Run sum control chart for monitoring the ratio of population means of a bivariate normal distribution

Sani Salihu Abubakar, Michael B. C. Khoo, Sajal Saha, Wei Lin Teoh

Research output: Contribution to journalArticle

Abstract

This article proposes a two-sided run sum ratio chart for monitoring the ratio of two normal variables. A Markov chain procedure is applied to evaluate the statistical performance of the chart by using both average run length (ARL) and expected average run length (EARL) criteria. A numerical comparison with the Shewhart ratio and synthetic ratio charts for the zero state analysis reveals that the run sum ratio chart has a better sensitivity in most cases. In particular, for the values of the coefficients of variation (Formula presented.) ∈ {(0.2, 0.2), (0.2, 0.01)}, the run sum ratio chart outperforms the two charts in contest for almost all shift sizes in the ratio of the two variables. In terms of the steady state analysis, the results indicate that the run sum ratio chart outperforms the synthetic ratio chart almost uniformly. The run sum ratio chart also surpasses the exponentially weighted moving average (EWMA) ratio chart in detecting all decreasing shifts when (Formula presented.) = (0.2, 0.2), while the former outperforms the latter for (Formula presented.) = (0.01, 0.2), when the sample size is small. An illustrative example of a real quality issue in a food industry is presented to demonstrate the implementation of the proposed chart.

Original languageEnglish
JournalCommunications in Statistics - Theory and Methods
Early online date14 Sep 2020
DOIs
Publication statusE-pub ahead of print - 14 Sep 2020

Keywords

  • coefficient of variation
  • deterministic shift
  • Ratio distribution
  • run sum chart
  • uniformly distributed shift

ASJC Scopus subject areas

  • Statistics and Probability

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