Synthetic Double Sampling X̄ Chart with Estimated Process Parameters

Abstract

The synthetic double sampling (SDS) X̄ chart comprises the double sampling (DS) X̄ and conforming run length (CRL) sub-charts. The SDS X̄ chart has been studied under the assumption of known process parameters in the literature. Nevertheless, in practice, process parameters are usually unknown and are estimated from an in-control Phase I dataset. This paper investigates the performance of the SDS X̄ chart with estimated process parameters, in terms of the average run length (ARL), average number of observations to signal (ANOS) and standard deviation of the run length (SDRL). The performance of the SDS X̄ chart with estimated process parameters by minimizing the out-of-control ARL and the out-of-control ANOS is compared with the corresponding chart’s performance with known process parameters. In addition, the minimum number of Phase I samples required by the SDS X̄ chart with estimated process parameters so that it has approximately the same in-control ARL and ANOS performances as the chart with known process parameters is studied. The ARL, ANOS and SDRL properties of the SDS X̄ chart with estimated process parameters differ significantly from that of the chart with known process parameters. Therefore, suitable optimal charting parameters are introduced so that the SDS X̄ chart with estimated process parameters has an adequate performance as its known process parameters counterpart without having to use large number of Phase I samples and sample size.

Key Words:

• Average number of observations to signal (ANOS)
• average run length
• parameter estimation
• standard deviation of the run length (SDRL)
• synthetic double sampling (SDS) chart.

Additional information

Notes on contributors

H.W. You

H. W. You is a Ph.D. student in the School of Mathematical Sciences, Universiti Sains Malaysia (USM). She holds a Bachelor of Applied Science degree in Applied Statistics from USM. Her research interest is in Statistical Process Control.

Michael B. C. Khoo

Michael B. C. Khoo is a Professor in the School of Mathematical Sciences, Universiti Sains Malaysia (USM). He received his Ph.D. in Applied Statistics in 2001 from USM. His research interest is in Statistical Process Control. He is a member of the American Society for Quality and serves as a member of the editorial boards of several international journals.

M.H. Lee

M. H. Lee is a Lecturer in the Faculty of Engineering, Computing and Science at Swinburne University of Technology Sarawak Campus, Malaysia. She received her B.Tech. degree from Universiti Sains Malaysia, her M.Sc. degree from Universiti Putra Malaysia and her Ph.D. degree from Universiti Sains Malayisa.

P. Castagliola

Philippe Castagliola graduated with a Ph.D. from the UTC (Universite de Technologie de Compiegne, France) in 1991. He is currently a Professor at the Universite de Nantes, Institut Universitaire de Technologie de Nantes, France. He is also a member of the IRCCyN (Institut de Recherche en Communications et Cybernetique de Nantes), UMR CNRS 6597. His research activity includes developments of new SPC techniques (non normal control charts, optimized EWMA type control charts, control charts with estimated parameters, multivariate capability indices, monitoring of batch processes, etc.)