Malfunctions　of　safety-critical　assets　during　missions　can　lead　to　severe　consequences　and　financial　losses.　In　order　to　manage　mission　risk　and　improve　mission　reliability,　a　mission　management　policy,　namely　mission　abort,　is　usually　adopted　based　on　real-time　degradation　signals.　This　paper　focuses　on　the　abort　management　problem　of　a　safety-critical　asset　that　performs　a　mission　during　a　certain　duration　of　time.　The　system　encounters　continuous　degradation　accumulation　due　to　random　shocks,　and　fails　when　degradation　magnitude　reaches　a　certain　level.　Considering　the　process　heterogeneity,　the　shock　arrival　intensity　and　core　degradation　parameters　are　stochastic　and　need　to　be　accurately　estimated　based　on　real-time　health　observation.　We　develop　the　abort　management　policy　integrating　parameter　learning,　modeled　as　a　Markov　decision　process　to　minimize　the　expected　total　cost.　We　study　the　structural　properties　of　the　value　function　and　cast　the　optimal　mission　abort　policy　into　an　optimal　control　limit　policy.　The　applicability　over　cost　management　and　reliability　support　is　exemplified　via　a　numerical　experiment.　©　Conference　Proceedings　of　the　29th　ISSAT　International　Conference　on　Reliability　and　Quality　in　Design,　RQD　2024.