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1 1. TAGUCHI ANALYSIS 1.1 Background the Principles of Dr. Genichi Taguchi's Quality Engineering, Or Taguchi Meth- Ods, As They

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1 1. TAGUCHI ANALYSIS 1.1 Background the Principles of Dr. Genichi Taguchi's Quality Engineering, Or Taguchi Meth- Ods, As They 1 1. TAGUCHI ANALYSIS 1.1 Background The principles of Dr. Genichi Taguchi's Quality Engineering, or Taguchi Meth- o ds, as they are often called in the United States, have had a dramatic impact on U.S. industry, particularly since the early 1980's, as more and more companies have started various programs and training metho ds with the hop e of achieving some of the successes that various Japanese companies have exp erienced over the last thirty or more years. Case studies detailing successes at the Ina Seito Tile Co., the Electri- cal Communication Lab oratory Japan, the Kawasaki Oil Re nery,aswell as seven other examples are given in Taguchi [130 ]. Many consultants travel throughout the U.S. presenting seminars and training workshops concerned with the learning and implementation of Taguchi metho ds, to ols and applications. Taguchi metho ds have b een used in such situations as VLSI circuit design Welch et al [142], non-destructive testing McEwan, Belavendram, and Ab ou-Ali [93], rob ot pro cess capability Black and Jiang [14], thickness of aluminum dep osits on silicon wafers Aceves, Hernandez, and Murphy [2], injection molded plastic comp onents Hanrahan and Baltus [63], as well as cruise control vacuum valves, shrinkage of sp eedometer cable, computer resp onse time, p owers supply circuits, noise reduction in hydraulic rollers, and in re- ducing the rework rate of diesel injectors Wu [143 ]. More examples may b e found in Dehned [37]. The American Supplier Institute holds an annual symp osium devoted solely to Taguchi Metho ds, with the rst held in 1983. In most quality or quality control situations, the goal is to pro duce output as uniformly near a target value as p ossible. The reduction of variation is now regarded 2 as a fundamental concept, b oth for those concerned with manufacturing and pro duc- tion and also for those fo cused on service or task pro cessing. The Taguchi metho d is aimed at the manufacturing situation. To understand the workings of Taguchi metho ds one must consider three p ossible situations concerning a qualitycharacteristic of interest. These three are: larger val- ues are b etter, smaller values are b etter, target value is b est. A qualitycharacteristic is an imp ortant dimension, prop erty or attribute of a manufactured output. The three cases will b e considered separately. For the case where a target value is b est, the aim of Taguchi metho ds is twofold: center some measured qualitycharacteristic around a target value, and minimize the variation around this target value. The famous Sony-USA compared with Sony-Japan example illustrates that b eing centered at the target value is not enough, that b eing correctly centered at the target and b eing within sp eci cation limits is b etter, but the b est situation is one of b eing centered at the target and having minimal variation around that target. See Sullivan, [124 ]. The realization that both the average output and the variability of the output are crucial is a tremendous improvementover the traditional engineering practice of only considering whether or not a part falls within sp eci cation limits. With regard to the implementation of not the concept of this idea, Taguchi has exerted a broad in uence and deserves much praise. Any deviation from the optimal value is considered bad, the severity of the deviation is usually measured by a quadratic loss function. The loss to the manufacturer or so ciety is considered to b e prop ortional to the square of the distance from the optimal value. Mathematically, this loss can b e 2 written: l Y = k Y T , where Y is the observed value and T is the optimal or target value. The constant, k , can b e determined based on the loss at a xed value of Y T . This xed value may represent the edge of the sp eci cation limits, or mightbe apoint at which it is felt that, say, 50 of the customers would complain or require warrantywork. The squared error loss is motivated bya Taylor series expansion. See Taguchi, [129] and [130 ]. Minimizing this loss or exp ected loss is consistent with 3 the two goals of the Taguchi Metho d. The squared error loss function is a continuous function, and is strictly increasing in jY T j, as opp osed to the discrete pass/fail nature of sp eci cation limits. This loss function is also e ectiveinconvincing p eople to worry ab out variation even when the pro cess is on target and mayeven b e within the desired sp eci cation limits. In particular, if the loss is expressed in dollar units, those at the managementlevel will now b e more concerned