### Abstract

Selective assembly is an effective approach for improving the quality of a product assembled from two components when the quality characteristic is the clearance between the mating components. A component is rejected if its dimension is outside specified limits of the dimensional distribution. Acceptable components are sorted into several classes by their dimensions, and the product is assembled from randomly selected mating components from the corresponding classes. We assume that the two component dimensions are normally distributed with equal variance, and that measurement error, if any, is also normally distributed. Taking into account the quality loss of a sold product, the selling price of an assembled product, the component manufacturing cost, and the income from a rejected component, we discuss the optimal partitioning of the dimensional distribution to maximize expected profit, including the optimal choice of the distribution limits or truncation points. Equations for a set of optimal partition limits are given and its uniqueness is established in the presence and absence of measurement error. It is shown that the expected profit based on the optimal partition decreases with increasing variance of the measurement error. In addition, some numerical results are presented to compare the optimal partitions for the cases when the truncation points are and are not fixed.

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

Title of host publication | Frontiers in Statistical Quality Control 9 |

Publisher | Physica-Verlag |

Pages | 173-190 |

Number of pages | 18 |

ISBN (Print) | 9783790823790 |

DOIs | |

Publication status | Published - 2010 |

Event | 9th International Workshop on Intelligent Statistical Quality Control - Beijing, China Duration: 2007 Sep 1 → 2007 Sep 1 |

### Other

Other | 9th International Workshop on Intelligent Statistical Quality Control |
---|---|

Country | China |

City | Beijing |

Period | 07/9/1 → 07/9/1 |

### Fingerprint

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Frontiers in Statistical Quality Control 9*(pp. 173-190). Physica-Verlag. https://doi.org/10.1007/978-3-7908-2380-6_12

**Selective assembly for maximizing profit in the presence and absence of measurement error.** / Matsuura, Shun; Shinozaki, Nobuo.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Frontiers in Statistical Quality Control 9.*Physica-Verlag, pp. 173-190, 9th International Workshop on Intelligent Statistical Quality Control, Beijing, China, 07/9/1. https://doi.org/10.1007/978-3-7908-2380-6_12

}

TY - GEN

T1 - Selective assembly for maximizing profit in the presence and absence of measurement error

AU - Matsuura, Shun

AU - Shinozaki, Nobuo

PY - 2010

Y1 - 2010

N2 - Selective assembly is an effective approach for improving the quality of a product assembled from two components when the quality characteristic is the clearance between the mating components. A component is rejected if its dimension is outside specified limits of the dimensional distribution. Acceptable components are sorted into several classes by their dimensions, and the product is assembled from randomly selected mating components from the corresponding classes. We assume that the two component dimensions are normally distributed with equal variance, and that measurement error, if any, is also normally distributed. Taking into account the quality loss of a sold product, the selling price of an assembled product, the component manufacturing cost, and the income from a rejected component, we discuss the optimal partitioning of the dimensional distribution to maximize expected profit, including the optimal choice of the distribution limits or truncation points. Equations for a set of optimal partition limits are given and its uniqueness is established in the presence and absence of measurement error. It is shown that the expected profit based on the optimal partition decreases with increasing variance of the measurement error. In addition, some numerical results are presented to compare the optimal partitions for the cases when the truncation points are and are not fixed.

AB - Selective assembly is an effective approach for improving the quality of a product assembled from two components when the quality characteristic is the clearance between the mating components. A component is rejected if its dimension is outside specified limits of the dimensional distribution. Acceptable components are sorted into several classes by their dimensions, and the product is assembled from randomly selected mating components from the corresponding classes. We assume that the two component dimensions are normally distributed with equal variance, and that measurement error, if any, is also normally distributed. Taking into account the quality loss of a sold product, the selling price of an assembled product, the component manufacturing cost, and the income from a rejected component, we discuss the optimal partitioning of the dimensional distribution to maximize expected profit, including the optimal choice of the distribution limits or truncation points. Equations for a set of optimal partition limits are given and its uniqueness is established in the presence and absence of measurement error. It is shown that the expected profit based on the optimal partition decreases with increasing variance of the measurement error. In addition, some numerical results are presented to compare the optimal partitions for the cases when the truncation points are and are not fixed.

UR - http://www.scopus.com/inward/record.url?scp=78649889691&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78649889691&partnerID=8YFLogxK

U2 - 10.1007/978-3-7908-2380-6_12

DO - 10.1007/978-3-7908-2380-6_12

M3 - Conference contribution

AN - SCOPUS:78649889691

SN - 9783790823790

SP - 173

EP - 190

BT - Frontiers in Statistical Quality Control 9

PB - Physica-Verlag

ER -