Aggregated Stochastic Processes and Maintenance Models

Lirong Cui (PhD, Professor)

Email: Lirongcui@bit.edu.cnSchool of Management & Economics,

Beijing Institute of Technology

November, 18, 2011

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

1. Basic Theory for Aggregated Stochastic Processes

（ 1 ） Definition ； (001-English.pdf)

（ 2 ） History of Related Researches (002-English.pdf)

（ 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)

1.Basic Theory for Aggregated Stochastic Processes

（ 3 ） Current researches

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..

(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..

2. Questions Considered in ASP

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

（ 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.

Figure 3-1. Ion Channels on cell membrane

3. Ion-Channel Modelling & Related ASP

Cited from some journal

（ 1 ） Brief introduction for Ion-Channel (Continued)

Figure 3-2. Records of single-channel currents

open

Shut

open duration Shut duration

…

…

… time t

Figure 3-3. Regularization of records of current records

3. Ion-Channel Modelling & 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)Q

Continued to 003.pdf

3. Ion-Channel Modeling & Related ASP

（ 3 ） Two ways for studying ASP for Ion ChannelMethod 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.

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

3. Ion-Channel Modeling & Related ASP

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

（ 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..

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.

4. ASP-Based Maintenance Models

（ 3 ） Method of Researches:

Building new models, Laplace transform + mathematical derivations.

4. ASP-Based Maintenance Models

Driven by theory

Driven by Engineering

Aggregated modes（ one mode including at least

one way ）Maint. models

ASP

Model analy.,Index formulae,Model compari..

Properties of ASP, Possible/potential applications

(Quality credit level, HRP, system monitoring etc..)

Applications (maint. Dec.-maki, optim. Manag.)

Same essence

Affecting each other, but different focus points

（ 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.

4. ASP-Based Maintenance Models

（ 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..

4. All related papers and Possible

Application Fields

谢 谢！

Thank you for attention!

Questions or Comments ?