ab out reducing variation. Consider next the situation where smaller values are b etter, but the resp onse or qualitycharacteristic of interest is non-negative. In this situation we are concerned 2 with the same loss, k Y T , except nowwe set the target value to zero and hop e 2 to minimize E Y , which represents the mean squared error, or mse, around zero. The nal situation is that in which the resp onse is again non-negative, but here 2 larger values are considered to b e b etter. The goal is to maximize E Y . Here the 2 Taguchi practitioner considers E 1=Y and again tries to minimize this quantity. The quantities to b e minimized stem from the desire to measure and reduce the variation relative to the target value. However, the Taguchi metho d do es not base its analysis directly on the ab ove quantities; the exact quantity to b e optimized for each of these three situations will b e given later. In using the recipro cal squared as the quantityofinterest, the larger is b etter situation now b ecomes that of smaller values b eing b etter, and we pro ceed as in the smaller is b etter situation. The rst step in implementing the Taguchi Metho d is that of parameter design. Parameters are various inputs susp ected or known to have an e ect on the quality characteristic, and might include such things as rate of ow, temp erature, humidity or reaction time. Parameter design is an investigation to determine whichvariables or parameters have an e ect on the qualitycharacteristic. This attempts to improve on quality while still at the design stage, as opp osed to intensive sampling plans that insp ect their way to high qualityby `catching' p o or output. Designing high quality and lowvariabilityinto the pro duct will not only b e muchcheap er than extensiveor exhaustive insp ection, but also will allow a pro duct to go from blueprint to usable pro duct in much less time. Variables susp ected to have some e ect on the quality 4 characteristic of interest are known as factors. At this p ointany exp ert knowledge of the sub ject matter should b e applied in the selection of variables to include as factors. Those variables susp ected to have the largest e ects on the qualitycharacteristic are generally considered rst but it is very p ossible to unknowingly omit variables that should have b een considered and also to include others that have no e ect on the qualitycharacteristic. Once chosen, these variables are then classi ed into one of two categories: control variables or noise variables. Control variables represent those parameters or factors which can b e controlled by the designer or manufacturer. In contrast, noise variables are those parameters whichmayhave an e ect on the quality characteristic but generally cannot b e controlled by the designer. Variables that are very exp ensiveorvery dicult to control may also b e considered noise variables. In order to screen these variables for their e ect on the qualitycharacteristic, a classical Taguchi designed exp erimenttakes place. Various settings are selected for eachofthecontrol variables and various settings are temporarily xed for eachof the noise variables. The controllable factors are placed into what is known as the inner array. The inner array is somewhat similar to the classical `design matrix'. Eachrow of this inner array represents one particular combination of settings for the control factors, or one `design p oint'. Thus an inner array with eightrows represents eight p ossible con gurations of the control factors. The noise factors are placed into what is termed the outer array. The settings for the outer array should representa range of p ossible noise conditions that will b e encountered in everyday pro duction, although in practice it is very common to consider only two or three levels for each of the control factors. Again, these settings are xed solely for the purp ose of the exp eriment, in general they will b e random. If the noise is assumed to have a linear e ect, the two settings would generally b e , when the noise factor is noise noise susp ected or known to have a quadratic e ect on the qualitycharacteristic, the p p 3=2; ; + 3=2 .\Thesechoices three settings would generally b e noise noise noise are apparently based on the assumption that the noise factors have approximately symmetric distributions" Kackar, [78]. The twoarrays are then crossed, which 5 means that every exp erimental condition called for by the inner array of control factors takes place at every condition called for by the outer array of noise factors. In this way all of the p oints in the inner array are exp osed to the same values of the noise factors in the outer array; it is hop ed that the temp orarily xed settings of the noise factors at the exp erimentation level will approximate the random conditions that will o ccur at the pro duction level.
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