Exhaust gases from paper plants usually contain fine particles that are removed by electrostatic precipitators. A typical precipitator contains thin wires that are charged to several thousands of volts. When the gases pass through the wires, the fine particles are attracted to the wires and to the dust-collector plates. The wires are vibrated periodically to remove the particles, which are then concentrated in receptacles, collected, and disposed of. Since the wires are subject to thermal stresses, they may experience breaks that reduce its effectiveness in removing the particles. Therefore, a periodic inspection policy is implemented. Under this policy, the wires are inspected at times x1, x2, x3, x4, … until a broken wire is detected. Repairs are immediately performed when breaks are found.
The cost per inspection is $150; the cost of undetected failure is $12; and the cost of repair is $225. The repair time is 12 hours. The p.d.f. of the wire breaks follow
where k = 0.000 04. Determine the first five inspection intervals that minimize the total cost.
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