This　paper　investigates　a　warm　standby　repairable　retrial　system　with　two　types　of　components　and　a　single　repairman,　where　type　1　components　have　priority　over　type　2　in　use.　Failure　and　repair　times　for　each　type　of　component　are　assumed　to　be　exponential　distributions.　The　retrial　feature　is　considered　and　the　retrial　time　of　each　failed　component　is　exponentially　distributed.　By　using　Markov　process　theory　and　matrix-analytic　method,　the　system　steady-state　probabilities　are　derived,　and　the　system　steady-state　availability　and　some　steady-state　performance　indices　are　obtained.　Using　the　Bayesian　approach,　the　system　parameters　can　be　estimated.　The　cost-benefit　ratio　function　of　the　system　is　constructed　based　on　the　failed　components　and　repairman＇s　states.　Numerical　experiments　are　given　to　evaluate　the　effect　of　each　parameter　on　the　system　steady-state　availability　and　optimize　the　system　cost-benefit　ratio　with　repair　rate　as　a　decision　variable.　©　2022　The　Author(s).　Published　by　Informa　UK　Limited,　trading　as　Taylor　&　Francis　Group.