University of Groningen. Chemometrical aspects of quality in pharmaceutical technology Boer, Jan Hendrik de

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1 University of Groningen Chemometrical aspects of quality in pharmaceutical technology Boer, Jan Hendrik de IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version Publisher's PDF, also known as Version of record Publication date: 1992 Link to publication in University of Groningen/UMCG research database Citation for published version (APA): Boer, J. H. D. (1992). Chemometrical aspects of quality in pharmaceutical technology: the application of robustness criteria and multi criteria decision making in optimization procedures for pharmaceutical formulations s.n. Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons). Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from the University of Groningen/UMCG research database (Pure): For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date:

2 CHAPTER 2 AN INTRODUCTION TO THE TAGUCHI METHODS One of the persons who has made a great impact on the world of quality improvementjcontro1 is the Japanese engineer Professor Genichi Taguchi. He has developed both a philosophy and a methodology for the process of quality improvement, which depend heavily on statistical concepts and tools. Many Japanese firms have applied these methods with great success. However, not everyone has been pleased by the methods that have been advocated by Taguchi, but, generally speaking, it can be said that the Taguchi methods had, and still have, a great influence on Japanese and (now also) Western quality thinking. It is even said that the great quality evolution of Japanese products over the last two decades is merely caused by the application of Taguchi's statistical methods. The methods for quality improvement as introduced and described in Part I1 of this thesis are partly based on the work of Taguchi. For a good understanding and placement of the techniques described in Part 11, the relevant parts of the Taguchi methods are explained in this chapter. In the next chapter, a review is given on the Taguchi methods enclosing praise, critique and variants on the Taguchi methods Tablet weight (mg) Figure 2.1: A 'kimplistic"(---) and a "realistic"(- ) view on quality. Taguchi's ideas can be separated into two fundamental concepts, which are: 1. The loss function, which is the concrete form of Taguchi's definition of quality: "The quality of a product is the loss caused by the product to society from the time the product is shipped". 2. Off-line quality control. A collection of methods to achieve the demanded quality. These methods enclose the following stages: 1) Systems or functional design 2) Parameter or targeting design 3) Allowance or tolerance design

3 20 Chapter 2 Part I The loss function A common way in Western companies to define quality is conformation to specification, or stated otherwise, that all parts are within specification limits. With this way of defining quality there is no need to improve quality. A product has good quality if its parts are within the stated limits, and this changes immediately to bad quality when one of the limits is past. If, in a pharmaceutical company, a tablet has to be produced with a target weight of mg, then a tablet of 260 mg has good quality and a tablet of 261 mg has an inferior quality. This is, in fact, an unnatural situation, a tablet with a weight of exactly 250 mg. is simply the best tablet and every deviation from this target weight is a loss of quality. This can best be demonstrated using Figure 2.1 which combines a "simplistic" with a "realistic" view on quality. In theory every product property examined should have its own loss function evaluated in order to reach an optimum quality strategy. However, the pattern of such a loss function depends on the process or product which is considered and is often difficult to establish. In general the goals of quality improvement (or the patterns of the belonging loss-functions) are often simplified to three types, which are: 1) 'Nominal the best7 e.g. dimension, weight (target=certain chosen value, depicted in Figure 2.2A) 2) 'Smaller the better' e.g. wear, noise, cost (target=o, depicted in Figure 2.2B) 3) 'Larger the better' e.g. strength, yield (target=w, depicted in Figure 2.2C) Figure 2.2: Loss finctions for A) nominal value, B) smaller the better and C) larger the better qualily characteri.stics.

4 An introduction to the Tawchi Methods 21 The quality characteristic of type 'nominal the best' which uses a specific target value combined with one particular loss function, the quadratic, is probably the most commonly used: Loss = constant * (deviation from target)2. If the constant in the quadratic equation is chosen properly then the quadratic loss function can be used for direct calculation of the financial loss induced by an offtarget quality characteristic. This last situation can be demonstrated using an example copied from reference 10: U.S.A. s spec. target spec. limit limit Color denaity of T.V. net Assumption: repairing cost A - 4 ($) Loss function JAPAN: L = 0.16(10/6)P Factory Percent Standard Loss Deviation Unit U.S.A. Japan Uniform Normal Almost nil 0.3% IO/JIZ 10/6 L - $1.33 L = $0.44 Figure 2.3: A greater uniformity around the target resulted in a lower loss per unit, even though some of the units were out of spec. This example, published in the Japanese newspaper 'Asahi, compares the cost and quality of units (TV-sets) produced at two Sony plants in the late 1970s' one in Japan and one in San Diego. All of the units shipped from the San Diego plant were within specification limits; some of the parts shipped from the Japanese plant were not. Nevertheless, the San Diego plant showed a loss per unit that was $39 greater than the loss registered by the Japanese plant. Why? Let's look more closely at the distributions (Figure 2.3). The process at the San Diego plant produced a uniform distribution, with some units out of specification. Those units were brought within specification because operators adjusted the color balance in the plant - a step that added cost and one that the Japanese plant did not take. Furthermore, a unit that had been adjusted to be just within specification was more likely to generate complaints from customers than a unit that was closer

