Modeling Breakdowns

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Modeling Breakdowns

• Jerry Banks
• Atlanta, GA 30319
• USA

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Modeling Downtimes and Failures

• Ignore it
• Adjust processing time
• Constant values for TTF and TTR
• Statistical distributions for TTF and TTR

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Ignore Downtime

• Not suggested
• Irresponsible
• Maybe OK to omit catastrophic downtimes if client
  understands
• Hurricanes
• Strikes
• Snow Storms
• Factor into results (5 days/year of production
  due to strikes)

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Factor in the Effect of Downtime

• Adjust process time of each job or part
• Acceptable only in limited circumstances
• Factoring in downtime will result in a loss of
  information about possible queues
• Queues and short term congestion are strongly
  influenced by randomness and variability

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Use Constant Durations

• OK if TTF is for PM on a fixed schedule

6
Use Statistical Distributions

• The appropriate technique

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Measuring TTF

• Wall-clock time
• Busy time
• Cycles
• Number of items produced

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Measuring TTR

• Pure time delay
• Requiring no resources
• Wait for resources plus time delay for actual
  repair

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Options when a Downtime Occurs

• Scrap
• Rework
• Resume processing after downtime is completed
• Complete processing before downtime occurs

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Example

• Single server
• Processing is e(7.5 min)
• TBA is e(10 min)
• TTF is e(1000 min)
• TTR is e(50 min)
• When failure occurs, current entity is removed
  and when repair is completed, entity finishes
  processing

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Simulation

• Six different treatments
• Five replications of each
• Each simulated for 100,000 minutes

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Simulation of Breakdowns
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Does it matter?

• IAT is expo 10.0 min
• Processing is expo 7.5 min
• TTF is 20 x TTR
• Examples
• TTF1000 min, TTR50 min
• TTF500 min, TTR25 min
• Smaller the TTF, the smaller is the average
  number in queue?

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TTF/TTR 20
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End