The Proton Improvement Plan-II (PIP-II) is a crucial upgrade to the Fermilab accelerator complex, featuring a new 800-MeV Superconducting Radio-Frequency (SRF) linear accelerator (LINAC) with 23 cryomodules operating at 2 K. The LINAC thermohydraulic conditions are satisfied by the cryogenic subsystems: Cryogenic Distribution System (CDS), a helium refrigerator cold box (CB), a warm compression station (WCS) and a helium recovery system (RSYS). The accelerator has a strict requirement of non-thermal cycling of the LINAC cryomodules during planned and unplanned subsystem outages. This paper presents an integrated reliability analysis of the PIPII cryoplant. The study evaluates both normal and abnormal operating modes, with a focus on identifying integrated scenarios that put subsystems components under stress. The conclusions of this study will help build redundancy to mitigate LINAC thermal cycling risks during planned and unplanned subsystem outages.