Tool replacement for production with a low fraction of defectives

In manufacturing industry, the tool replacement cost is, in many cases, a significant portion of the production cost. Early tool replacement increases the production cost. Overdue tool replacement, however, results in poor production quality. Accordingly, improving production quality while maintaining a low production cost is essential. The index Cpk is regarded as a yield-based index. For a fixed Cpk value, the production yield and fraction of defectives can be calculated. In this paper, we present an analytical approach using Cpk to determine the optimal tool replacement time. An accurate process capability must be calculated, particularly when the data contain assignable cause variation. Tool wear is a dominant and inseparable component in many machining processes (a systematic assignable cause), and ordinary capability measures become inaccurate because process data are contaminated by the assignable cause variation. Considering process capability changes dynamically, an estimator of Cpk is investigated. The closed form of the exact sampling distribution is derived. An effective tool management procedure for determining the optimal tool replacement time is presented for processes with a low fraction of defectives. For illustrative purposes, an application example involving tool wear is presented.