We use a probabilistic model to show that the development of a large number of small production units facing independent risks of failure must be accompanied by an approximately proportional increase in the number of repairmen. We derive the cost function of a machine in working condition, which increases with the cost of an installed machine and with the repair cost and failure probability, and decreases with repairman efficiency. We provide a very simple proof and generalize the results of Arrow et al. (1972). We also show that it is redundant to require installers to hire the number of repairmen necessary to reach a fixed availability level for each installed machine.
- C61: Optimization Techniques • Programming Models • Dynamic Analysis
- D24: Production • Cost • Capital • Capital, Total Factor, and Multifactor Productivity • Capacity
- J3: Wages, Compensation, and Labor Costs
- O33: Technological Change: Choices and Consequences • Diffusion Processes