Abstract
Selective assembly is an effective approach for improving the quality of a product which is composed of two mating components. This article studies optimal partitioning of the dimensional distributions of the components in selective assembly. It extends previous results for squared error loss function to cover general convex loss functions, including asymmetric convex loss functions. Equations for the optimal partition are derived. Assuming that the density function of the dimensional distribution is log-concave, uniqueness of solutions is established and some properties of the optimal partition are shown. Some numerical results compare the optimal partition with some heuristic partitioning schemes.
| Original language | English |
|---|---|
| Pages (from-to) | 1545-1560 |
| Number of pages | 16 |
| Journal | Communications in Statistics - Theory and Methods |
| Volume | 40 |
| Issue number | 9 |
| DOIs | |
| Publication status | Published - 2011 Jan |
| Externally published | Yes |
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Keywords
- Asymmetric loss
- Log-concave density
- Match gauging
- Stochastic ordering
- Variation reduction
ASJC Scopus subject areas
- Statistics and Probability
Cite this
Optimal partitioning of probability distributions under general convex loss functions in selective assembly. / Matsuura, Shun.
In: Communications in Statistics - Theory and Methods, Vol. 40, No. 9, 01.2011, p. 1545-1560.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Optimal partitioning of probability distributions under general convex loss functions in selective assembly
AU - Matsuura, Shun
PY - 2011/1
Y1 - 2011/1
N2 - Selective assembly is an effective approach for improving the quality of a product which is composed of two mating components. This article studies optimal partitioning of the dimensional distributions of the components in selective assembly. It extends previous results for squared error loss function to cover general convex loss functions, including asymmetric convex loss functions. Equations for the optimal partition are derived. Assuming that the density function of the dimensional distribution is log-concave, uniqueness of solutions is established and some properties of the optimal partition are shown. Some numerical results compare the optimal partition with some heuristic partitioning schemes.
AB - Selective assembly is an effective approach for improving the quality of a product which is composed of two mating components. This article studies optimal partitioning of the dimensional distributions of the components in selective assembly. It extends previous results for squared error loss function to cover general convex loss functions, including asymmetric convex loss functions. Equations for the optimal partition are derived. Assuming that the density function of the dimensional distribution is log-concave, uniqueness of solutions is established and some properties of the optimal partition are shown. Some numerical results compare the optimal partition with some heuristic partitioning schemes.
KW - Asymmetric loss
KW - Log-concave density
KW - Match gauging
KW - Stochastic ordering
KW - Variation reduction
UR - http://www.scopus.com/inward/record.url?scp=79952671529&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79952671529&partnerID=8YFLogxK
U2 - 10.1080/03610920903581002
DO - 10.1080/03610920903581002
M3 - Article
AN - SCOPUS:79952671529
VL - 40
SP - 1545
EP - 1560
JO - Communications in Statistics - Theory and Methods
JF - Communications in Statistics - Theory and Methods
SN - 0361-0926
IS - 9
ER -