Economic Models of an x^^- Chart with a Tardiness Penalty in Finite Due Time Processes

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  • 短納期の工程における納期遅れペナルティを考慮したx^^-管理図の経済性モデルに関する研究
  • タンノウキ ノ コウテイ ニ オケル ノウキ オクレ ペナルティ オ コウリョ シタ x カンリズ ノ ケイザイセイ モデル ニ カンスル ケンキュウ

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The concept of the PDCA cycle was originally developed by Walter Shewhart during the 1930s and taken up and promoted very effectively from the 1950s by W. Edwards Deming. Consequently, it has become a key role in the quality control field. Recently, more attention is being given to the PACA and CAPD processes of quality management for raising efficiency in industries (Matsui (2005), Shiba and Walden (2001), Ikezawa (1985), etc.). When an x^^- control chart is used in a production process, two cases may take place. One case starts from deciding control lines and maintains the process using them; the other case starts from searching the assignable cause in the out-of-control state. In this paper, at first, both the PDCA and CAPD models of an x^^- control chart with a tardiness penalty are presented based on these two cases, and their mathematical formulations are explained in detail. Then, both models based on the 3σ rule and ARL (Average Run Length) rule are studied. Moreover, from an economic viewpoint, the problems of setting the optimal time parameters are numerically analyzed to minimize the total expectation cost Ct. Finally, by comparing both models, it is proven that Ct of the PDCA model is cheaper than Ct of the CAPD model when the due time is short, and Ct of the CAPD model is cheaper than Ct of the PDCA model when the due time is long in finite due time processes.

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