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Approach
The LIFEWISE technique for the optimisation of plant management is intended to maximise the value of an operator's maintenance or inspection budget. The probabilistic cost risk optimisation (CRO) approach requires multi-disciplinary skills in decision theory, probabilistic degradation modelling, and engineering financial analysis. The method is centred on financial appraisal using net present value (NPV) analysis. This fully quantitative technique is applicable to components for which failure databases exist, or for failure mechanisms for which the damage can be easily modelled. Fully quantitative cost-risk optimisation (CRO) using LIFEWISE is the logical extension of semi-quantitative Risk Based Inspection (RBI) using RISKWISE™. Quantitative risk-based methods use more rigorous analysis routines to set priorities for equipment inspection and maintenance.  Fig.1. Applicability of qualitative and quantitative assessment methods
Formulating the probabilistic decision model
The input information required for probabilistic CRO includes a probabilistic life model and uncertainty distributions in the model input parameters. The associated uncertainty distributions are subjected to a probabilistic analysis to yield the failure probability as a function of forward time. A NPV cost analysis is also performed using input on the cost of a planned control, repair or replacement, as well as the consequence cost of a failure (including business interruption, remediation, property loss and litigation or liability costs). An expected failure consequence is derived by combining the probability of failure and the consequential failure cost. The decision model is therefore formulated by considering the net value of the maintenance action with the consequential failure cost. In the event the maintenance action is delayed, the expected consequence of failure in the year in which the action is performed is derived in the same way. Similarly, after the action is performed, the revised probability of failure is used to derive the expected consequence of failure after the action.  Fig.2. Repeated sampling of input values from the probability distributions generates the cumulative probability of failure over time for the modelled damage mechanism
Expressing failure consequence as an expected value
The LIFEWISE method applied to fossil fuel-fired power plant by ASME, derives a consequence of failure by combining probability of failure and the consequential failure cost. The effect of the failure on the financial health of the organization is evaluated using an expected value approach. The expected value (EV) of an alternative (Dn), of a number (N) of possible alternatives, each with a probability of occurrence of the event associated with the decision (Pj) and a corresponding value (Vj), is defined as follows: 
The expected value of a decision alternative is the sum of the weighted values arising from the decision alternative. The decision model considers the net present value, as described in Appendix A, of the maintenance action and the consequential failure cost. The measure of value (Vj) used is that of NPV because it uniquely describes the affects the time value of money, tax credits arising from depreciation and all other positive and negative cash flows. The application of the expected value approach to the financial value of the consequence of failure is the key to the formulation of the decision model which combines the failure probability and the financial analysis. The product of the failure probability over time, and the consequence cost gives rise to the evolution of risk as a monetary value, as a function of time. The optimum repair or replacement time is based on the time at which the risk equals the planned cost of repair or replacement. In the event the maintenance action is delayed, the expected consequence of failure in the years to the year in which the action is performed, can be derived in the same way. Similarly, after the action the revised probability of failure is used to derive the expected failure consequence after the action.  Fig.3. The decision model is based on the product of the failure probability and the consequential costs of failure, resulting in an expression for the cost of failure versus time
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