Variable interval sampling in economical designs for online process control of attributes with misclassification errors

Abstract

Online process control consists of inspecting a single item at every mth items produced, where m is an integer greater than two. Based on the results of the inspection, one decides if the process is in-control (the fraction of conforming item is p₁—state I) or out-of-control (the fraction of conforming item is p₂—state II). If the inspected item is non-conforming, the process is designated as out-of-control and production is stopped for possible adjustment; otherwise, production goes on. In this paper, a contribution to online process control is presented, where the inspection system is considered to be subject to classification errors. After every adjustment, the sampling interval is L units (L⩾m), and in the case of non-adjustment, the sampling interval is m units. The expression for the average cost per produced item is calculated, and optimum parameters (the sampling intervals L and m) are obtained by a direct search. The procedure is illustrated by a numerical example.

Keywords:

• quality control
• online process control for attributes
• economical design
• misclassification errors
• Markov chain
• variable inspection interval

Acknowledgements

The authors acknowledge the referees for their valuable comments and suggestions. This research was supported partially by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES).