Using Stochastic RAM Analysis to Establish an Optimal Operating Policy

1. Using Stochastic RAM Analysis to Establish an Optimal Operating Policy 8th IMA International Conference on Modelling in Industrial Maintenance and Reliability Oxford University July 10, 2014 Jacob T. Ormerod Vero Beach, Florida, USA jake@openrealiability.org

2. A word about OpenReliability.org • Currently developing in the R Statistical Programming environment. • Weibull Analysis – Abernethy Reliability Methods, package abrem • (formerly package weibulltoolkit) • Stochastic Simulator for Reliability Analysis, package stosim • Spare Parts Analysis – Multi-Eshelon Techniques for Recoverable Item Control (METRIC, MOD-METRIC, VARI-METRIC, . . .) Jacob T. Ormerod Vero Beach, Florida, USA jake@openrealiability.org

3. The Example Problem • Simple enough for my 87 year old mother to understand. • Sophisticated enough that solution without stochastic approach is too difficult. • Completely implemented in the R system. (commercial software not required) • This paper describes the development of useful contributed package functions. • In this environment we call a collection of useful functions that can be made to work together a “toolkit”. This is not intended to be the development of a mindless user application. Jacob T. Ormerod Vero Beach, Florida, USA jake@openrealiability.org

4. Multi-train Feed Inventory Primary Reactor

5. Charge Unit 1B Charge Unit 1C Charge Unit 1A Primary Reactor Charge Unit 2A Charge Unit 2B Charge Unit 2C Example Problem RBD Charge Unit 3A Charge Unit 3B Charge Unit 3C Storage Discharge Accumulator Charge Storage

6. Example Problem Statement • The charge storage has a capacity for 16 hours of replacement time for a single charge train. • An accumulator unit operation has the ability to replenish the complete storage inventory in 2weeks, but will be operated to attempt to top off the tank after any consumption.It is assumed that the accumulator operates on excess capacity from the charge feed system and does not reduce flow available to the primary reactor. • The storage discharge unit has a capacity for replacement of a single charge train. • The primary reactor system requires 3 days to restart upon any sudden, partial loss of charge flow. However, it can be turned down to 60% of production given an hour’s notice. The operators of this unit need to have a policy that will enable them to optimize total production from the primary reactor. This is expected to be accomplished by establishing a reserve inventory to be held in storage, which should then trigger turndown of the primary reactor to avoid damaging shutdown.

7. Single Train Operational Data Input Table Values Analytical Summary

8. Getting Random Values for a Simulated History Times To Failure Times To Repair

9. Building the Simulated History Times To Failure Times To Repair Simulated History Event Queue Pull the first event for the Simulation History from the Queue

10. Building the Simulated History Times To Failure Times To Repair Simulated History Event Que Delay the history time for remaining events in the Queue by repair time of last event

11. Building the Simulated History Times To Failure Times To Repair Simulated History Event Queue Add the new event TTF to current EventClock time to get history time for new random event.

12. Building the Simulated History Times To Failure Times To Repair Simulated History Event Queue Sort the Queue, then Pull the next event for the Simulation History from the Queue

13. Building the Simulated History Times To Failure Times To Repair Simulated History Event Que Delay the history time for remaining events in the Queue by repair time of last event

14. Building the Simulated History Times To Failure Times To Repair Simulated History Event Queue Add the new event TTF to current EventClock time to get history time for new random event.

15. Building the Simulated History Times To Failure Times To Repair Simulated History Event Queue Sort the Queue, then Pull the next event for the Simulation History from the Queue

16. Building the Simulated History Times To Failure Times To Repair Simulated History Event Queue Delay the history time for remaining events in the Queue by repair time of last event

17. Building the Simulated History Times To Failure Times To Repair Simulated History Event Queue Add the new event TTF to current EventClock time to get history time for new random event.

18. Building the Simulated History Times To Failure Times To Repair Simulated History Event Queue Continue Building the Simulated History

19. Building the Simulated History Times To Failure Times To Repair Simulated History Event Queue Continue Building the Simulated History

20. Building the Simulated History Times To Failure Times To Repair Simulated History Event Queue Continue Building the Simulated History

21. Building the Simulated History Times To Failure Times To Repair Simulated History Event Queue Continue Building the Simulated History

22. Building the Simulated History Times To Failure Times To Repair Simulated History Event Queue Continue Building the Simulated History

23. Building the Simulated History Times To Failure Times To Repair Simulated History Event Queue Continue Building the Simulated History

24. Building the Simulated History Times To Failure Times To Repair Simulated History Event Queue Continue Building the Simulated History

25. Building the Simulated History Times To Failure Times To Repair Simulated History Event Queue Continue Building the Simulated History

26. Building the Simulated History Times To Failure Times To Repair Simulated History Event Queue Continue Building the Simulated History

27. Building the Simulated History Times To Failure Times To Repair Simulated History Event Queue Continue Building the Simulated History

28. Building the Simulated History Times To Failure Times To Repair Simulated History Event Queue

29. Creating the OpLine Detail Sim Histories OpLine Detail Train1 Train2 Train3

30. Exploring the OpLine Detail X

31. Input Table Values Analytical Summary

32. Exploring the OpLine Detail

33. Production History with Inventory Suport

34. Logic for Production from Multi-Train system with Inventory

35. Logic for Production from Multi-Train system with Inventory

36. Logic for Production from Multi-Train system with Inventory

37. Completion of Model Analysis Usage MultiTrainWithInventory(model, CapacityHrs, ReserveHrs, RefillTime, DischargeCap=1, TurndownLimit=0.6, TurndownTime=1, ProgRpt=FALSE)

38. Expanded Considerations • MulitiTrainWithInventory was designed to take restraining parameters of the example problem as variables. This enables its proactive use in design. • What is the value of additional storage capacity? • Is a single train discharge capability too limiting? • What is an effective accumulator design?

39. Expanded Considerations • With simulated history for the system so developed what other kind of questions can be posed? • What does the distribution of annual availability look like? • What is the confidence in meeting availability commitments? • If the charge feed system crosses a contractual barrier, what might the effect of contract performance penalties be?

40. Expanded Considerations • What other type of problems are suited to stochastic, discrete event modeling? • Multiple supply systems of varied capacity and design. • Service to multiple customers from a pipeline network. • Distribution of available product to clients during curtailment. • Account for compression and piping (pumping) limitations. • Account for pressure drop in pipeline system. • More Ideas???

41. Thank You