Learning curve

[julia_tegami]

[ FlexSim 24.2.2 ]

How can I change processing times based on a learning curve?

I am running a rampup simulation on a line, and I want to assign a formula to the processing time of each station that represents this learning curve7. In this case, I want to use Y= A*X^B, where Y is the time to produce unit X, A is the time to produce the first unit (for example, 15 seconds), X is the cumulative number of units produced, and B is the logarithm of the learning rate divided by the logarithm of 2. In other words, as the operator produces items, each item would have a decrease in its processing time. Would it be possible to do this?

Thank you in advance!

[moehlmann_fe · Accepted solution]

You can use the input statistic (current.stats.input.value) as X and enter your formula into the processing time field using the methos of the "Math" class.

https://docs.flexsim.com/en/25.1/Reference/CodingInFlexSim/FlexScriptAPIReference/Data/Math.html

[julia_tegami]

How do I apply input statistics?

[julia_tegami]

Could you help me with a practical example?

[moehlmann_fe]

The expression "current.stats.input.value" will return the total input of the object, which is the X in your formula. A would be a fixed factor and B the exponent in a Math.pow() function.

process-time-formula.fsm

[julia_tegami]

So these graphs show that as the simulation time increases, the processing time, which was initially 10, decreases by 1% with each item inserted? Would this be our learning curve?

[moehlmann_fe]

Yes and no. The time decreases with each item but not by 1%. That would be A*0.99^X (exponential decay). With your formula, each improvement by N% requires double the number of processes than the last.

[julia_tegami]

Basically, I would like to know how many machines it would take the trainee operator to reach the station cycle time. For example, the production line cycle time is 15 seconds, and the trainee operator takes 5 times that time on the first machine. Considering a learning rate of 80%, how many machines or how long would it take him to reach 15 seconds for the station. This study is done to understand what would be the ideal amount of material available (buffer) for the station, until the production line alone can deliver the material to the next station on time without the operator needing to stop, that is, after how long or how many machines, the line reaches the cycle time and is supplied without the need for a buffer. I don't know if I was clear, but if you have any questions, please contact me. Thanks!

[moehlmann_fe]

That would just be solving x^(log2(0.8)) = 0.2 for x, no?

In FlexSim you could install the components of the staytime line chart (Advanced Tab in properties -> Install) and check the table of the Statistics Collector to see after how many items the process time falls below 15s.

[julia_tegami]

but shouldn't it become linear when it reaches the post time (in this case 15)?

and how to apply the " x^(log2(0.8)) = 0.2 for x"?

[moehlmann_fe]

I don't know why you are asking me this. You defined the function in your original post. And the function A*X^B is a continuously falling function with a lower limit of 0 for B < 0.

And log2(0.8) is just a number, let's call it c. So solving x^c = 0.2 just requires to raise both sides to the power of 1/c. Then x is the number of processes until the original processing time has decreased by 80%.

[julia_tegami]

Ok, thanks for the help!