Question: An expensive piece of equipment is used in the masking operation for semiconductor manufacture. A capacitor in the equipment fails randomly. The capacitor costs $7.50, but if it burns out while the machine is in use, the production process must be halted. Here the replacement cost is estimated to be $150. Based on past experience, the lifetime distribution of the capacitor is estimated to be
How often should the capacitors be replaced in order to minimize the expected monthly cost of planned and unplanned replacement?