Pii: s0378-3758(02)00216-

An annotated bibliography of application papers using certain classes of fractional factorial and Tania Prvana, Deborah J. Streetb;∗ aSchool of Mathematics and Statistics, University of Canberra, Canberra, Australia bSchool of Mathematical Sciences, University of Technology, Sydney, Australia In this paper we provide an annotated bibliography of about 140 papers which have appeared in journals in a variety of areas in the last 5 years and in which a fractional factorial design has been used. For each reference, we have indicated the design or designs used and whether or not the responses are given in the paper. The level of detail given in these papers makes them suitable sources for examples in a course on the design and analysis of experiments. c 2002 Elsevier Science B.V. All rights reserved.
Factorial designs were introduced in the agricultural area by Fisher (1926) in the 1920s and taken up enthusiastically both there, and in the manufacturing and engineer- ing areas, partly due to the e orts of Tippett (1934). More recently, Taguchi (1987) is credited with being responsible for the extensive use of fractional factorial designs in industry in both Japan and the US. Bisgaard (1992) gives an eclectic history of factorial designs and their use in industry. Theoretical developments, notably the con- struction of fractional factorial designs, may be found in Kempthorne (1952), McLean and Anderson (1984) and Montgomery (1991).
Despite the large number of fractional factorial designs that are used in industry at the moment, most undergraduate textbooks on experimental design continue to present examples from the 1940s and 1950s. The list of case studies provided in Bisgaard (1992) goes some way to alleviating this problem but of the 131 case studies that he cites, the latest ones were published in 1975 and only 10 are fromthe 1970s at all. By E-mail address: deborah@it.uts.edu.au (D.J. Street).
0378-3758/02/$ - see front matter c 2002 Elsevier Science B.V. All rights reserved.
T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 A table showing the areas in which we have found fractional factorial designs used choice, all his examples are industrial. Most textbooks make no mention of the fact that fractional factorial designs are also used in investigations in areas as diverse as law, marketing and medicine. Examples of the areas in which we have found fractional factorial designs used may be found in Table 1.
In this paper we give an annotated bibliography of around 140 papers in a variety of application areas, as tabulated in Table 1. With the exception of about 20 papers, chosen because there were few in that application area, all the papers given have the original responses given. About 30% of the papers we originally reviewed did not have the raw data. Many papers do not mention the statistical software used to perform the analyses, but of those that do Statgraphics and SAS proved to be the most popular.
T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 The bibliography is divided into ÿve sections depending on the type of design that was used. Thus we have listed separately those papers that used two (or more) distinct designs and those which used a Box–Behnken, central composite or Plackett–Burman design and the remainder of the papers are in a section called simply fractional factorial In the next section, we recall the deÿnitions of the designs that we have chosen to A factor is any attribute of the experimental units which may a ect the response observed in the experiment. Those factors which are applied by the experimenter are called treatment factors and any factors which are inherent attributes of the units are called block factors. The possible values that a factor can take are called the levels of Each of the possible combinations of the treatment factor levels is called a treatment combination. A complete factorial design (FD) is one in which each of the treatment combinations appears an equal number of times. If all the treatment factors have 2 levels then we talk about a 2k design. A FFD is one in which only a subset of the treatment combinations appear. We use 2k−p to denote a 1=2p fraction of a 2k design.
A foldover design is a 2k−p FFD which has been doubled in size by including the complementary treatment combinations; that is, the treatment combinations obtained by changing all 1’s to 0’s and 0’s to 1’s.
A balanced incomplete block design (BIBD) with parameters (v; b; r; k; ) consists of b blocks each of size k. The number of treatments in the design is v, all treatments are replicated r times and every pair of treatments appears in restrictions are placed on the values of v; b; r; k, and . In particular, counting the occurrences of treatments, vr=bk and by counting pairs of treatments, (v−1)=r(k−1).
Because of these relationships we usually talk about a (v; k; ) BIBD.
A v factor Box–Behnken design (BBD) is formed from the v × b incidence matrix of a BIBD and a complete 2k design written with the factors as rows (Table 2). The ÿrst 1 in each block in the incidence matrix is replaced by the levels of the ÿrst factor in the 2k design, the second 1 in each block is replaced by the levels of the second factor in the 2k design and so on. Each zero in the incidence matrix is replaced by a row of k zeroes. Centre points may also be added. These designs were introduced by T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 A central composite design for three factors A FFD in which all of the main e ects can be estimated independently of any in- teraction terms is said to be of resolution III. A FFD in which all of the two-factor interactions can be estimated independently of main e ects and other two factor inter- actions is said to be of resolution V. The foldover of a FFD of resolution III is of resolution IV. In general a FFD is of resolution R if no p factor interaction is aliased with another interaction containing less than R − p factors.
