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Planning the configuration and maintenance of equipment’s groups of similar types taking into account the reliability and cost characteristics


A.A. Sukhobokov – Ph. D. (Eng.), Associate Professor, Department «Information Processing and Control Systems», Bauman Moscow State Technical University; Head of Department of Upstream Oil&Gas, SAP DBS CIS (Moscow)
R.Z. Galimov – Undergraduate, Department «Information Processing and Control Systems», Bauman Moscow State Technical University
A.A. Zolotov – Undergraduate, Department «Information Processing and Control Systems», Bauman Moscow State Technical University

The problem of cost optimizing for equipment’s maintenance and repair may be formulated as problem of searching the minimum sum the necessary budget for maintenance and repair of equipment which provides the required value of availability factor of equipment Kg. Kg is the probability that the object will be operational at an arbitrary point in time, except for specified periods during which the using of the object is not assumed for its intended purpose. When problem is solving for a group of similar devices or a limited number of near device’s types, it is reduced to searching the size of the budget under which a given number of devices from their common pool will operational. The problem of designing the equipment’s group with near device’s types is to determine the specification of device's types included in the group, under which the maximum value of Kg is achieved within the specified budget of project.
In Markovian models, fault-tolerance is described by the birth-death processes. The solution of both problems based on the apparatus of Markov models becomes more complicated when the number of device types rises because the dimensionality of the state space increases. In order to overcome the emerging difficulties, the method of quasi-equivalent aggregation of Markov models’ states is used. This method allows to evaluate the current parameters with a certain error.
The initial data for solving both problems is a set of functions describing the cost of maintenance of one device of each type depending on the failure and recovery rates. Functions must be specified for all types of devices. Depending on the presence or absence of experience in operating devices under real conditions, these rates can be calculated on the basis of actual data or from the operating manual. Since the method of enumeration of all values will be extremely resource-intensive due to the number of variants, the stochastic gradient descent method is used to search for optimal values.
In the examples presented in the paper, both problems are solved for a cluster of servers that process big data. Each server is represented as a device consisting of four components (Hard disk, Motherboard, RAM, CPU), which can be of several types. Failure statistics are collected based on the results of real work. The total cost of server maintenance consists of the cost of maintenance all four components. Two types of recovery services were investigated, requiring 1 and 3 hours. Each service is produced by one or more re-sources without mutual assistance.

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