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59 Provided by Reliasoft To determine the optimum time for such a preventive mainte- nance action (replacement), a mathematical model has been formulated that describes the associated costs and risks. In devel- oping the model, it is assumed that if the unit fails before time t, a corrective action will occur and if it does not fail by time t, a preventive action will occur. In other words, the unit is replaced upon failure or after a time of operation, t, whichever occurs ï¬rst. Thus, the optimum replacement time can be found by minimiz- ing the cost per unit time, CPUT(t). CPUT(t) is given by: Where: R(t) = reliability at time t. CP = cost of planned replacement. CU = cost of unplanned replacement. The optimum replacement time interval, t, is the time that mini- mizes CPUT(t). This can be found by solving for t such that: APPENDIX E Mathematical Model to Determine Optimum Parts Replacement = Total Expected Replacement Cost Expected Cycle Length = + â( ) ( )[ ] ( )â« C R t C R t R s ds P U t ⢠⢠1 0 â â = ( )[ ]CPUT t t 0
