Algorithm of prompt detection of dependability characteristics variation

The Aim of the paper is to develop an algorithm of prompt detection of the moment of dependability characteristics variation in a system that consists of a set of homogeneous elements, assuming that failures of such elements occur at random moments in time, are a Poisson flow of events and, consequently, the time intervals between them are an exponential probability distribution. In order to solve the problem, it is suggested using one of the classical algorithms of detection of “imbalance” of a discrete random process, i.e. spontaneous change of one of its probabilistic characteristics. As such a characteristic, the exponential distribution parameter θ was chosen, that is uniquely associated with the mean time between failures Тmn: θ = 1/Тmn. It is believed that the imbalance consists in the discontinuous variation of parameter θ from the initial steady state θ = θ0 to the level of minimal (expected, maximum allowable, critical) imbalance, when θ = θ1 > θ0. In this paper, the imbalance is detected using the cumulative sum algorithm (CUSUM) as it has certain optimal properties and is widely used in practice. For this algorithm, the required design ratios, descriptions of its properties and features are provided. The paper proposes a procedure for synthesizing the control algorithm with desired properties, in the course of which, based on the user-selected values of desired mean time between false alarms , initial basic level θ0 and nominal imbalance θ1 > θ0, the value of decision boundary Н is identified, the speed of algorithm action is estimated trough the calculation of the average lag in the detection of nominal imbalance , along with its efficiency for various values of d, that quantitatively characterize the value of imbalance: d=θ1/ θ0. For the purpose of practical implementation of the synthesis procedure, the paper cites reference data, that was obtained by means of simulation and that ensures the development of the control algorithm with required characteristics. It is noted that the presented synthesis procedure can, in principle, also be used for cases of gradual (continuous) change of parameter θ. However, the statistical properties of the control procedure will remain unclear as they require sufficiently intense additional research.

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