Journal Published Online: 11 June 2019
Volume 49, Issue 2

The Variable Sampling Interval EWMA Chart with Estimated Process Parameters

CODEN: JTEVAB

Abstract

The exponentially weighted moving average (EWMA) X¯ chart with the variable-sampling-interval (VSI) feature is usually scrutinized under the assumption of known process parameters. However, in practice, process parameters are usually unknown, and they need to be estimated from the in-control Phase-I data set. With this in mind, this article proposes the VSI EWMA X¯ chart in which the process parameters are estimated. A Markov Chain approach is adopted to derive the run-length properties of the VSI EWMA X¯ chart with estimated process parameters. The standard deviation of the average time to signal (SDATS) is employed to measure the practitioner-to-practitioner variation in the control chart’s performance. This variation occurs because different Phase-I datasets are used among practitioners to estimate the process parameters. Based on the SDATS criterion, this article provides recommendations regarding the minimum number of required Phase-I samples. For an optimum implementation, this article develops two optimization algorithms for the VSI EWMA X¯ chart with estimated process parameters, i.e., by minimizing the (i) out-of-control expected value of the average time to signal (AATS) and (ii) out-of-control expected value of the AATS (EAATS) for the cases of deterministic and unknown shift sizes, respectively. With the implementation of these new design procedures, the VSI EWMA X¯ chart with estimated process parameters is not only able to achieve a desirable in-control performance, but it is also able to quickly detect changes in the process.

Author Information

Teoh, Wei Lin
School of Mathematical and Computer Sciences, Heriot-Watt University Malaysia, Putrajaya, Malaysia
Ong, L. V.
Department of Physical and Mathematical Science, Faculty of Science, Universiti Tunku Abdul Rahman, Kampar, Perak, Malaysia
Khoo, Michael B. C.
School of Mathematical Sciences, Universiti Sains Malaysia, Gelugor, Penang, Malaysia
Castagliola, Philippe
Université de Nantes & LS2N UMR 6004, Laboratoire des Sciences du Numérique de Nantes, Carquefou, France
Chong, Z. L.
Department of Physical and Mathematical Science, Faculty of Science, Universiti Tunku Abdul Rahman, Kampar, Perak, Malaysia
Pages: 29
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Stock #: JTE20180058
ISSN: 0090-3973
DOI: 10.1520/JTE20180058