8.1 Standard Inspection Policy

A unit should operate for an infinite time span and is checked at successive times T _?. ( ? = 1, 2, ), where T ₀ = 0 (see Figure 8.1). Any failure is detected at the next checking time and is replaced immediately. A unit has a failure distribution F(t)with finite mean ? whose failure rate h(t)is not unchanged by any check. It is assumed that all times needed for checks and replacement are negligible. Let c ₁ be the cost of one check and c ₂ be the loss cost per unit of time for the time elapsed between a failure and its detection at the next checking time, and c ³ be the replacement cost of a failed unit. Then, the total expected cost until replacement is

Figure 8.1: Process of sequential inspection with checking time T _?

where throughout this chapter, we use the notation

Differentiating the expected cost C ₁( T ₁, T ₂, ) with T _k and putting it equal to zero,

where fis a density function of F. The optimum checking intervals are decreasing when fis PF ₂ (P lya frequency function of order 2), and Algorithm 1 for computing the optimum inspection schedule is given in ^[1].