Modeling Complex Systems k out of n

[smeitzner]

Using BlockSim or Weibull++ 6.0 (or some other calculation) how do you model a machining cell where 6 machines do identical operations and each produces 1/6 of the total production requirement? There are several similar cells, each dedicated to part of the complete machining process. All 6 machines in a cell must operate to make the full production volume, therefore they are in effect serial to the full manufacturing operation, but each is responsible for 1/6 of the production so they can be considered partially parallel. In effect if any one machine is down for maintenance the system is crippled but not halted.

[RS Support]

I understand the setting, what I am missing is what type of an answer are you looking for when you say modeling?

[Dr. Dave Olwell]

I assume these are repairable systems, so the metric of interest is really availability.

What I would do is model the system at several levels of capability. Fully capable would be a 6 of 6 system, or series, as you point out. Partially capable might be a 5 of 6 system or a 4 of 6 system. I would use BlockSim to calculate these availabilities.

I too am not sure what you are trying to model: the distribution of "up" time or some further quantity that depends on up time, like through put. Please advise.

You may need the distribution of the exact number of operating stations as a function of time. That too can be done in BlockSim, but I'd advise you get the help of someone who is proficient in the program as it is not a standard function.

Best wishes,

Dr. Dave Olwell

[Joe Dzekevich]

Hum...this is my second try at this. You want to do a Markov Rewards analysis. For each UP state, assign it a 1.0. For each DOWN state, assign it a 0. For each UP state, assign it a REWARDS value of 1.66667 (1/6). For availability, sum the up states. For rewards, solve the CDF. The system rewards CDF will give you the average perfomance (work-load) of the system. A tool like SHARPE can do this.

Regards,
Joe