5 22 Chauter 2 Pan l to the target and didn't have to be reworked; those units therefore incurred a higher level of field repair costs. Thus, the more uniform distribution around the target turned out to be less expensive, even though some shipped parts were out of specifcation. This example illustrates the power of being able to measure costs associated with quality improvement and opens the door to a whole new way of thinking about cost and quality. The way Taguchi has transformed this quality improvement process to a reduction of loss (expressed in yens or dollars) shows also that he probably had trouble convincing the management of the need to keep improving quality. For a thorough introduction of quality improvement methods in a company it is essential that all levels of that company are convinced of using these methods, especially the top level. Taguchi probably thought that these people are more capable of thinking in terms of money than in terms of quality characteristics and it was very smart of him to use these kind of loss functions where the loss is expressed in money terms. However, generally speaking, loss functions probably serve best as an important background concept rather than a practical working tool. One of the misunderstandings with the traditional/western way of quality thinking is that it is not needed to improve quality above the specification limit because the product is already good. But a product with increased quality (closer to the target) performs better and induces less complaints from customers. The latter reason is more important than most people think as it will not only save the manufacturer cost in replacing defect products, but it wil also contribute to an increased confidence and good will of the customer towards the manufacturer. An other misunderstanding is that quality improvement beyond production within specification limits is a cost increasing operation. Many people think that this quality improvement can only be reached by adapting the production process to production with narrower specification limits or by using components or raw material with higher quality. This way of quality improvement is called by Taguchi "the NASA method, which means that an initial prototype is produced, from this prototype the reliability and stability is studied and problems are corrected by requesting better components or elements. Not much fantasy is required to imagine that this a very expensive way to improve quality. The Taguchi method, however, is to improve quality by changing the design of a product so that it becomes less sensitive to variability. This means that the product is more robust to all sorts of quality decreasing factors. To reach this goal he developed the concept of Off-line quality control. Off-line quality control The performance of a product or process depends on a large number of factors. The problem is to find such settings of these factors that the product performs well under a number of conditions and during its intended life time. For this demand the product has to be robust against a number of factors/variables that disturb the function of it,

6 An introduction to the Taguchi Methoh 23 these factors are called noise factors. Taguchi has classified the noise factors into three types: 1) Outer noise: environmental variables that affect the performance of a product. For example: temperature, dust, humidity. 2) Inner noise: changes in material properties through usage, product deterioration, wear. 3) Variational noise: differences between the individual manufactured units, manufacturing variations. Products are said to have good quality if they are robust against these three types of noise. Outer and inner noise are from these three types the most important. Through design, robustness against these two types of noise has to be achieved. The following procedure describes Taguchi's product development strategy. I Product I design Process design Manufacturing : 1 : 1 Toble 2.1: The three stages of product development and the possibilities of countmneaswes against various types of noise, with 0 - Countmncm possible and X - Cowltermcm impossible. A product's development cycle can be separated into three stages, which are: product design, process design and manufacturing. In Table 2.1 copied from ref. 8 is shown in what stage countermeasures against the three types of noise factors can be taken. As can be seen countermeasures against environmental variables and product deterioration are only possible at the product design stage. Therefore, the product design phase is the most important one. To arm against the noise effects Taguchi has developed a product development procedure containing three stages which are: 1) System design: a prototype of a certain product is made using specialized knowledge, statistical design of experiments is not relevant at this stage. 2) Parameter design: the optimum levels of the individual factors are determined using experimental design and other statistical methods with the following objectives: a) the product should have the demanded quality characteristics (on target) b) these characteristics should be robust to the noise factors 3) Tolerance design: if the parameter design step did not achieve the required results then this step can be used to decrease production tolerances, which involves a cost increase. Especially the parameter design step gives the best opportunity to build in and/or to

