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Aggregated Stochastic Processes and Maintenance Models

Aggregated Stochastic Processes and Maintenance Models. Lirong Cui (PhD, Professor) Email: Lirongcui@bit.edu.cn School of Management & Economics, Beijing Institute of Technology November, 18, 2011. Outlines. Basic Theory for A ggregated S tochastic P rocesses ( ASP )

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Aggregated Stochastic Processes and Maintenance Models

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  1. Aggregated Stochastic Processes and Maintenance Models Lirong Cui (PhD, Professor) Email: Lirongcui@bit.edu.cn School of Management & Economics, Beijing Institute of Technology November, 18, 2011

  2. Outlines • Basic Theory for Aggregated Stochastic Processes (ASP) • Questions Considered in ASP • Ion-Channel Modeling & Related ASP • ASP-Based Maintenance Models • All related papers and Possible Application Fields

  3. 1. Basic Theory for Aggregated Stochastic Processes （1）Definition；(001-English.pdf) （2）History of Related Researches (002-English.pdf) （3）Current researches

  4. 1.Basic Theory for Aggregated Stochastic Processes（3）Current researches Current research fields: Ion-Channel Modeling and Data Analyses； Maintenance Models； Scholars：UK：Alan G. Hawkes, Frank Ball. Australian USA：Haijun Li China：BIT（Lirong Cui et al.）、Yanshan University, Northwest University, Minzu University of China (last three ones for Master dissertations mainly)

  5. 2. Questions Considered in ASP (1) Stochastic Properties: Property reservation of for underlying stochastic processes, e.g., Markovian property, Stochastic order comparison, Properties and characteristics for ASP, How to classify the state space etc.. Most researches: Underlying stochastic process, is Markovian, or Semi- Markov ( under a fixed state classification) (2) Probability for Events: To find the probability of the related events for ASP, including in steady-state and instantaneous cases for probability and conditional probability. (3) Time Distributions: Some duration time distributions (including joint probability distributions), age, residual lifetime, mean, variance, etc..

  6. 2. Questions Considered in ASP (4) Convergence Problems: Convergence speeds of ASP under various state classifications. (5) Computation Problems: Reverse Laplace & Laplace-Stieltjes numerical problems, algorithms. (6) Applications: Where ASP can be used, reverse problems, parameter inferences etc..

  7. 3. Ion-Channel Modeling & Related ASP （1）Brief introduction for Ion-Channel （2）Related ASP for Ion Channel （3）Two ways for studying ASP for Ion Channel （4）Journals for related publications

  8. 3. Ion-Channel Modelling & Related ASP （1）Brief introduction for Ion-Channel In 1976, Neher E. & Sakmann B. published a paper in “Nature” to invent a method for recording single-channel currents, because of this work, they got the Nobel Prize in Medicine on Biophysics in 1991. Cited from some journal Figure 3-1. Ion Channels on cell membrane

  9. … … open Shut time t … open duration Shut duration 3. Ion-Channel Modelling & Related ASP （1）Brief introduction for Ion-Channel (Continued) Figure 3-2. Records of single-channel currents Figure 3-3. Regularization of records of current records

  10. 3. Ion-Channel Modeling & Related ASP （2）Related ASP for Ion Channel Given a finite state continuous time Markov Chain with a infinitesimal generator matrix (we assume all states are communicated each other) Continued to 003.pdf

  11. 3. Ion-Channel Modeling & Related ASP （3）Two ways for studying ASP for Ion Channel Method 1: Laplace & Laplace-Stieltjes transform, in details, there are two ways: (a). Alan G. Hawkes’ way, to use physical explanations to show the results (Proc. R. Soc. London B). (b). Frank Ball’s way, to use mathematical derivation to give the results (JAP, AAP) Method 2: Direct way, Rubino & Sericola’s way (to use the uniformation technique for Markov Chain, direct to Semi-Markov Chain) (JAP, RESS) Note: (1) computation problems faced for Method 1 are mainly inversion of Laplace or Laplace-Stieltjes transforms, fortunately, this hand has been some very good results, e.g. (Int. J. Numer. Method Eng.2004, 60:979-993). However, method 2 usually needs more complicated algorithms. (2) Both methods need some matrix theory knowledge.

  12. 3. Ion-Channel Modeling & Related ASP （4）Journals for related publications： Alan G. Hawkes, Proc. R. Soc. London B; Frank Ball, JAP, AAP, Math. Biosci. Biophys. J. G Rubino & B. Sericola, JAP, RESS Here I strongly recommend：Article： Proc. R. Soc. London: B. 300, p1-58. Important paper list：see document:004

  13. 4. ASP-Based Maintenance Models （1）State aggregation-based maintenance models （2）Related researches and state-of-art （3）Method of researches （4）Ways of state aggregation

  14. 4. ASP-Based Maintenance Models （1） State aggregation-based maintenance models ● Failures & Repairs or Maintenance actions drive the movement of ASP； ● Different classifications, different maintenance models； ●it differs from Ion-Channel：steady-state, instantaneous, different classifications, indexes, structures for systems etc.. ●Classifications at present：Fixed， Random. ●Maintenance models (MM)： fixed state classification MM；failure neglected MM；failure effect delayed MM；Random classification MM；single-unite；multi-unite（series, parallel, K/n etc.）；sojourn time-based classification MM；Cycle environment –based classification MM (like switching models) etc..

  15. 4. ASP-Based Maintenance Models （2）Related researches and state-of-art： Questions have been studied: Maintenance modeling, probability for some events, time distributions, some indexes formulae (single-unit, series, parallel) Questions have not been studied: Speed of convergence, parameter inference, maintenance strategies etc.. National Natural Science Foundation of China (NSFC)： （1）ASP-based maintenance models and analyses（70671009）； （2）A study on derivative maintenance modelling and its related problems in terms of modes of state aggregations（71071020）. Schalors：BIT：Lirong Cui（崔利荣）,Yanshan university, Northwest university, Minzu university of China, Washington state university: Haijun Li, UK： Alan G Hawkes.

  16. Applications (maint. Dec.-maki, optim. Manag.) Model analy., Index formulae, Model compari.. Affecting each other, but different focus points Driven by theory Same essence Aggregated modes （one mode including at least one way） Maint. models ASP Driven by Engineering Properties of ASP, Possible/potential applications (Quality credit level, HRP, system monitoring etc..) 4. ASP-Based Maintenance Models （3）Method of Researches: Building new models, Laplace transform + mathematical derivations.

  17. 离子通道模型、对于固定分类情况 下的维修时间 参数 基于参数 基于工作时间参数 、工作时间与维修时间组合 的维修性模型研究（ 4. ASP-Based Maintenance Models （4）Ways of state aggregation see document 005 Recent published / submitted papers by speaker （a）IIE Transactions (one published, one under review)； （b）IEEE Transactions on Reliability (2010,No. 4) ; （c）Mathematical and Computer Modeling （d）Journal of Systems Engineering and Electronics （e）Other work.

  18. 4. All related papers and Possible Application Fields （1）Related papers： Hawkes, Ball, Cui et al. papers (SCI，EI)， and BIT PhD, master dissertations, Yanshan university master dissertation, Northwest univer. Master dissertation, Minzu university of China Master dissertation, Some Proceedings. （2）Possible application fields： Reliability, Quality Management, Human resource planning, insurance, network reliability, supply chain management etc..

  19. 谢 谢！ Thank you for attention! Questions or Comments ?

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