A central composite design (CCD) has three parts. The ÿrst is a resolution V FFD, the second is points on the axes of each of the factors, located equidistant fromthe origin, and the third is some points at the origin. The points on the axes are called the star points or the axial points. A CCD for three factors with axial points at distance 1.6 fromthe origin and 2 centre points appears in Table 3.
Plackett and Burman (1946) introduced symmetric designs with factors with 2, 3, 5 or 7 levels in which main e ects could be estimated if interactions are ignored. The two-level designs with N runs, where N is not a power of two, are the designs that are commonly referred to when the phrase Plackett–Burman design is used but Rogan et al. (1994) uses a three-level PBD. The aliasing structure of these designs can get complicated; see Hamada and Wu (1992) and Box and Draper (1987). The design in A screening design is a design used to determine which of a set of factors are active. A response surface design is one used to estimate the parameters of a surface modelling the response given the factors studied. Five of the papers use the Doehlert uniform shell design (Doehlert, 1970). These designs have d2 + d + 1 points for d factors: one at the origin and the other points on a sphere centered at the origin.
T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 A table showing the main uses of each of the designs discussed in this paper In Table 5 the main uses of each of the designs described in this paper are indicated.
1. Altria, K.D., Clark, B.J., Filbey, S.D., Kelly, M.A. and Rudd, D.R. (1995). Appli- cation of chemometric experimental designs in capillary electrophoresis: a review This is a brief review paper of the use of FD, FFD, PBD and CCD in capillary electrophoresis. No data sets are given, but references to some are given.
2. Andersson, P.M., Lundstedt, T. and Abramo, L. (1996). Synthesis and optimiza- tion of 1-pyrrolemethane sulfonate by means of experimental design (1996). Jour- with two centre points used as a screening experiment are given. As the results were not conclusive the design was expanded to a 25−1 with three centre points design by foldover and the responses are given. Two active factors were used in a Doehlert design. Data also given for this experiment.
3. Arbaisah, S.M., Asbi, B.A., Junainah, A.H. and Jamilah, B. (1996). Determination of optimumconditions for pectinesterase extraction fromsoursop fruit (Anona muricata) using response surface methodology. Food Chemistry 55, 289–292.
One response variable froma 25−2 design and froma two factor CCD with 5 4. Arnoldsson, K.C. and Kaufmann, P. (1994). Lipid class analysis by normal phase high performance liquid chromatography, development and optimization using multivariate methods. Chromatographia 38, 317–324.
The responses froma blocked, four-factor 8 run PBD are given. Optimisation steps, involving a 23 design with centre point and a 32 design, are described but no 5. Beijersten, I. and Westerlund, D. (1995). Derivatization of dipeptides with 4- uoro- 7-nitro-2,1,3-benzoxadiazole for laser-induced uorescence and separation by Micellar electrokinetic chromatography. Journal of Chromatography 716, One response variable froma 25−1 FFD and froma three factor CCD with 4 T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 6. Boleda, M.D., Briones, P., Farres, J. and Tyÿeld, L. Pi R. (1996). Experi- mental design—a useful tool for PCR optimization. Biotechniques 21, Tutorial-type presentation of both FFD and polymerase chain reaction (PCR).
One response variable froma 25−2 FFD and froma two factor CCD with 3 centre points are given. Some references to applications of FFD in various 7. Bucher, R.A. and Loos, A.C. (1994). Parametric statistical analysis of electrostatic powder prepregging. Journal of Advanced Materials 25, 44–50.
One response froma three-factor 12 run PBD is given. The three active factors are used in a face-centred CCD with 6 centre points. The estimated equations and several response surfaces are given.
8. Bzik, T.J., Henderson, P.B. and Hobbs, J.P. (1998). Increasing the precision and accuracy of top-loading balances: application of experimental design. Analytical This paper compares PBDs and ‘one-at-a-time’ weighing schemes. Results for 9. Carlson, A.D., Hofer, J.D. and Riggin, R.M. (1997). Development of an opti- mized peptide map for recombinant activated human protein c by means of an experimental design strategy. Analytica Chimica Acta 352, 221–230.
A 12-run PBD was used to screen seven factors for their e ect on the relative peak height this being given for 19 peptide fragments. A 23 design was then used to determine signiÿcant main and interaction e ects and the relative peak height 10. Chen, H.C. (1996). Optimizing the concentrations of carbon, nitrogen and phos- phorus in a citric acid fermentation with response surface method. Food Biotech- The response variables froma replicated 23 experiment, a series of experiments along the path of steepest ascent, and a CCD experiment are given. Estimated coe cients, and graphs of the response surface are also given.