7 24 Chapter 2 Part I increase the quality of a product/process. Therefore the rest of this chapter concentrates on the parameter design step. The quality increasing results are reached by exploiting the possible effects of the control factors. Four possible type of effects can be distinguished: 1) control factors affecting the mean, are used to adjust the mean (also called signal or adjustment factors) 2) control factors affecting the variability, are used to reduce variability 3) control factors affecting both the mean and variability, are usually used to reduce variability 4) control factors neither affecting mean nor variability, are used to relax requirements/tolerances with the objective to reduce cost Before designing any experiment it is important to know all the factors that could eventually affect the quality of the product. After summing these factors they are ordered into two types of classes: 1) control factors: factors that can be set and controlled by the engineer. 2) noise factors: factors that normally cannot be controlled, however for the experimental part of this design step the noise factors must be controlled to determine their possible effects. The challenge is now to setup experiments in such a way that settings of the control factors are determined which give a product with good quality characteristics and with the least possible influence of the noise factors. For the experimental section Taguchi has developed a number of tools which are known as orthogonal arrays, linear graphs and signal-to-noise ratios. Orthogonal arrays Orthogonal arrays (orthogonal array's) are experimental designs consisting of either the set of control factors or the set of noise factors. Taguchi has 'developed' a large amount of experimental designs, of which the majority already existed. He most commonly used 2k factorial designs, 2k-p fractional factorials, Plackett-Burman designs, 3k factorials, designs constructed from the Latin square, Graeco-Latin square and hyper-graeco-latin square. He also used all sorts of combinations of the mentioned designs to permit factors with different number of levels to appear in the same experimental design. For each of the orthogonal array's a code is available of the form La(bC), where a is the number of experiments, b the number of levels for each factor and c the number of columns in the array. For example the ~ ( 2 orthogonal ~ ) array is the same as a 274 fractional factorial design. With this &(27) orthogonal array the effect of maximal 7 factors in 8 experiments can be determined (this is of course only possible if there does not exists any interaction between the 7 factors). But the &(27) orthogonal array can also be used for 4 factors where 3 of the four factors have 2"* degree interactions among each other, while other combinations are also possible (see the linear graphs

8 An introduction to the Taguchi Methoh 25 section). To simplify the allocation of the main effects and interactions to the appropriate columns of the orthogonal array Taguchi has developed linear graphs. For an ordinary Taguchi analysis two orthogonal array's are needed, one for the control factors (called the inner array) and one for the noise factors (called the outer array). Figure 2.4: An example of a cross-product m q; factors A, B and C form the conuol may (an LJ, factors X, Y and Z form the (rotated) noise may (ah0 an LJ. Each of the mays has setlings I - IV. Nwnbers 15 through 22 are fictive response values. Out of these two orthogonal array's a cross-product design is constructed (see Figure 2.4 for an example), for each setting of the control factors in the inner array the complete noise factor (outer) array has to be executed to determine the effect of the environmental factors. Linear graphs Linear graphs are simple tools for the allocation of effects (main effects and interactions) to the columns of an orthogonal array. Linear graphs consists of dots, lines and numbers. A dot represents a main effect, a line between two dots represents the interaction between the two connected main effects (dots). Each of the dots and lines is numbered, the numbers representing the columns of the orthogonal array. In Figure 2.5 the set of linear graphs belonging to the L, orthogonal array is shown. For the larger orthogonal array's a larger set of belonging linear graphs is available. The method works as follows: - select the smallest orthogonal array that could hold the effects to be estimated - construct a graph according to the linear graph rules with effects (main and interaction) to be estimated - select one of the standard linear graphs defined for the chosen orthogonal array which closely resembles the constructed graph and modify the selected graph to match the required graph - use the modified graph to assign the effects to the columns of the orthogonal array Signal-to-noise ratios A signal-to-noise (S/N) ratio is a performance measure, which estimates the effect of the noise factors on the quality characteristic. For each of the three optimization goals a S/N ratio has been developed. These S/N ratios are proposed to provide a product design that simultaneously places the response on a target and a minimum variance. The S/N ratios are defined as follows:

9 26 Chapter 2 Part I Figure 2.5: Linear graphs belonging to the L, orthogonal array. 1) Nominal-the-best situation: S/N, = 10 1og(F/s2-l/n) 2) Smaller-the-better situation: S/N, = -10 log(l/n 2 y?) 3) Larger-the-better situation: S/N, = -10 log(l/n Z(l/y?)) A S/N ratio is calculated for each value of the inner array over the complete outer array as is shown in Table 2.2, so B refers to summing over the outer array values and s is the standard deviation calculated over the outer array values, expressing the variability induced by the noise factors). The nominal-the-best S/N ratio is directly related to the coefficient of variation (cv=100 sm, i.e. S/Nt = 10 log (100'/cv2-l/n) and like the cv the S/Nt ratio measures the variability relative to the mean. Each S/N ratio is constructed in such a way that it has to be maximized, this is done for convenience. A complete Taguchi analyses includes an analysis of the SIN ratio (dispersion) and an analysis of (location). Examples of typical Taguchi experiments Example 1 (cake mix) This example has been copied from Ref. 2. A manufacturer of cake mixes wants to introduce a new cake mix into the consumer market. The goal is that a cake mix is formulated that turns out reasonably well into a cake even if the consumer does not exactly follow the instructions on the box.

