Proposal of a Single Critical Value for the Lenth Method

Abstract

Different critical values deduced by simulation have been proposed that greatly improve Lenth’s original proposal. However, these simulations assume that all effects are zero — something not realistic — producing bigger than desired critical values and thus significance levels lower that intended. This article, in accordance with Box [2] well known idea that Experimental Design should be about learning and not about testing and based on studying how the presence of a realistic number and size of active effects affects critical values, proposes to use t = 2 for any number of runs equal or greater than 8. And it shows that this solution, in addition of being simpler, provides under reasonable realistic situations better results than those obtained by simulation.

Key Words:

• Industrial experimentation
• Lenth method
• pseudo standard error
• significant effects
• unreplicated factorial designs.

Additional information

Notes on contributors

Sara Fontdecaba

Sara Fontdecaba has a Degree in Statistics from Universitat Politecnica de Catalunya (UPC) — BarcelonaTech and is a funded Ph.D. student at the Statistics Department of UPC. She is currently doing research in the topics of discrete time series analysis and design of experiments. She currently gives practical lectures at the Barcelona Industrial Engineering School. She has given presentations in different applied statistics seminars and she has collaborated in different consultancy projects.

Pere Grima

Pere Grima is a Professor at the Universitat Politecnica de Catalunya — BarcelonaTech, where he also obtained his Ph.D. One of the areas he specialises in is experimental design and he has more than ten years of experience in helping companies to implement statistical methods for quality control and improvement. He has been an advisor for the European Quality Award and has acted as a consultant to several multinational companies in Six Sigma projects.

Xavier Tort-Martorell

Xavier Tort-Martorell has a Degree in Industrial Engineering, a Ph.D. in the same field and a Master’s Degree in Statistics by the University of Wisconsin. He is currently a Professor at the Department of Statistics at UPC. He is the Director of UPC’s Master’s programme in TQM and the Six Sigma Black Belt training courses. Dr. Tort-Martorell has been a consultant in quality management and techniques to many firms and has taught seminars at many private and public organisations.