### Abstract

We consider the problem of adjusting a machine that manufactures parts in batches or lots and experiences random offsets or shifts whenever a set-up operation takes place between lots. The existing procedures for adjusting set-up errors in a production process over a set of lots are based on the assumption of known process parameters. In practice, these parameters are usually unknown, especially in short-run production. Due to this lack of knowledge, adjustment procedures such as Grubbs' (1954, 1983) rules and discrete integral controllers (also called EWMA controllers) aimed at adjusting for the initial offset in each single lot, are typically used. This paper presents an approach for adjusting the initial machine offset over a set of lots when the process parameters are unknown and are iteratively estimated using Markov Chain Monte Carlo (MCMC). As each observation becomes available, a Gibbs Sampler is run to estimate the parameters of a hierarchical normal means model given the observations up to that point in time. The current lot mean estimate is then used for adjustment. If used over a series of lots, the proposed method allows one eventually to start adjusting the offset before producing the first part in each lot. The method is illustrated with application to two examples reported in the literature. It is shown how the proposed MCMC adjusting procedure can outperform existing rules based on a quadratic off-target criterion.

Original language | English (US) |
---|---|

Pages (from-to) | 499-520 |

Number of pages | 22 |

Journal | Journal of Applied Statistics |

Volume | 31 |

Issue number | 5 |

DOIs | |

State | Published - Jun 1 2004 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Journal of Applied Statistics*,

*31*(5), 499-520. https://doi.org/10.1080/02664760410001681765

}

*Journal of Applied Statistics*, vol. 31, no. 5, pp. 499-520. https://doi.org/10.1080/02664760410001681765

**A sequential Markov Chain Monte Carlo approach to set-up adjustment of a process over a set of lots.** / Colosimo, B. M.; Pan, R.; del Castillo, E.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A sequential Markov Chain Monte Carlo approach to set-up adjustment of a process over a set of lots

AU - Colosimo, B. M.

AU - Pan, R.

AU - del Castillo, E.

PY - 2004/6/1

Y1 - 2004/6/1

N2 - We consider the problem of adjusting a machine that manufactures parts in batches or lots and experiences random offsets or shifts whenever a set-up operation takes place between lots. The existing procedures for adjusting set-up errors in a production process over a set of lots are based on the assumption of known process parameters. In practice, these parameters are usually unknown, especially in short-run production. Due to this lack of knowledge, adjustment procedures such as Grubbs' (1954, 1983) rules and discrete integral controllers (also called EWMA controllers) aimed at adjusting for the initial offset in each single lot, are typically used. This paper presents an approach for adjusting the initial machine offset over a set of lots when the process parameters are unknown and are iteratively estimated using Markov Chain Monte Carlo (MCMC). As each observation becomes available, a Gibbs Sampler is run to estimate the parameters of a hierarchical normal means model given the observations up to that point in time. The current lot mean estimate is then used for adjustment. If used over a series of lots, the proposed method allows one eventually to start adjusting the offset before producing the first part in each lot. The method is illustrated with application to two examples reported in the literature. It is shown how the proposed MCMC adjusting procedure can outperform existing rules based on a quadratic off-target criterion.

AB - We consider the problem of adjusting a machine that manufactures parts in batches or lots and experiences random offsets or shifts whenever a set-up operation takes place between lots. The existing procedures for adjusting set-up errors in a production process over a set of lots are based on the assumption of known process parameters. In practice, these parameters are usually unknown, especially in short-run production. Due to this lack of knowledge, adjustment procedures such as Grubbs' (1954, 1983) rules and discrete integral controllers (also called EWMA controllers) aimed at adjusting for the initial offset in each single lot, are typically used. This paper presents an approach for adjusting the initial machine offset over a set of lots when the process parameters are unknown and are iteratively estimated using Markov Chain Monte Carlo (MCMC). As each observation becomes available, a Gibbs Sampler is run to estimate the parameters of a hierarchical normal means model given the observations up to that point in time. The current lot mean estimate is then used for adjustment. If used over a series of lots, the proposed method allows one eventually to start adjusting the offset before producing the first part in each lot. The method is illustrated with application to two examples reported in the literature. It is shown how the proposed MCMC adjusting procedure can outperform existing rules based on a quadratic off-target criterion.

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UR - http://www.scopus.com/inward/citedby.url?scp=3442892330&partnerID=8YFLogxK

U2 - 10.1080/02664760410001681765

DO - 10.1080/02664760410001681765

M3 - Article

AN - SCOPUS:3442892330

VL - 31

SP - 499

EP - 520

JO - Journal of Applied Statistics

JF - Journal of Applied Statistics

SN - 0266-4763

IS - 5

ER -