Have a look at the following paper, which you can download for free as it is published with an open access option: "Preventive maintenance scheduling of multi-component systems with interval costs" by Gustavsson, Patriksson et al (Computers & Industrial Engineering, 2014). The full link is found below:

http://www.sciencedirect.com/science/article/pii/S0360835214000527

Thank you very much Both of you.

Both articles are very useful. I liked them a lot. But Interest to me are a way of alternating coercive repairs and preventive settings of modes of operation and replacement of obsolete components. And the criteria for making decisions about initiating corrective maintenance. In this case it comes to reliability, which must be ensured during operation. So the way in which workers carry out maintenance of all technical equipment is very important. It is important to decide which are the criteria that determine whether it is necessary emergency repair of the system or it can work to next preventive activities. And just in this connection It is necessary to determine what is the optimal amount of time between two consecutive maintenances. What measurements and what repairs are contained in preventive activities. I need to decide whether urgent, unplanned repairs should fully recover operability of the system, or is it sufficient to provide only repair compulsory for people safety during the operation of facilities; then when it is makes prevention to set all parameters and functions in such a way that the system be completely undamaged.

Once again - thank you both.

Have you thought about using simulation along with the optimization tools to solve your problem? The simulation takes into account the variability of the occurrences of an event as well as the complexity of everything that surrounds it. Using the optimization methods you can use Mathematical Programming as well as the Meta Heuristic to model your problem, so you can use the information about the constraints, for example

indication of process idleness or full resource utilization. The great advantage of using these methods is the possibility of finding in advance the best result for a given

Context and find out what the problems are.

Thank you very much Isis Lima,

The idea to use Meta Heuristic for modeling might be excellent. I do not know this software, so I'll look into it.

Once again, thank you very much for the excellent idea.

The heuristic goal it's not a software but a branch of operational research that can help model optimization of combinatorial optimization problems (not necessarily your case, but if so, it's a great science to use).

Speaking about software, I know some simulations like: Simul8, Flexsim, Arena ... but if you are going to design your problem using Linear Programming, Nonlinear, Integer (or not) to find the optimization of your problem, I recommend the LINDO software (Linear Interactive and Discrete Optimizer).

Isis Lima, Thanks so much for helpful tips !

PhD student Julia Garipova, of which I am director, worked on the topic related to optimize the operational reliability. We have solved many important problems in this area, such as the selection criteria for the way to alternate different types of repairs quantitative indicators to assess the outcome of razlichnide strategies for maintenance, etc., But not yet problem solved with the optimization of certain activities. If you do not mind, she will contact you for collaboration.

Anton

An excellent "practical" (theory downplayed) and accessible example, touting the use of @RISK (a superset of Microsoft Excel) appears in chapter 23 (pages 143-148) of "Decision Making Under Uncertainty with RISKOptimizer" by Professor Wayne Winston of Indiana University.  Very reasonably, he models the machine useful life by a Weibull distribution, and assumes replacing it just before a failure is significantly less disruptive and expensive than recovering from such a failure.

Above discussion is very interesting, As my opinion in practical the basic reliability technique like Weibul analysis may be enough for understanding of our machine behavior to predict useful life time , at least 95% CL and the key is how to collect the quality data that represent true its normal operation and set up to machine  databased.

Thank you very much Professor Edward Williams, your ideas will be very helpful to me.

Thank you very much Professor Santad Khandipanichakul. Your ideas are very valuable for my work.

Hello Anton Georgiev!

I am available.

I'll be happy if you can help.

Best regards

Isis C. Lima

Hi Prof Georgiev, interesting problem. Is the system under consideration a multi-component one? If so, based on the constraints mentioned, simulation is the best way to go. We've solved a similar problem in the recent past, where the goal was to find the best maintenance strategy for a complex power system in the presence of limited maintenance teams and operational uncertainties. Though your case is a little different, the idea developed in that work should be applicable to a significant extent. You could inbox me if you would like to know more about the work. Thanks

Dear Isis Lima, Thanks so much for showing from you kindness and civility. My PhD student Julia was interested in your proposal and will try to take advantage of your advice. If she has any problems she will turn to you to benefit from the huge your knowledge in this field / your articles are impressive with professionalism and originality of ideas /

With great respect to you

Anton Georgiev

Hello mister Hindolo George-Williams,

Thanks a lot for the proposed favor. If this is no object, I would be very grateful to read your article about the maintenance strategy. We also have some ideas in our articles. It is possible to work together on issues of operational reliability and publish general ideas in one or more articles.

