Determining the optimal probing lot size for the wafer probe operation in semiconductor manufacturing

In this study, we reformulated the problem of wafer probe operation in semiconductor manufacturing to consider a probe machine (PM) which has a discrete Weibull shift distribution with a nondecreasing failure rate. To maintain the imperfect PM during the probing of a lot of wafers, a minimal repair policy is introduced with type II inspection error. To increase the productivity of the PM, this paper aims to find an optimal probing lot size that minimizes the expected average processing time per wafer. Conditions and uniqueness for the optimal lot size are explored. The special case of a geometric shift distribution is studied to find a tighter upper bound on the optimal lot size than in previous study. Numerical examples are performed to evaluate the impacts of minimal repair on the optimal lot size. In addition, the adequacy of using a geometric shift distribution is examined when the actual shift distribution has an increasing failure rate.