EXACT RUN LENGTH DISTRIBUTION OF THE DOUBLE SAMPLING X-BAR CHART WITH ESTIMATED PROCESS PARAMETERS

Authors

  • Wei Lin Teoh
  • M. S. Fun
  • Sin Yin Teh
  • Michael B C Khoo
  • W. C. Yeong

DOI:

https://doi.org/10.7166/27-1-978

Keywords:

run length, double sampling, estimated parameters

Abstract

Since the run length distribution is generally highly skewed, a significant concern about focusing too much on the average run length (ARL) criterion is that we may miss some crucial information about a control chart’s performance. Thus it is important to investigate the entire run length distribution of a control chart for an in-depth understanding before implementing the chart in process monitoring. In this paper, the percentiles of the run length distribution for the double sampling (DS) X chart with estimated process parameters are computed. Knowledge of the percentiles of the run length distribution provides a more comprehensive understanding of the expected behaviour of the run length. This additional information includes the early false alarm, the skewness of the run length distribution, and the median run length (MRL). A comparison of the run length distribution between the optimal ARL-based and MRL-based DS X chart with estimated process parameters is presented in this paper. Examples of applications are given to aid practitioners to select the best design scheme of the DS X chart with estimated process parameters, based on their specific purpose. 

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Author Biography

Sin Yin Teh

School of Management, Senior Lecturer

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Published

2016-05-10

How to Cite

Teoh, W. L., Fun, M. S., Teh, S. Y., Khoo, M. B. C., & Yeong, W. C. (2016). EXACT RUN LENGTH DISTRIBUTION OF THE DOUBLE SAMPLING X-BAR CHART WITH ESTIMATED PROCESS PARAMETERS. The South African Journal of Industrial Engineering, 27(1), 20–31. https://doi.org/10.7166/27-1-978

Issue

Vol. 27 No. 1 (2016)

Section

General Articles

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