Aggregated Stochastic Processes and Maintenance Models

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Aggregated Stochastic Processes and Maintenance
Models
Lirong Cui (PhD, Professor) Email
Lirongcui_at_bit.edu.cn School of Management
Economics, Beijing Institute of
Technology November, 18, 2011
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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

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1. Basic Theory for Aggregated Stochastic
Processes
(1)Definition(001-English.pdf) (2)History of
Related Researches (002-English.pdf) (3)Current
researches
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1.Basic Theory for Aggregated Stochastic
Processes (3)Current researches
Current research fields Ion-Channel
Modeling and Data Analyses Maintenance
Models ScholarsUKAlan G. Hawkes, Frank
Ball. Australian
USAHaijun Li ChinaBIT(Lirong Cui
et al.)?Yanshan University, Northwest University,
Minzu University of China (last three ones for
Master dissertations mainly)
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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..
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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..
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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
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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
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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
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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
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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 Balls way, to use mathematical derivation
to give the results (JAP, AAP) Method 2 Direct
way, Rubino Sericolas 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, 60979-993). However,
method 2 usually needs more complicated
algorithms. (2) Both methods need some
matrix theory knowledge.
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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
recommendArticle Proc. R. Soc. London B. 300,
p1-58. Important paper listsee document004
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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
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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-Channelsteady-state,
instantaneous, different classifications,
indexes, structures for systems etc..
?Classifications at presentFixed, Random.
?Maintenance models (MM) fixed state
classification MMfailure neglected MMfailure
effect delayed MMRandom classification
MMsingle-unitemulti-unite(series, parallel, K/n
etc.)sojourn time-based classification MMCycle
environment based classification MM (like
switching models) etc..
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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).
SchalorsBITLirong Cui(???),Yanshan
university, Northwest university, Minzu
university of China, Washington state university
Haijun Li, UK Alan G Hawkes.

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4. ASP-Based Maintenance Models
(3)Method of Researches Building new models,
Laplace transform mathematical derivations.
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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.
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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..
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? ?! Thank you for attention! Questions or
Comments ?