation.

You did not indicate whether the 10 assembly stations are sequential (every assembly must pass through all 10 stations) or parallel (10 identical stations making the same part). I will assume sequential.

You seem to want to focus only on inspection yield. When I worked with automatic assembly stations, I always calculated total yield instead of inspection yield. Total yield is net of process fallout from misfed parts, misformed parts which do not fit the nest, machine faults, and all other causes of yield loss in a station. You may want to tally analogous causes of lost productive takt time in your manual assembly stations. If one station does not complete a machine cycle for one of these reasons, there may not be a inspectable part generated to inspect, which diminishes station throughput but may not be reflected in the denominator of inspection yield. In summary, your process model is an approximation of reality. IMO you have to decide what to include or exclude from the model.

Last edited:

#### Marlin60

##### Starting to get Involved
John,

Thank you for the reply. The 10 stations are a progressive manufacturing process, similar to automotive assembly and all units pass through the 10 stations before going to our test cells. Unfortunately our data collection is not mature enough for net yield i.e. reworks, time lost, etc during assembly. Those things happen, but we don't record it.

My interest in using Rolled Throughput Yield is because it would allow us to merge the data collected by Production in Test and the data collected by my team (in-line and end-of-line audits) into a single metric. There's a benefit there from a report-out perspective.

Last edited by a moderator:

#### Semoi

##### Involved In Discussions
Hi:
if you have a significant amount of rework a combined yield does not make sense unless you adjust the calculation to account for the rework. However, if (a) the rework rate is negligible, and (b) the failure rates are independent you do not run into a mathematical problem. The sampling rate is irrelevant as long as the current yield estimates are representative of the actual yields.
Hope this helps.

#### Marlin60

##### Starting to get Involved
Semoi,

Thanks for the reply. Unfortunately I do not have tracking on reworks on the line, which are likely significant. I do have tracking for reworks from Final Test and our end-of-line audit.

#### Semoi

##### Involved In Discussions
Hi Marlin60,
you said that before and I understood that. However, before (!) you calculate the total yield you should clarify whether or not the calculation makes sense. Personally, I would ask the operators or shift leaders how often reworks are done. A rough estimate could be enough to start with. Then you could perform several calculations, where you change this estimate and thus obtain a range in which the total yield probably lies. In addition, your calculation could trigger the demand to document the reworks for the different processes and thus enable you to optimise your processes. In the end this is what matters, if your rework rate is not negligible.

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