TY - JOUR

T1 - A probabilistic approach to optimal quality usage

AU - Rachev, S. T.

AU - Dimitrov, B.

AU - Khalil, Z.

N1 - Funding Information:
**Puesem-ch supported by the Natural Science and Engineering Research Council of Canada; Grant ~:A9{~5.

PY - 1992

Y1 - 1992

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{lunate} A is being used instead of a product with characteristics y ε{lunate} B, then a loss φ{symbol}(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{lunate} A is being used instead of a product with characteristics y ε{lunate} B, then a loss φ{symbol}(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 - http://www.scopus.com/inward/record.url?scp=44049113583&partnerID=8YFLogxK

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

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

M3 - Article

AN - SCOPUS:44049113583

VL - 24

SP - 219

EP - 227

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 8-9

ER -