10 An introduction to the Taguchi Methods 27 Nr Design Vsuiables T F S E t Enwonmental variables ii s, SMl t:; :i 1 :! Table 2.2: Eqerimental design and the hedonic rmh used for the cake mir m ple. In this example the manufacturer is only concerned about the environmental variables temperature (T) and baking time (t). The design factors are the amount of flour (F), the amount of sugar (S) and the amount of egg powder (E). The object of this project is the creation of cake mix that has less variability towards the environmental factors than the standard recipe which has been developed by the product development laboratory so far. In Table 2.2 the design for the experiment which was conducted has been depicted, the commonly used standard condition is indicated by the zeros (which is in fact the prototype cake). Each factor has been tested at a lower level (-) and at a higher () level. For the control factors F, S and E a Z3 factorial design (plus 1 design point for the standard conditions) has been constructed, which is the left side of the table. At the top a 2' factorial design (plus 1 design point for the ideal values (according to the box instructions) for t and T) has been placed for the noise factors t and T. At each combination of experimental settings of both designs a cake has been made, so a total of 9*5=45 cakes were produced. The cakes were evaluated by a taste panel. The evaluation of a cake is expressed in a hedonic index, which ranges from 1 (bad) to 7 (best). At the right hand side of the table the results for each of the inner array settings calculated over the outer array are given, these results are y, standard deviation and S/N,. The manufacturer is not interested in the best tasting cake mix, but in a cake mix that tastes reasonably good even when baked under environmental conditions that are not exactly the conditions mentioned in the recipe on the box. Fortuitous, in this case there is no problem, the best tasting cake mix is also the one that is most robust to the noise factors which is setting nr. 7 with F=, S=- and E=. Example 2 (power circuit) This example is often used to clarify the use of different types of control factors and as an example of a cheap optimization of quality. The object was a power circuit where the optimization goals are an output voltage of 115 V, a low variability around this target value and the use of inexpensive components. A prototype of the circuit has been built and two components were identified as having the greatest effect on the output voltage (y, response). These components, the

11 28 Chapter 2 Part I transistors' h, and the resistance value (R) of a resistor, affect the response as shown in Figure 2.6; h, affects both variability and the mean value, R has only influence on the mean value of y. To achieve an inexpensive power circuit only third-grade elements were used. A disadvantage of these cheap components is the rather large variability of them. The lifetime of the circuit was estimated to be about 10 years, in that period the h, of the transistor deteriorates by 30%. So if factor A is set to 20 the targetvalue of 115 V is indeed reached but due to the large variability of A (between 14 and 26) also a rather large variability of the output voltage (between 98 V and 121 V) is observed. As can be seen in Figure 2.6 the transistor has a nonlinear relationship with the response and this phenomenon was exploited. Increasing the h, from 20 to 40 results in an even larger absolute variability of the transistor's h, (between 28 and 52) but this results in a considerable smaller variability of the outputvoltage (between 122 V and 127 V). Unfortunately the targetvalue is now not reached fi is 125 V instead of 115 V), but, this can be solved by the resistor, which has a linear relationship with the response (right hand side of of Figure 2.6), its value was adjusted from 60 to 40 to adjust to the target. Transistor : h, Resistor: resistance Figure 2.6: The influence of the transistor's h, and the resistance of the resistor on the output voltage. In this example no classification towards control and noise factors could be made because the control and noise factors were the same. This type of analysis is also known as sensitivity analysis. REFERENCES 1. G.E.P. Box, S. Bisgaard, The scientific context of quality improvement, Quality Progress, June 1987, pp G.E.P. Box, S. Bisgaard, C. Fung, An explanation and critique of Taguchi's contributions to quality engineering, Report no. 28, University of Wisconsin- Madison, USA, March P.M. Burgam, Design of experiments - the Taguchi way, Manufacturing

12 An introduction to the Taguchi Methods 29 Engineering, May 1985, pp J. Cullen, An introduction to Taguchi methods, Quality Today, September B. Gunter, A perspective on the Taguchi methods, Quality Progress, June 1987, pp J.S. Hunter, Statistical design applied to product design, J. Qual. Techn., 17, 4, 1985, pp R.N. Kackar, Off-line quality control, Parameter design, and the Taguchi method, J. Qual. Techn., 17, 4, 1985, pp R.N. Kackar, Taguchi's quality philosophy: Analysis and commentary, Quality progress, December 1986, pp R.H. Lochner, J.E. Matar, Designing for quality; an introduction to the best of Taguchi and western methods of statistical experimental design, Chapman and Hall, London-Madras, L.P. Sullivan, Reducing variability: A new approach to quality, Quality Progress, July 1984, pp L.P. Sullivan, The power of Taguchi methods, Quality Progress, June 1987, pp J.J. Pignatiello Jr., J.S. Ramberg, Discussion of ref. 7, J. Qual. Techn., 17, 4, 1985, pp G. Taguchi, Introduction to quality engineering; designing quality into products and processes, American Supplier Institute, Dearnborn, USA, 1986