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The economic assessment of process control quality using a
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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
. q2 ^, T6 s9 `8 F6 c0 Y5 [ Received 17 August 1999; received in revised form 5 November 1999; accepted 22 November 1999 6 A, h6 _2 J$ c3 x% ?2 [3 \* b 1 c6 a7 ~' t# v8 o. IAbstract # K/ u M Y' M& hThis 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; u9 ~/ J# W; L9 @5 X1 G8 Y Ltd. All rights reserved. 7 d/ n+ R" u7 d# T 6 V% `3 d4 z5 D% d* C6 X* lKeywords: Taguchi; Process economics; Control quality; Stability; Performance / V7 m0 W1 ?$ Z) f% e4 Q ! N8 I0 a6 Y5 m& }* `- ~* S1. Introduction The chief requirements of a practical control system 6 T3 n( } s5 v2 D7 [5 Kare that it should have good stability and performance0 ?/ C# @" f' s1 C2 [* u5 Q A product is normally considered to be of acceptable properties. Hence, these will be treated here as the( H8 ]& w e. L0 _, J9 m+ s quality if its characteristics lie within specification limits ‘‘characteristics’’ of a process control system. A wide 2 `! A. k' {7 H) [! v0 {set by the customer. Techniques such as statistical pro- variety of measures have already been developed to ' k& w+ g( X; q9 I+ Pcess control [1] are commonly used in manufacturing quantify these characteristics. These include time-based% Y7 Y: l7 ]1 R& |/ v; I1 |: t8 A industries to ensure that key process variables — and measures (such as rise-time, overshoot and integral- 8 r* x$ G4 I6 Q }: [9 Hhence product characteristics — remain within range. square error), frequency-domain measures (such as sin-+ |2 ?% K7 c+ c) {5 K: f5 X7 | However, an alternative approach to quality control is gular value analysis [3] and operator-based methods) [4– ; w$ I; L4 ^0 l6 Y3 l, Zbased on the work of Taguchi et al. [2]. This approach is 6]. All these methods — explicitly or implicitly — assign( [( p- \ ?$ n3 @ \+ N# ? built around the simple premise that a product has the an ideal value for the characteristic they are trying to! K6 O$ g2 X1 | ‘‘best’’ quality when all its characteristics are exactly at measure, and the closer the actual value is to the ideal 2 q6 l7 O+ m. ~2 jtheir specified values, and quality losses occur when value, the better that system characteristic. In this sense,! T# M, _6 w! g these characteristics move away from these values even they conform to Taguchi’s quality approach. 9 `) \1 r8 B1 r# W5 N% x+ e5 Yif they remain within specification. This paper applies One of the major attractions of a Taguchi-based4 K$ v# I7 }5 C, [; p+ }# S9 ?9 ]% z the Taguchi approach to gauge the ‘‘quality’’ of a pro- measure is that it can quantify control quality in economic + `) Y3 B" T; Z; {8 vcess control system by the extent to which its ‘‘char- terms. The general framework was originally applied to / N. ?( W4 `. d* Q1 [+ iacteristics’’ deviate from desired values. assess the design quality of manufactured products, but+ C% d7 v4 s/ n) G. k has since been used to measure the quality of manu-) r' C- B! _8 l$ K) P * Corresponding author. Tel.: +61-2-9632-2381; fax: +61-2-9632- facturing processes [7] and computer software [8]. It has 7 ]- D1 e$ J! o2381. been applied to the problem of controller tuning [9] but |