Hazard-rate tolerance method for an opportunistic-replacement policy

A model for a system with several types of units is presented. A unit is replaced at failure or when its hazard (failure) rate exceeds limit L, whichever occurs first. When a unit is replaced because its hazard rates reaches L, all the operating units with their hazard rate falling in the interval (L-u, L) are replaced. This policy allows joint replacements and avoids the disadvantages resulting from the replacement of new units, down time, and unrealistic assumptions for distributions of unit life. The long-run cost rate is derived. Optimal L and u are obtained to minimize the average total replacement cost rate. Application and analysis of results are demonstrated through a numerical example