Steady State Availability and Estimation of the Time to reach the Steady State for the Preamplifier System in a Sonar

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This paper presents some results from an analytical study of reliability and availability of a preamplifier system designed for graceful degradation in the event of failure of some non-critical components and sub-assemblies in sonar. The preamplifier is one of the important subsystems in the sonar. It provides the interface between the transducers and other modules of the sonar. The low level signals from the sonar transducers are amplified by the preamplifier for further processing and classification of targets. The preamplifier consists of four identical PCB (printed circuit board) cards. Each card consists of a number of components. The failure of a non-critical component in a card will only degrade the output of the card but will not cause the card to be non-functional. Similarly the failure of a single card will not result in the total failure of the system. The total failure occurs only when all the four cards fail. Thus the system works with certain acceptable degraded performance when certain non-critical components fail in a card and less than four cards fail in the system.The availability of the system with graceful degradation (with acceptable degraded performance) has been modeled as a Markov process using Chapman-Kolmogorov equations. The steady state availability of the preamplifier is estimated considering all possible system states for the preamplifier.Most of the studies discuss the steady state availability[1], but the time over which the steady state is reached is not addressed. This aspect, which is of practical significance, is also discussed in the paper.