The　fault　diagnosis　and　inspection　policy　were　discussed　for　a　system　which　has　two　operating　states　(normal,　abnormal)　and　a　failure　state.　The　system　is　inspected　periodically.　The　purpose　of　inspection　is　to　identify　the　state　of　system　and　adopt　appropriate　repair　strategy　by　measuring　the　value　of　diagnosis　parameter.　Because　the　system　is　deteriorated　gradually　and　a　replacement　is　expensive,　several　imperfect　repairs　are　allowed　until　a　replacement　is　needed.　The　objective　of　this　paper　is　to　determine　the　optimal　critical　value　of　diagnosis　parameter　and　the　optimal　inspection　cycle　such　that　the　expected　profit　per　unit　in　steady　states　is　maximized.　Reliability　indexes　of　the　system　are　also　derived.　Probability　analysis　and　vector　Markov　process　are　used　in　this　paper.　Researches　on　the　numerical　example　show　the　feasibility　of　the　policy.