Constructing optimal router bit life sequential experimental designs: New results with a case study

ABSTRACT

Consider the experiment to improve router bit life as reported in Phadke (1986). The goal of the experiment was to increase the life of the router bit before it gets dull, which causes excessive dust formation and consequent expensive cleaning operation to smooth the edges of the boards. A 32-run experimental design was used including seven two-level factors and two four-level factors (cf. Table 1). In this experiment and others, factorial designs with a mixture of two-level and μ( > 2)-level factors may be adopted. Sequential experiments composed of initial experiments and follow-up experiments are widely used to resolve ambiguities involving the aliasing of factorial effects. This article investigates the construction and theoretical properties of optimal designs for sequential experiments with a mixture of α two-level and β μ-level factors for the first time. Constructing optimal design for the router bit life sequential experiment will be discussed for a practical use. From the numerical results, it is found that using a uniform design as the initial experimental design for the router bit life experiment is highly recommended to get an efficient router bit life sequential experimental design. The novelty and significance of the work are evaluated by comparing our results to the existing literature.

KEYWORDS:

• Follow-up design
• Follow-up map
• Optimal design
• Router bit life experiment
• Sequential design

MATHEMATICS SUBJECT CLASSIFICATION:

• 62K05
• 62K15

Acknowledgments

The author greatly appreciate helpful suggestions of the two referees and the Editor in Chief Prof. N. Balakrishnan that significantly improved the paper. The author also thank Prof. Kai-Tai Fang for his kind support. This work was partially supported by the UIC Grants (Nos. R201409 and R201712) and the Zhuhai Premier Discipline Grant.