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The economic assessment of process control quality using a
Taguchi-based method

R. Di Mascioa,*, G.W. Bartonb aSchool of Quantitative Business Methods and Operations, University of Western Sydney, PO Box 10, Kingswood NSW 2747, Australia bDepartment of Chemical Engineering, University of Sydney, Sydney NSW 2006, Australia

Received 17 August 1999; received in revised form 5 November 1999; accepted 22 November 1999

Abstract
This paper derives a measure of dynamic control quality within the Taguchi framework (G. Taguchi, E.A. Elsayed, T. Hsiang, Quality Engineering in Production Systems, McGraw-Hill, New York, 1989) which estimates product quality (in economic terms) by the losses incurred when specified product characteristics depart from their nominal values. In this sense, a control system may be  viewed  as  a  ‘‘product’’  with  stability  and  performance  properties  as  its  required  characteristics.  The  degree  to  which  system inputs and outputs depart from their nominal values is used to give an estimate of stability and performance quality, respectively. Displaying control quality graphically with stability and performance qualities as the two axes can be used to highlight the trade-o between  these  two characteristics.  This  technique  was  used  to  evaluate  the  quality  oered  by  four  model-based  controllers  on  a distillation column model responding to a typical disturbance, and how the presence of measurement and valve dynamics aected control quality. It is anticipated that the measures derived in this paper (being both time-based and economic) may prove useful in conveying control quality in a common language understood by engineers, operators and management. 2000 Elsevier Science
Ltd. All rights reserved.

Keywords: Taguchi; Process economics; Control quality; Stability; Performance

1.  Introduction                                                                         The  chief  requirements  of  a  practical  control  system
                                                                                             are that it should have good stability and performance
A product is normally considered to be of acceptable                   properties.    Hence, these will  be treated here as  the
quality if its characteristics lie within specification limits                ‘‘characteristics’’  of  a  process  control  system.  A  wide
set by the customer. Techniques such as statistical pro-                   variety of  measures    have already been developed    to
cess  control  [1]  are  commonly  used  in  manufacturing                   quantify these characteristics. These include time-based
industries  to  ensure  that  key  process  variables  —  and             measures    (such as  rise-time, overshoot    and integral-
hence  product  characteristics  —  remain  within  range.                   square error), frequency-domain measures (such as sin-
However, an  alternative  approach  to  quality  control  is                gular value analysis [3] and operator-based methods) [4–
based on the work of Taguchi et al. [2]. This approach is                   6]. All these methods — explicitly or implicitly — assign
built around the simple premise that a product has the                      an  ideal  value  for  the  characteristic  they  are  trying  to
‘‘best’’ quality when all its characteristics are exactly at                measure, and the closer  the actual value is to the ideal
their  specified    values, and quality losses  occur when       value, the better that system characteristic. In this sense,
these characteristics move away from these values even                      they conform to Taguchi’s quality approach.
if  they  remain  within  specification.  This  paper  applies                One of the  major    attractions of  a Taguchi-based
the Taguchi approach to gauge the ‘‘quality’’ of a pro-                   measure is that it can quantify control quality in economic
cess  control  system  by  the  extent  to  which  its  ‘‘char-             terms. The general framework was originally applied  to
acteristics’’ deviate from desired values.                                  assess the design quality of manufactured products, but
                                                                           has  since  been  used  to  measure  the  quality  of  manu-
  *  Corresponding author. Tel.: +61-2-9632-2381; fax: +61-2-9632-          facturing processes [7] and computer software [8]. It has
2381.                                                                      been applied to the problem of controller tuning [9] but