### Abstract

Assume that lot quality characteristics obey a normal distribution. Kanagawa et al. have proposed the (x̄, s) control chart which enable the user to monitor both changes of the mean and variance simultaneously. Further, the results of Watakabe and Arizono enable the user to evaluate the performance for out-of-control state in the case of using the (x̄, s) control chart. On the other hand, Taguchi has presented an approach to quality improvement in which reduction of deviation from the target value is the guiding principle. In this approach, the loss is expressed as a quadratic form with respect to the difference between the measured value x of a product characteristic X and the target value T of a product quality characteristic. Then, we can evaluate the process quality based on the Taguchi's loss criterion. We consider here the economical operation of the (x̄, s) control chart in conformity with the expected total operation cost function based on the sampling cost and the loss due to derivation in the process quality. First, we consider the economical operation of the (x̄, s) control chart in the situation that the loss to be considered is known. Further, the economical operation of the (x̄, s) control chart is also discussed under any loss instead of a known loss. Then, the relationship between the two economical operations proposed here corresponds to the relationship between the lot tolerance per cent defective plans under the fixed fraction defective and the average outgoing quality limit plans under any fraction defective in rectifying inspection plans.

Original language | English |
---|---|

Pages (from-to) | 1115-1132 |

Number of pages | 18 |

Journal | International Journal of Production Research |

Volume | 41 |

Issue number | 6 |

DOIs | |

Publication status | Published - Apr 15 2003 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Industrial and Manufacturing Engineering
- Management Science and Operations Research

### Cite this

*International Journal of Production Research*,

*41*(6), 1115-1132. https://doi.org/10.1080/0020754021000042427

**Economical operation of (x̄, s) control chart indexed by Taguchi's loss function.** / Kobayashi, Jun'ichi; Arizono, Ikuo; Takemoto, Y.

Research output: Contribution to journal › Article

*International Journal of Production Research*, vol. 41, no. 6, pp. 1115-1132. https://doi.org/10.1080/0020754021000042427

}

TY - JOUR

T1 - Economical operation of (x̄, s) control chart indexed by Taguchi's loss function

AU - Kobayashi, Jun'ichi

AU - Arizono, Ikuo

AU - Takemoto, Y.

PY - 2003/4/15

Y1 - 2003/4/15

N2 - Assume that lot quality characteristics obey a normal distribution. Kanagawa et al. have proposed the (x̄, s) control chart which enable the user to monitor both changes of the mean and variance simultaneously. Further, the results of Watakabe and Arizono enable the user to evaluate the performance for out-of-control state in the case of using the (x̄, s) control chart. On the other hand, Taguchi has presented an approach to quality improvement in which reduction of deviation from the target value is the guiding principle. In this approach, the loss is expressed as a quadratic form with respect to the difference between the measured value x of a product characteristic X and the target value T of a product quality characteristic. Then, we can evaluate the process quality based on the Taguchi's loss criterion. We consider here the economical operation of the (x̄, s) control chart in conformity with the expected total operation cost function based on the sampling cost and the loss due to derivation in the process quality. First, we consider the economical operation of the (x̄, s) control chart in the situation that the loss to be considered is known. Further, the economical operation of the (x̄, s) control chart is also discussed under any loss instead of a known loss. Then, the relationship between the two economical operations proposed here corresponds to the relationship between the lot tolerance per cent defective plans under the fixed fraction defective and the average outgoing quality limit plans under any fraction defective in rectifying inspection plans.

AB - Assume that lot quality characteristics obey a normal distribution. Kanagawa et al. have proposed the (x̄, s) control chart which enable the user to monitor both changes of the mean and variance simultaneously. Further, the results of Watakabe and Arizono enable the user to evaluate the performance for out-of-control state in the case of using the (x̄, s) control chart. On the other hand, Taguchi has presented an approach to quality improvement in which reduction of deviation from the target value is the guiding principle. In this approach, the loss is expressed as a quadratic form with respect to the difference between the measured value x of a product characteristic X and the target value T of a product quality characteristic. Then, we can evaluate the process quality based on the Taguchi's loss criterion. We consider here the economical operation of the (x̄, s) control chart in conformity with the expected total operation cost function based on the sampling cost and the loss due to derivation in the process quality. First, we consider the economical operation of the (x̄, s) control chart in the situation that the loss to be considered is known. Further, the economical operation of the (x̄, s) control chart is also discussed under any loss instead of a known loss. Then, the relationship between the two economical operations proposed here corresponds to the relationship between the lot tolerance per cent defective plans under the fixed fraction defective and the average outgoing quality limit plans under any fraction defective in rectifying inspection plans.

UR - http://www.scopus.com/inward/record.url?scp=0242269833&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0242269833&partnerID=8YFLogxK

U2 - 10.1080/0020754021000042427

DO - 10.1080/0020754021000042427

M3 - Article

AN - SCOPUS:0242269833

VL - 41

SP - 1115

EP - 1132

JO - International Journal of Production Research

JF - International Journal of Production Research

SN - 0020-7543

IS - 6

ER -