BAYESIAN ESTIMATE OF TELECOMMUNICATION SYSTEMS PREPAREDNESS

Abstract

The paper assumes a Bayesian estimate of the telecommunication systems availability ratio. Downtime and uptime are described by gamma distributions with positive integer parameters. Estimates of the distribution parameters are obtained using the maximum likelihood method. For the set samples, the values of the desired probability distribution densities are found and an expression for estimating the availability ratio is derived. Numerical estimates for the standard and assumed estimates are given. For a system with two states, a Bayesian estimate of the availability function with consideration of downtime and serviceable condition takes into account the features of backup equipment and the effect of its failure defined by performance reliability and features that ensure the reliability of information signals. The proposed Bayesian approach has the following advantages: it is possible to conduct quantitative estimates with lack of sufficient statistics on functional use indicators; it takes into account all destabilizing factors of various nature; the presence of a lower mean square error compared to traditional methods. To implement the proposed approach that estimates the availability ratio, confidence probabilities are introduced relative to the indicator of failure flows and equipment recovery. The parameters of the a priori information can be determined by different methods or on the basis of sufficient statistical data. To illustrate the discussed calculation algorithm, a digital data transmission system of a standard satellite navigation system consisting of terminal, radio equipment, and a transponder is considered. To estimate the required values, we used data on interruptions in the operation of equipment due to its malfunction during a conditional year. The frequency of downtime caused by signal propagation conditions and equipment failures was evaluated. It was shown that the gamma distribution is suitable for describing the frequency distribution of downtime. The frequency distribution of the cyclicity coefficient with the condition of the selected time interval was also taken into account. Sample mathematical expectations and mean square deviations of the downtime coefficient were found. As a result, the numerical example shows the correctness of using the Bayesian estimate of weighted equipment preparedness.

Keywords

• the availability ratio
• gamma distribution
• uptime and downtime cycles
• estimation of the parameters