Optimal designs of the variable parameters X estimated process parameters chart with
Document Type
Article
Publication Date
1-1-2021
Abstract
Among adaptive charts, the variable parameters chart shows the best performance as it varies all charting parameters. The existing variable parameters chart is designed by assuming that process parameters are known. However, process parameters are rarely known but are usually estimated based on Phase-I data. Hence, the variable parameters (X) over bar chart with estimated parameters is proposed. Formulae to evaluate various performance measures are derived through Markov chains. This paper shows that adopting the optimal charting parameters by incorrectly assuming that process parameters are known results in a large deterioration on the actual performance, especially for small shifts, a small number of subgroups, and small sample sizes. Subsequently, this paper proposes algorithms to obtain the optimal charting parameters for estimated parameters that show better performance, especially for small shift sizes, number of subgroups, and sample sizes. Finally, from an illustrative example, the proposed variable parameters (X) over bar chart is able to detect more out-of-control samples.
Keywords
Average time to signal, Estimated parameters, Known parameters, Optimal charting parameters, Subgroups, Variable parameters
Divisions
Faculty_of_Business_and_Accountancy
Funders
RUI (Individual) Grant by Universiti Sains Malaysia (USM) (1001/PKOMP/8011136)
Publication Title
International Journal of Industrial Engineering-Theory Applications and Practice
Volume
28
Issue
3
Publisher
Univ Cincinnati Industrial Engineering
Publisher Location
UNIV CINCINNATI, CINCINNATI, OH 45221-0116 USA