<p>Existing research on standby repairable systems with partial failure universally assumes that components in partial failure states are repairable. However, in industries with high continuous production demands, repairing these components during system operation would generate substantial amounts of semi-finished products or interrupt production lines, resulting in significant economic losses. Therefore, this paper incorporates the concept of irreparability of components in partial failure states into a standby (cold and warm standby) repairable system with partial failure and priority, which can be used to simulate Programmable Logic Controller (<i>PLC</i>) systems in the field of automation. The system comprises one main component and one standby component. The main component has usage and repair priority, and operates in three states: normal, partial failure, and complete failure, with distinct repair strategies corresponding to different failure states. Based on this, assuming each component’s working time follows an exponential distribution and its repair time follows a general distribution, we employ the methods of supplementary variable and Laplace transform to derive the explicit Laplace transform expressions for the key transient/steady-state reliability indices of the system, including transient/steady-state availability, failure frequency, mean time to first failure, and renewal frequency, etc. Furthermore, an expected profit function for the system is constructed based on the reliability analysis results. Finally, sensitivity analysis is performed on the steady-state reliability indices, providing theoretical support for system optimization design in engineering practice.</p>