Journal of Korean Society for Quality Management (품질경영학회지)

Korean Society for Quality Management (한국품질경영학회)
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Economic Design of Three-Stage $\bar{X}$ Control Chart Based on both Performance and Surrogate Variables

성능변수와 대용변수를 이용한 3단계 $\bar{X}$ 관리도의 경제적 설계

  • Kwak, Shin-Seok (Policy Planning Division, Daejeon City Hall) ;
  • Lee, Jooho (Department of Information & Statistics, Chungnam National University)
  • 곽신석 (대전광역시 기획조정실) ;
  • 이주호 (충남대학교 정보통계학과)
  • Received : 2016.07.29
  • Accepted : 2016.10.04
  • Published : 2016.12.31
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Abstract

Purpose: Two-stage ${\bar{X}}$ chart is a useful tool for process control when a surrogate variable may be used together with a performance variable. This paper extends the two-stage ${\bar{X}}$ chart to a three stage version by decomposing the first stage into the preliminary stage and the main stage. Methods: The expected cost function is derived using Markov-chain approach. The optimal designs are found for numerical examples using a genetic algorithm combined with a pattern search algorithm and compared to those of the two-stage ${\bar{X}}$ chart. Sensitivity analysis is performed to see the parameter effects. Results: The proposed design outperforms the optimal design of the two-stage ${\bar{X}}$ chart in terms of the expected cost per unit time unless the correlation between the performance and surrogate variables is modest and the shift in process mean is smallish. Conclusion: Three-stage ${\bar{X}}$ chart may be a useful alternative to the two-stage ${\bar{X}}$ chart especially when the correlation between the performance and surrogate variables is relatively high and the shift in process mean is on the small side.

Keywords

Acknowledgement

Supported by : 충남대학교

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