# Lean Question

Six Sigma – iSixSigma Forums Old Forums General Lean Question

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• #50634

newbie
Participant

When calculating a a timeline for a current state VSM and using Littles Law

(Process Lead Time = Inventory (pieces) / Average Completion Rate)
to transform inventory piece counts into time, is the “Average Completion Rate” taken for the individual process step or for the VS as a whole?
THANKS!!

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#174299

[email protected]
Participant

This may help— Let me know ok.
The major intuitive insight that waste elimination by process improvement drove faster
lead time was due to Henry Ford. The Model T originally sold for \$850 and took 14 days
to produce. Process improvement eliminated nearly all the waste and the same car was
produced in 33 hours and sold for \$345 at higher total profit. Kiichiro Toyota essentially
adapted this process to the production of a variety of cars using what is now known as
Lean Six Sigma and Complexity reduction tools. This phenomenon has been observed in
other transactional (non-manufacturing) microeconomic processes such as product
development, marketing, planning, budgeting, etc4. Lead time is measured from the time
of injection of raw material into the process to its completion as finished goods.5. The
Lead Time of any process is governed by Littles Law4, The time per cycle of production
from injection of work into a process to its completion is:
Lead Time of any Process= Number of Units of Work In Process W = = time/cycle
Average Completion Rate D
= ô (5)
As an example of Littles Law, if a process has WIP of 50 units and has an average
completion rate of 2 units per hour, then the average time for a unit of WIP to transit the
process is:
Lead Time of Process = 50 units = 25 hours
2units hour
Thus a manufacturing cycle is completed every 25 hours.

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#174313

Ron
Member

What is your question? Littles Law is in regards to cueing theory and has nothing to do with cycle time or lead time.
When calculating cycle times for a process or value stream you need to take multiple observations of each step in the value stream and average these. Add the cycle times together and you have the value stream cycle time…add delivery packaging, transportation this equals lead time

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#174319

Darth
Participant

Sorry Ron, Little’s Law is sufficiently generic to apply to a lot of things.  With respect to process lead time, the equation simply becomes…the PLT..process lead time…how long it will take the next item up to get through is equal to the WIP divided by the Exit Rate.

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#174317

newbie
Participant

Understood.  If I have queued inventory before a given process, is its wait time determined – using Littles Law – by the avg completion rate of the process before it or the avg completion rate of the entire value stream?
And how do you add cycle times when they are rate metrics?  It was my impression these are not additive.  Are you using process time and cycle time interchangeably?
Thanks!

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#174321

Darth
Participant

Let’s try it this way.  You have an item waiting to make its way through Process Step X.  There are currently 100 items already being worked on in that process.  Items exit Process Step X at 10 items/hour.  It will take 10 hours for that waiting item to exit Process Step X.  Of course the exit rate will vary for each item so the average exit rate might make sense or if you want to get fancy you can use a distribution of exit rates.  You can do these calculations at the process level or overall at the macro level.  Depends on what you are trying to undestand.

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#174325

newbie
Participant

Crystal, thanks Darth.  So if I am simply trying to create your run-of-the-mill current state VSM with the appropiate time line (ie lead time), for each of my inventory queues (ie “triangles”) am I using  exit rate for the process the inventory is “waiting” on or am I to use the exit rate for the entire value stream (ie the average daily production rate for the VS).

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#174329

Darth
Participant

I’d probably start with the micro process level and use the process exit rate.

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#174331

newbie
Participant

Thanks Darth!!

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#174335

Ron
Member

I disagree Littles Law (little Known kinda sorta law) is very specific. You can stretch anything beyond its intended use. That doesn’t make it applicable.
The question was however sufficiently vague that one could apply just about anything

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#174336

Ron
Member

In queueing theory, Little’s result, theorem, lemma, or law says:

The long-term average number of customers in a stable system N, is equal to the long-term average arrival rate, ë, multiplied by the long-term average time a customer spends in the system, T, or:

For those not famkilar with Littles sorta kinda law.

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#174343

Darth
Participant

This might actually be equivalent to saying that the average time it will take for an item to go through a process (PLT process lead time) is equal to the average number of things in the process (WIP in the system) divided by the exit rate from that process.

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