11. De Meo, M., Laget, M., Digiorgio, C., Guiraud, H., Botta, A., Castegnaro, M. and Dumenil, G. (1996). Optimization of the salmonella=mammalian microsome assay for urine mutagenesis by experimental designs. Mutation Research: Reviews in One response variable fromtwo di erent 23−1 FFDs and froma Doehlert design 12. Dyvik, K., Dyrstad, K. and Tronstad, A. (1995). Relationship between viscosity and determined injection pressure in angiography catheters for common roentgen contrast media. Acta Radiologica 36, 43–49.
For each of 8 contrast media, a 22 FD with 3 centre points and a 25−1 FFD with 3 centre points were conducted. Estimated equations and graphs of the results 13. Embuscado, M.E., Marks, J.S. and BeMiller, J.N. (1994). Bacterial cellulose .2.
optimization of cellulose production by Acetobacter-xylinum through response surface methodology. Food Hydrocolloids 8, 419–430.
T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 The response variable froma seven factor BBD used as a screening design and a four factor CCD with 7 centre points are given. Various contour plots and response surfaces are also given. The predicted values at the optimum settings 14. Gomes, D.J., Gomes, J. and Steiner, W. (1994). Production of highly thermostable xylanase by a wild strain of thermophilicfungus. Thermoascus aurantiacus and partial characterization of the enzyme. Journal of Biotechnology 37, 11–22.
Responses froma 23, along a path of steepest ascent and for a 32 design are 15. Gratteri, P. Furlanetto, S., Laporta, E., Pinzauti, S. and Leardi, R. (1996). De- velopment and set-up of drug electroanalysis by experimental design: a survey.
This paper discusses three applications of sequential experimental design. The ÿrst uses a PBD, a FFD and a Doehlert design. The second uses a PBD, D-optimal design and a FD. The third example uses a three-quarter FFD and a CCD. Results are given for all designs as well as estimated e ects, and some plots.
16. Haltrich, D., Laussamayer, B. and Steiner, W. (1994). Xylanase formation by Scle- rotium rolfsii—e ect of growth substrates and development of a culture medium using statistically designed experiments. Applied Microbiology and Biotechnology One response froma folded seven factor, 12-run PBD with one centre point are given. Then a 24 design was used to determine whether further reductions in the number of active factors could be achieved (response not given). Finally the responses froma two factor CCD with two centre points are given. The accuracy 17. Haltrich, D., Preiss, M. and Steiner, W. (1993). Optimization of a culture medium for increased xylanase production by a wild strain of Schizophyllum-commune.
Enzyme & Microbial Technology 15, 854–860.
Responses froma 23, along a path of steepest ascent and for a three factor orthogonal CCD with 2 centre points are given. The equation and some graphical 18. Hows, M.E.P., Perrett, D. and Kay, J. (1997). Optimisation of a simultaneous separation of sulphonamides, dihydrofolate reductase inhibitors and ÿ-lactamanti- biotics by capillary electrophoresis. Journal of Chromatography 768, 97–104.
One response variable froma three factor BBD with three centre points is given as is the corresponding estimated equation. Some contour plots are given and as well as a comparison of the predicted and observed response at the optimum setting. At the same time as the BBD was carried out, the experimenters carried out a trial and error optimisation which they note took 45 runs to arrive at a 19. Junqua, M., Duran, R., Gancet, C. and Goulas, P. (1997). Optimization of micro- bial transglutaminase production using experimental designs. Applied Microbiol- ogy & Biotechnology 48, 730–734.
A 25 design with ÿve centre points was used to determine the active factors for each of two response variables. A four factor BBD with six centre points was T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 used to calculate “the optimum concentrations that might be more relevant for other experimental domains”. A two factor CCD with 5 centre points was used to optimise one of the response variables.
20. Kern, M., Nidetzky, B., Kulbe, K.D. and Haltrich, D. (1998). E ect of nitrogen sources on the levels of aldose reductase and xylitol dehydrogenase activities in the xylose-fermenting yeast. Candida tenuis. Journal of Fermentation & Bioengi- A seven-factor 26-run folded PB design with two centre points was used as a screening design. The factor levels and standardised e ects are given for this experiment. The results of a follow-up complete 23 experiment are given, as well as a discussion of the results of this experiment.
21. Koch, I., Harrington, C.F., Reimer, K.J. and Cullen, W.R. (1997). Simplex optimi- sation of conditions for the determination of antimony in environmental samples by using electrothermal atomic absorption spectrometry. Talanta 44, 771–780.
