Stochastic Analysis of a Priority Standby System under Preventive Maintenance

• Main Authors: Khalaf S. Sultan, Mohamed E. Moshref
• Format: Article
• Language: English
• Published: MDPI AG 2021-04-01
• Series: Applied Sciences
• Subjects: standby unit; regenerative point technique; reliability measures; mean time to system failure; steady-state availability; cost analysis
• Online Access: https://www.mdpi.com/2076-3417/11/9/3861

In this paper, we propose a system of two dissimilar units: one unit prioritizes operation (priority unit), and the other unit is kept as a cold standby (ordinary unit). In this system, we assume that the failures, repairs, and preventive maintenance (PM) times follow arbitrary distributions for both units, except for the fact that the repair time of the ordinary unit follows an exponential distribution. The priority unit has normal, partial failure or total failure modes, while the ordinary unit has normal or total failure modes. The PM of the system can be started after time <i>t</i> when (i) the priority unit is in the normal or partial failure modes up to time <i>t</i> and (ii) the standby unit is available up to time <i>t</i>. PM can be achieved in two types: the costlier type with probability <i>p</i> and the cheaper type with probability <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>p</mi><mo>)</mo></mrow></semantics></math></inline-formula>. Under these assumptions, we investigate the reliability measures of the system using the regenerative point technique. Finally, we show a numerical example to illustrate the theoretical findings and show the effect of preventive maintenance in the reliability measures of the proposed system.