A probabilistic approach to optimal quality usage

S. T. Rachev; Boyan Dimitrov; Zainaab Khalil

doi:10.1016/0898-1221(92)90200-2

A probabilistic approach to optimal quality usage

S. T. Rachev, Boyan Dimitrov, Zainaab Khalil

Kettering University

Research output: Contribution to journal › Article › peer-review

Abstract

<div class="line" id="line-31"> <span style="color: rgb(46, 46, 46); font-family: Arial;"> The production process of a certain item exhibits some quality characteristics governed by a probability measure μ(A). The consumption (or usage) of all items of this production is described by another probability measure ν(B), where A and B are elements in the product space of all quality characteristics of the totality of produced items. When a product with characteristics x ϵ A is being used instead of a product with characteristics y ϵ B, then a loss ϕ(x,y) is incurred. Any ditribution plan θ(A,B) of the product for consumption produces a total expected loss τφ(θ) = Eφ(x, y). Using some general results in the theory of probability metrics, under given marginals, we develop models for finding the optimal distribution plan θ and the corresponding minimal total losses τφ and establish some particular forms and inequalities. A brief discussion of the results follows. </span></div>

Original language	American English
Journal	Computers Mathematics with Applications
Volume	24
DOIs	https://doi.org/10.1016/0898-1221(92)90200-2
State	Published - Oct 1 1992

Disciplines

Mathematics

Access to Document

10.1016/0898-1221(92)90200-2License: Unspecified

Cite this

@article{f8d46b8611434fe4a9b4473bb9fc1c7d,

title = "A probabilistic approach to optimal quality usage",

abstract = " The production process of a certain item exhibits some quality characteristics governed by a probability measure μ(A). The consumption (or usage) of all items of this production is described by another probability measure ν(B), where A and B are elements in the product space of all quality characteristics of the totality of produced items. When a product with characteristics x ϵ A is being used instead of a product with characteristics y ϵ B, then a loss ϕ(x,y) is incurred. Any ditribution plan θ(A,B) of the product for consumption produces a total expected loss τφ(θ) = Eφ(x, y). Using some general results in the theory of probability metrics, under given marginals, we develop models for finding the optimal distribution plan θ and the corresponding minimal total losses τφ and establish some particular forms and inequalities. A brief discussion of the results follows. ",

author = "Rachev, {S. T.} and Boyan Dimitrov and Zainaab Khalil",

year = "1992",

month = oct,

day = "1",

doi = "10.1016/0898-1221(92)90200-2",

language = "American English",

volume = "24",

journal = "Computers Mathematics with Applications",

}

TY - JOUR

T1 - A probabilistic approach to optimal quality usage

AU - Rachev, S. T.

AU - Dimitrov, Boyan

AU - Khalil, Zainaab

PY - 1992/10/1

Y1 - 1992/10/1

N2 - The production process of a certain item exhibits some quality characteristics governed by a probability measure μ(A). The consumption (or usage) of all items of this production is described by another probability measure ν(B), where A and B are elements in the product space of all quality characteristics of the totality of produced items. When a product with characteristics x ϵ A is being used instead of a product with characteristics y ϵ B, then a loss ϕ(x,y) is incurred. Any ditribution plan θ(A,B) of the product for consumption produces a total expected loss τφ(θ) = Eφ(x, y). Using some general results in the theory of probability metrics, under given marginals, we develop models for finding the optimal distribution plan θ and the corresponding minimal total losses τφ and establish some particular forms and inequalities. A brief discussion of the results follows.

AB - The production process of a certain item exhibits some quality characteristics governed by a probability measure μ(A). The consumption (or usage) of all items of this production is described by another probability measure ν(B), where A and B are elements in the product space of all quality characteristics of the totality of produced items. When a product with characteristics x ϵ A is being used instead of a product with characteristics y ϵ B, then a loss ϕ(x,y) is incurred. Any ditribution plan θ(A,B) of the product for consumption produces a total expected loss τφ(θ) = Eφ(x, y). Using some general results in the theory of probability metrics, under given marginals, we develop models for finding the optimal distribution plan θ and the corresponding minimal total losses τφ and establish some particular forms and inequalities. A brief discussion of the results follows.

UR - https://doi.org/10.1016/0898-1221(92)90200-2

U2 - 10.1016/0898-1221(92)90200-2

DO - 10.1016/0898-1221(92)90200-2

M3 - Article

VL - 24

JO - Computers Mathematics with Applications

JF - Computers Mathematics with Applications

ER -

A probabilistic approach to optimal quality usage

Abstract

Disciplines

Access to Document

Other files and links

Cite this