An eight factor, 12-run PBD and a ÿve factor, 8 run PBD were used to de- termine the four factors that e ected the response. The levels of these factors were then optimised using the composite modiÿed simplex optimisation method.
Responses for this third experiment only are given.
22. Lumpkin, N.E., King, W. and Tansley, T.L. (1996). Reÿnement of low-resistance Ni–Ge–Au Ohmic Contacts To n+ GaAs using screening and response surface experiments. Journal of Materials Research 11, 1238–1243.
One response variable froma 27−3 and a three factor CCD with 2 centre points are given. Conÿrmatory runs were made and the results presented.
23. Masson, F., Lebert, A., Talon, R. and Montel, M.C. (1997). E ects of physico- chemical factors in uencing tyramine production by Carnobacterium divergens.
Journal of Applied Microbiology 83, 36–42.
A Doehlert uniform-shell design was used to determine the levels of three factors. For each combination in the Doehlert design, a two factor, four run PBD was carried out. Estimated coe cients are given, as are some response 24. Morris, V.M., Hargreaves, C., Overall, K., Marriott, P.J. and Hughes, J.G. (1997).
Optimization of the capillary electrophoresis separation of ranitidine and related compounds. Journal of Chromatography 766, 245–254.
After a discussion of the results fromtwo screening designs, both FFDs, re- sponses froma three factor CCD and froma two factor CCD are given. Repro- ducibility of the systemwas looked at.
25. Pagliarini, E., Peri, C., Zanoni, B. and Ghizzardi, M. (1996). Optimization of olive paste expression—maximizing yield by central composite design approach.
Journal of the Science of Food & Agriculture 71, 470–474.
One response variable froma 24 FD used as a screening design, and froma three factor CCD with four centre points are given. Some response surfaces are 26. Pean, J.M., Venierjulienne, M.C., Filmon, R., Sergent, M., Phantanluu, R. and Benoit, J.P. (1998). Optimization of HSA and NGF encapsulation yields in PLGA microparticles. International Journal of Pharmaceutics 166, 105–115.
T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 Two response variables froma 210−6 design are given. For the two most sig- niÿcant factors a Doehlert design was used in the optimization step and the data 27. Pham, P.L., Taillandier, P., Delmas, M. and Strehaiano, P. (1998). Optimization of a culture medium for xylanase production by. Bacillus sp. using statistical exper- imental designs. World Journal of Microbiology & Biotechnology 14, 185–190.
One response variable froma 23 design augmented with 5 centre points, from the points on a path of steepest ascent and froma two factor CCD with 5 centre points are given. Some contour plots are given.
28. Pizarro, C., Fernandeztorroba, M.A., Benito, C. and Gonzalezsaiz, J.M. (1997).
Optimization by experimental design of polyzcrylamide gel composition as sup- port for enzyme immobilization by entrapment. Biotechnology & Bioengineering One response variable froma two factor CCD with ÿve centre points, three replicates of a 22 design with four centre points and three replicates of a two fac- tor CCD with 3 centre points are given, together with estimated response surface equations and response surface plots.
29. Rodriguez, L.C., Garcia, R.B., Campana, A.M.G. and Sendra, J.M.B. (1998). A new approach to a complete robustness test of experimental nominal conditions of chemical testing procedures for internal analytical quality assessment. Chemo- metrics & Intelligent Laboratory Systems 41, 57–68.
The paper advocates the use of PBDs to study the topic of the title. Responses for a seven-factor, 8 run PBD, two 13 replicates of a 33 designs, and two three- factor, 4 run PBDs are given, as is the analysis of them.
30. Rowlands, H. and Pham, D.T. (1995). Application of the Taguchi method to the design of a robot sensor. Robotica 13, 607–617.
A comparison of the information obtained from 25, 25−1 and 25−2 experiments in this area. Good diagramof the experimental set-up. Results are presented as 31. Sanchez, N., Martinez, M. and Aracil, J. (1997). Selective esteriÿcation of glyc- erine to 1-glycerol monooleate. 2. Optimization studies. Industrial & Engineering Longitudinal data of four response variables froma blocked 22 design with four centre points are given. Because a signiÿcant curvature e ect was found for each response, the design was extended to a blocked two factor CCD with four centre points. The estimated second-order response surface is given for each of the four 32. Shumate, D.A. and Montgomery, D.C. (1996). Development of a TIW plasma etch process using a mixture experiment and response surface optimization. IEEE Transactions on Semiconductor Manufacturing 9, 335–343.
