2. Calculation Details

A commercial software (apmOptimizer) was used for the optimization. The software employs a combination of analytic methods (Birolini 1999) for calculating the fleet Life-Cycle Cost (LCC), and identifying cost and failure drivers. The analytic methods include:

•  Markov chains for modeling spare parts supply, demand, and spare waiting times.

•  Block mean failure rate calculations that account for component failure distributions, reliability models, scheduled maintenance, inspections, and the mission profile.

While analytic calculation is not as flexible as Monte-Carlo simulations, the analytic method is much faster. The speed of evaluating each model allowed for fast optimization of the maintenance and logistic policies using modified Dynamic Programming.

Dynamic Programming algorithms (Cormen, Leiserson, Rivest & Stein 2009) are ideal for bottom-up optimization of trees where the tree branches are independent.

However, in the fleet case, the branches are not completely independent: A central stock services the three sites, therefore a failure in one site affects spare part availability in the other sites. A modified dynamic programming algorithm was used to account for the inter-site dependencies. For example: The Markov chain model that describes the GPS voter spare parts supply and demand accounts for all 11 operating units, serviced by a single central stock.

The optimization goal is to achieve high reliability and availability while minimizing the LCC. Optimization was achieved by using the following optimization modules:

• Optimal LOR: Level Of Repair Analysis – Optimization i.e. Repair/Discard policy. Repair is usually cheaper than buying a new component, however, long repair time (compared to procurement time) may require large and expensive safety stock. Therefore, the discard strategy is sometimes advantageous even when a repair is cheaper than buying a new component.

• Optimal PM: Preventive Maintenance Optimization. Periodic maintenance is required for components that exhibit an aging behavior (failure rate increases with time) and cannot be inspected for degradation. In our case scheduled maintenance is relevant to the mechanical gyros.

• Optimal PdM: Predictive Maintenance Optimization – inspections schedule. Periodic inspections are used to identify flap degradation. Beyond a degradation threshold, preventive maintenance is used to rejuvenate the flaps.

• Optimal I: Inventory Optimization. Optimal I find the optimal combination of spare parts that minimizes the fleet LCC. The optimal spare part combination is as cheap as possible while ensuring a low probability of downtime due to stock out.

To emulate the case of under-maintained fleets, an initial maintenance policy was defined with few spare parts, inspections, and scheduled maintenance events. In each optimization step some maintenance actions / spare parts were changed to find the optimal combination.

3. Results

Fleet availability at each site as well as the fleet LCC were calculated at each step of the optimization process. Table 1 presents a summary of fleet availabilities at the various sites and the total LCC at each optimization step:

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