摘要
The basic purpose of a quality loss function is to evaluate a loss to customers in a quantitativemanner.Although there are several multivariate loss functions that have been proposed and studied inthe literature,it has room for improvement.A good multivariate loss function should represent anappropriate compromise in terms of both process economics and the correlation structure amongvarious responses.More important,it should be easily understood and implemented in practice.According to this criterion,we first introduce a pragmatic dimensionless multivariate loss functionproposed by Artiles-Leon,then we improve the multivariate loss function in two respects:one ismaking it suitable for all three types of quality characteristics;the other is considering correlationstructure among the various responses,which makes the improved multivariate loss function moreadequate in the real world.On the bases of these,an example from industrial practice is provided tocompare our improved method with other methods,and last,some reviews are presented inconclusion.
The basic purpose of a quality loss function is to evaluate a loss to customers in a quantitativemanner.Although there are several multivariate loss functions that have been proposed and studied inthe literature,it has room for improvement.A good multivariate loss function should represent anappropriate compromise in terms of both process economics and the correlation structure amongvarious responses.More important,it should be easily understood and implemented in practice.According to this criterion,we first introduce a pragmatic dimensionless multivariate loss functionproposed by Artiles-Leon,then we improve the multivariate loss function in two respects:one ismaking it suitable for all three types of quality characteristics;the other is considering correlationstructure among the various responses,which makes the improved multivariate loss function moreadequate in the real world.On the bases of these,an example from industrial practice is provided tocompare our improved method with other methods,and last,some reviews are presented inconclusion.
基金
ThisworkissupportedbytheNationalNaturalScienceFoundationofChinaunderGrant79900018]AeronauticalScienceFoundationofChinaunderGrant02J55001