Describes a 25−1 experiment, a mixture experiment and response surface design on three factors. Responses are given for the mixture experiment only. Discussion of the ÿrst design and parameter estimates from the third are included.
33. Srinivas, D., Rao, K.J., Theodore, K. and Panda, T. (1995). Direct conversion of cellulosic material to ethanol by the intergeneric fusant Trichoderma reesei QM T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 9414=Saccharomyces cerevisiae NCIM 3288. Enzyme & Microbial Technology One response variable froma three factor BBD with 6 centre points, and the es- timated equation, are given. A two factor CCD with 5 centre points was then used to optimize pH and temperature and the responses are given as is the estimated 34. Taylor, R.W., Barren, J.P., Nick, R.J. and Cawse, J.N. (1997). Nonlinear e ects on yield and color for an intermediate in an industrial process. Polymer Testing 16, One response variable froma 26−1 design with 5 centre points used as a screen- ing design is given. Based on this analysis a three factor CCD was run and the results of this design are also given.
35. Thorsteindottir, M., Westerlund, D., Andersson, G. and Kaufmann, P. (1997).
Multivariate evaluation of the separation performance in micellar electrokinetic capillary chromatography of peptides—experimental screening. Chromatographia One response variable froma 29−5 design and froma D-optimal design that was used subsequently to investigate the interactions of some of the factors are given.
36. Tsirk, A., Gronowitz, S. and Hornfeldt, A.B. (1998). Multivariate optimization and mechanistic considerations of the amine induced ring-opening reaction of 2-alkyl-3-bromo-5- methylthiophene-1,1-dioxides. Tetrahedron 54, 1817–1834.
Three responses from15 experiments consisting of 8 factorial points, 4 axial points and 3 centre points are given, as is the response surface equation. Then some responses are given along the path of steepest ascent and from a two factor CCD with two centre points and a half-replicate.
37. Veglio, F. (1996). The optimization of manganese dioxide bioleaching media by fractional factorial experiments. Process Biochemistry 31, 773–785.
One response variable froma 27−3, a 25−1 (at two time points), and a replicated 23 (the validation study), are given.
38. Veglio, F., Beolchini, F. and Ubaldini, S. (1998). Empirical models for oxygen mass transfer—a comparison between shake ask and lab-scale fermenter and application to manganiferous ore bioleaching. Process Biochemistry 33, 367–376.
Results of a 33 factorial design are given. Since interactions were not signiÿ- cant, six further 33−1 FFDs on other factors were carried out and the data given.
The data for six 22 with one centre point factorial designs are given also.
39. Bodea, A. and Leucuta, S.E. (1998). Optimization of propranolol hydrochlo- ride sustained-release pellets using Box–Behnken design and desirability function.
Drug Development & Industrial Pharmacy 24, 145–155.
Four response variables froma three factor BBD with three centre points and the estimated equations are given. Some contour plots are given as is a table comparing the predicted and observed responses at the optimum settings.
T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 40. Chen, H.C. (1994). Response-surface methodology for optimizing citric acid fer- mentation by Aspergillus foetidus. Process Biochemistry 29, 399–405.
Two response variables froma three factor BBD with three centre points and the estimated equations are given. Some contour plots are given as is a table comparing the predicted and observed responses at the optimum settings.
41. Degroot, J.A., Doughty, A.T., Stewart, K.B. and Patel, R.M. (1994). E ects of cast ÿlmfabrication variables on structure development and key stretch ÿlmproperties.
Journal of Applied Polymer Science 52, 365–376.
Five response variables froma three factor BBD with three centre points are given, as well as the estimated equations obtained from three of these variables.
42. de la Maza, A., Manich, A.M., Coderch, L., Bosch, P. and Parra, J.L. (1995). The formation of liposomes in vitro by mixtures of lipids modeling the composition of the stratumcorneum. Colloids & Surfaces A–Physicochemical & Engineering Three response variables froma three factor BBD with three centre points and the estimated equations are given. Some contour plots are given.
43. de la Maza, A., Manich, A.M., Coderch, L., Baucells, J. and Parra, J.L. (1996).
Lipid composition in uence on the surfactant-induced release of the contents in liposomes formed by lipids modelling the stratum corneum. Colloids & Surfaces A—Physicochemical & Engineering Aspects 113, 259–267.
One response variable froma three factor BBD with three centre points is given, as well as the corresponding estimated equation. Some contour plots are given.