With the greatest respect

Anton Georgiev

Some of the ideas that I explore are:

third chapter of the abstract https://www.researchgate.net/publication/314620549_Abstract_of_a_dissertation_for_vouchsafe_with_scientific_degree_Doctor_of_Science_DEVELOPMENT_RESEARCH_AND_ANALYSIS_OF_NEW_OPPORTUNITIES_FOR_INCREASING_OPERATION_RELIABILITY_ELECTRONIC_SYSTEMS_RAZRABO .

https://www.researchgate.net/publication/291353863_Osiguravane_ss_zapasni_elementi_na_slozni_elektronni_sistemi_pri_nadezdnostno_orientiranio_tehnicesko_obsluzvane

BLOCKS MAINTENANCE STRATEGY WITH REPAIRS, WHOSE AMOUNT DEPENDS ON THE TIME OF ONSET OF FAILURE pp. 53-61.

Strictly Periodic Maintenance Strategy for Electronic Systems https://www.researchgate.net/publication/266794050_Strictly_Periodic_Maintenance_Strategy_for_Electronic_Systems

https://www.researchgate.net/publication/291346673_Blokova_strategia_s_minimalni_avarijni_i_plni_profilakticni_vzstanovavania_pri_tehniceskoto_obsluzvane_na_elektronni_sistemi BLOCK STRATEGY FOR MAINTENANCE WITH MINIMAL EMERGENCY REPAIRS AND FULL PREVENTIVE REFUNDS OF ELECTRONIC SYSTEMS

BLOCK STRATEGY WITH AREAS OF INACTIVITY FOR MAINTENANCE OF ELECTRONIC SYSTEMS https://www.researchgate.net/publication/291346571_Blokova_strategia_ss_zoni_na_bezdejstvie_pri_tehniceskoto_obsluzvane_na_elektronni_sistemi

They are in Bulgarian language, because they are published in Bulgarian journals. but the timing diagram may be are eloquent.

In this regard, I look for ways to optimize the timing for maintenance. My idea is to link the term prevention to the level of reliability of any specific electronic equipment. As this period for prophylactics is not fixed in size and adapt to the specific situation.

Thesis Abstract of a dissertation for vouchsafe with scientific deg...

Article Осигуряване със запасни елементи на сложни електронни систем...

Article Strictly Periodic Maintenance Strategy for Electronic Systems

Article Блокова стратегия с минимални аварийни и пълни профилактични...

Article Блокова стратегия със зони на бездействие при техническото о...

Dear Prof. Georgiev,

I´d like to show you some of my research that has been done in the field of optimization of preventive maintenance intervals using the theory of the semi-Markov processes and the Monte Carlo simulation method.

We used the optimality criterion based on two reliability indicators, achieved availability and inherent availability. Some description you can find in these papers:

https://www.researchgate.net/publication/301574253_Simulation_Approach_for_Optimal_Maintenance_Intervals_Estimation_of_Electronic_Devices

https://www.researchgate.net/publication/319028488_Computer-aided_analysis_of_reliability_and_preventive_maintenance_optimization_of_radio_communication_equipment_based_on_multivariate_Monte_Carlo_simulation

The source code of the model implemented in C++ that can be easily integrated into Matlab programs can be found here:

https://www.researchgate.net/publication/314232345_MEX_function_for_multivariate_analysis_of_reliability_indices_depending_on_maintenance_periodicity_of_radio_communication_equipment

Also, we continue the research directed to the prediction of the optimal maintenance strategy with varied maintenance periodicity during the operation.

Kind regards,

Alexander