What was found
DURING CRUISE AT FL360, & NOTICED A SLOW CABIN PRESSURIZATION LOSS. CABIN ALTITUDE NEVER CLIMBED MORE THAN 500 FEET PER MINUTE. PILOTS DONNED OXYGEN MASKS, STARTED DESCENDING & DECLARED AN EMERGENCY. COMPLETED EMERGENCY CHECKLIST. AS ACFT WAS COMING TO A REASONABLE ALTITUDE, PAX OXYGEN MASKS DEPLOYED. ELECTED TO DIVERT. LANDED SAFELY. THE OUTFLOW VALVE WAS REPLACED & TEST FLIGHT CONDUCTED, OPERATIONS CHECKED OK.