44. Goskonda, S.R., Hileman, G.A. and Upadrashta, S.M. (1994). Controlled release pellets by extrusion-spheronization. International Journal of Pharmaceutics 111, Two response variables, one collected at 4 time points, from a four factor BBD are given, as well as the estimated equations obtained. Two additional points were run to test for lack of ÿt and two batches were made at the optimal setting.
45. Guerrero, S., Alzamora, S.M. and Gerschenson, L.N. (1996). Optimization of a combined factors technology for preserving banana puree to minimize colour changes using the response surface methodology. Journal of Food Engineering One response variable froma three factor BBD with three centre points at each of ÿve time points is given, as well as the estimated equation obtained at each time point. Some contour plots are given.
46. Gulrajani, M.L. and Sinha, S. (1993). Studies in degumming of silk with aliphatic amines. Journal of the Society of Dyers & Colourists 109, 256–260.
Eight response variables collected froma three factor BBD with three centre points are given, as well as the corresponding estimated equations. Some contour plots are given as are the results of experiments performed at the optimum values.
47. Hierlemann, A., Weimar, U., Kraus, G., Schweizerberberich, M. and Gopel W.
(1995). Polymer-based sensor arrays and multicomponent analysis for the de- tection of hazardous organic vapours in the environment. Sensors & Actuators T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 This paper compares a full factorial, a BBD and an artiÿcial neural network for dealing with the problemin the title. They conclude that a BBD can reduce the calibration time by 90% with no reduction in resolution. No data are given.
48. Khan, M.A., Dib, J. and Reddy, I.K. (1996). Statistical optimization of ketoprofen- Eudragit(r) S100 coprecipitates to obtain controlled-release tablets. Drug Devel- opment & Industrial Pharmacy 22, 135–141.
Three response variables froma three factor BBD with three centre points are given as is one of the estimated equations obtained. Some contour plots are given and there is a comparison of the predicted and observed responses at the optimum 49. Patel, R.M., Butler, T.I., Walton, K.L. and Knight, G.W. (1994). Investigation of processing-structure-properties relationships in polyethylene blown ÿlms. Polymer Engineering & Science 34, 1506–1514.
One response variable froma three factor BBD with no centre points are given as is the corresponding estimated equation. Some contour plots are given.
50. Raghavan, C.V., Babu, R.S., Chand, N. and Rao, P.N.S. (1996). Response surface analysis of power consumption of dough sheeting as a function of gap, reduction ratio, water, salt and fat. Journal of Food Science & Technology-Mysore 33, Two response variables fromeach of ÿve three factor BBD with three centre points are given, as well as the estimated equations obtained by combining the 75 observations for each response variable. Various contour plots are given.
51. Sastry, S.V., Reddy, I.K. and Khan, M.A. (1997). Atenolol gastrointestinal ther- apeutic system: Optimization of formulation variables using response surface methodology. Journal of Controlled Release 45, 121–130.
Five response variables froma three factor BBD with three centre points are given as are the corresponding estimated equations. Some contour plots are given as well as the observed values at the calculated optimal setting.
52. Shah, R.D., Kabadi, M., Pope, D.G. and Augsburger, L.L. (1995). Physico- mechanical characterization of the extrusion-spheronization process. Part II: Rhe- ological determinants for successful extrusion and spheronization. Pharmaceutical Four response variables froma three factor BBD with three centre points are given. The estimated equation from one of these is given.
53. Singh, S.K., Dodge, J., Durrani, M.J. and Khan, M.A. (1995). Optimization and characterization of controlled release pellets coated with an experimental latex.I.
Anionic drug. International Journal of Pharmaceutics 125, 243–255.
Three response variables froma three factor BBD with three centre points are given as are the corresponding estimated equations. Some contour plots are 54. Wesling, P. and Emamjomeh, A. (1994). TAB Inner-lead bond process char- acterization for single-point laser bonding. IEEE Transactions on Components Packaging & Manufacturing Technology Part A 17, 142–148.
A three factor BBD was used to fabricate four sets of experimental samples that were used for as-fabricated testing, high-temperature aging and thermal cycling.
T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 Only as-fabricated results were reported (including second order response surface 55. Abdullah, B., Gardini, F., Paparella, A. and Guerzoni, M.E. (1994). Growth mod- elling of the predominant microbial groups in hamburgers in relation to the mod- ulation of atmosphere composition, storage temperature, and diameter of meat particle. Meat Science 38, 511–526.
Twenty replicates of each of the combinations of a three factor CCD with 6 centre points were prepared and analysed at various times. The maximum numbers obtained after ÿtting a Gompertz equation to this longitudinal data are given and analysed using a regression model. Several contour plots are given.
56. Altesor, C., Corbi, P., Dol, I. and Knochen, M. (1993). Application of experimen- tal design to the development of a multicomponent derivative spectrophotometric method: simultaneous determination of sulfamethoxazole and trimethoprim. Ana- Two response variables froma three factor CCD with one centre point are given. Second order response surfaces are discussed in the text but never given explicitly. Lastly, the accuracy and precision of analytical determinations was 57. Barnabas, I.J., Dean, J.R., Tomlinson, W.R. and Owen S.P. (1995). Experimental design approach for the extraction of polycyclic aromatic hydrocarbons from soil using supercritical carbon dioxide. Analytical Chemistry 67, 2064–2069.
One response variable froma blocked four factor CCD with six centre points are given. Statistics on lack of ÿt for linear, quadratic and cubic response surfaces are given, as are the coe cients for the quadratic model ÿtted.
58. Bautista, D.A., Sylvester, N., Barbut, S. and Gri ths, M.W. (1997). The deter- mination of e cacy of antimicrobial rinses on turkey carcasses using response surface designs. International Journal of Food Microbiology 34, 279–292.
Responses fromthree two factor CCDs, the equations obtained, and the corre- sponding response surfaces are given.
59. Bergman, I., Svensson, B.H. and Nilsson, M. (1998). Regulation of methane pro- duction in a Swedish acid mire by pH, temperature and substrate. Soil Biology The e ects of three factors on methane production for the upper and lower levels of three samples (6 scenarios) are measured where the factors were varied accord- ing to a CCD with the number of runs varying from 14 to 18. Signiÿcant regres- sion coe cients are given for each of the scenarios. No designs or data are given.
60. Brown-Brandl, T.M., Beck, M.M., Schulte, D.D., Parkhurst, A.M. and Deshazer, J.A. (1997). Physiological responses of tom turkeys to temperature and humidity change with age. Journal of Thermal Biology 22, 43–52.
Results froma three factor uniform-precision, rotatable CCD are discussed. The estimated equations are presented, as are some graphs of responses but the original T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 61. Chaair, H., Heughebaert, J.C., Heughebaert, M. and Vaillant, M. (1994). Statis- tical analysis of apatitic tricalciumphosphate preparation. Journal of Materials Three response variables froma six factor CCD with 3 centre points and using a half replicate are given. The coe cients of second order response surface for 62. Collar, C. and Martinez, C.S. (1993). Amino acid proÿles of fermenting wheat sour doughs. Journal of Food Science 58, 1324–1328.
For each of two conditions (yeast present and absent) a three factor CCD with 1 centre point was carried out and the amino acid proÿle, consisting of informa- tion on 23 amino acids, is given for each run. These proÿles are compared using factor analysis. Plots summarising the ÿndings are given.
63. Dredan, J., Zelko, R., Antal, I., Bihari, E. and Racz, I. (1998). E ect of particle size and coating level on the di use re ectance of wax matrices. Journal of Phar- macy & Pharmacology 50, 139–142.
The response variable froma two factor, face-centred CCD and the correspond- ing estimated equation are given. A plot of the response is given.
64. Fedina, L.T., Zelko, R., Fedina, L.I., Szabados, Z.S., Szanto, M. and Vakulya G.
(1997). The e ect of surfactant and suspending agent concentration on the e ec- tive particle size of metered-dose inhalers. Journal of Pharmacy & Pharmacology The response variable froma two factor, face-centred CCD is given, as is the estimated second-order response surface. The surface is plotted.
65. Haltrich, D., Laussamayer, B., Steiner, W., Nidetzky, B. and Kulbe, K.D. (1994).
Cellulolytic and hemicellulolytic enzymes of Sclerotium rolfsii—optimization of the culture medium and enzymatic hydrolysis of lignocellulosic material. Bio- Two replicates of one response variable froma two factor CCD with two centre points are given. A graph of the ÿtted response surface design is given, together with the predicted equation. The optimum conditions were veriÿed by experiment.
66. Hasnat, K., Murtaza, S. and Tasch A.F. (1994). A Manufacturing sensitivity anal- ysis of 0:35 mLDD MOSFET’s. IEEE Transactions on Semiconductor Manu- A half fraction of a seven factor rotatable CCD with 1 centre point was used but the experimental data are not given. Second order response surface equations are given for six electrical responses. The statistical distribution of electrical para- meters was predicted via a Monte Carlo approach using these response surface 67. Jimenez, L., Delatorre, M.J., Maestre, F., Ferrer, J.L. and Perez, I. (1997). Organo- solv pulping of wheat straw by use of phenol. Bioresource Technology 60, Six response variables froma three factor CCD with one centre point are given.
The analysis and a discussion are included.
68. Jimenez, L., Maestre, F., Delatorre, M. and Perez I. (1997). Organosolv pulping of wheat straw by use of methano-water mixtures. TAPPI Journal 80, 148–154.
T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 Five response variables froma three factor CCD with no centre points are given. The analysis and a discussion are included.
69. Jimidar, M., Hamoir, T., Degezelle, W., Massart, D.L., Soykenc, S. and Van- dewinkel, P. (1993). Method development and optimization for the determination of rare earth metal ions by capillary zone electrophoresis. Analytica Chimica Acta Three response variables froma two factor CCD with 1 centre point are given.
Quadratic response surface equations and some graphical displays of them are 70. Kleinebudde, P. and Lindner, H. (1993). Experiments with an instrumented twin- screw extruder using a single-step granulation=extrusion process. International Journal of Pharmaceutics 94, 49–58.
Five response variables fromtwo replicates of a two factor CCD with one centre point are given, as are the ÿtted equations and some response surface 71. Liadakis, G.N., Tzia, C., Oreopoulou, V. and Thomopoulos, C.D. (1998). Isola- tion of tomato seed meal proteins with salt solutions. Journal of Food Science 63, Four response variables froma two factor CCD with 5 centre points, and a full 72. Llompart, M.P., Lorenzo, R.A., Cela, R. and Pare, J.R.J. (1997). Optimization of a microwave-assisted extraction method for phenol and methylphenol isomers in soil samples using a central composite design. Analyst 122, 133–137.
Four response variables froma three-factor, face-centered CCD with three cen- tre points are given. Some coding errors appear to have been made in the CCD.
73. Mager, P.P. (1997). How design statistics concepts can improve experimentation in medicinal chemistry. Medicinal Research Reviews 17, 453–475.
This is a tutorial paper with some applications and is suitable as supplemen- tary material in a post-graduate experimental design course (honours or above).
Some designs and actual data from medicinal chemistry are given for illustrative 74. Oh, S., Rheem, S., Sim, J., Kim, S. and Baek, Y. (1995). Optimizing conditions for the growth of Lactobacillus casei YIT 9018 in tryptone-yeast extract-glucose medium by using response surface methodology. Applied & Environmental One response variable froma ÿve factor CCD with 8 centre points in two blocks is given. The estimated equation for an adequate model is given. Partial 75. Ostberg, T. and Gra ner, C. (1994). Calcium alginate matrices for oral multiple unit administration 3. In uence of calcium concentration, amount of drug added and alginate characteristics on drug release. International Journal of Pharmaceu- Eight response variables froma two factor uniformprecision CCD with ÿve centre points are given, as are the estimated equations and some response surface T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 graphs. Three combinations of levels not used in the experiment were used to conÿrmthe predictive capabilities of the model.
76. Ruchatz, F., Kleinebudde, P. and Muller, B.W. (1997). Residual solvents in bio- degradable micro-particles, in uence of process parameters on the residual solvent in microparticles produced by the aerosol solvent extraction system (ASES) process. Journal of Pharmaceutical Sciences 86, 101–105.
Six responses froma two factor CCD with 2 centre points and the axial points replicated twice are given. For each response the response surface coe cients are given, as are some appropriate plots.
77. Saim, N., Dean, J.R., Abdullah, M.P. and Zakaria, Z. (1998). An experimental design approach for the determination of polycyclic aromatic hydrocarbons from highly contaminated soil using accelerated solvent extraction. Analytical Chem- Seventeen response variables froma three factor CCD with 2 centre points are given, along with the estimated response surface coe cients.
78. Sen, R. and Swaminathan, T. (1997). Application of response-surface methodol- ogy to evaluate the optimum environmental conditions for the enhanced production of surfactin. Applied Microbiology & Biotechnology 47, 358–363.
One response variable froma four factor CCD with 6 centre points, the esti- mated equation and contour plots are given.
79. Varesio, E., Gauvrit, J.Y., Longeray, R., Lanteri, P. and Veuthey, J.L. (1998).
Central composite design in the chiral analysis of amphetamines by capillary electrophoresis. Electrophoresis 18, 931–937.
Four response variables froma face-centred ÿve factor CCD with two centre points and using a half-replicate are given. The second-order response surface coe cients and plots for each of the four responses are given.
80. Zaman, A.A. and Fricke, A.L. (1996) E ect of pulping variables on enthalpy of kraft black liquors: empirical predictive models. Industrial & Engineering Chem- Two response variables froma four factor CCD with 1 centre point are given but are missing for two of the axial points. The coe cients for two second-order response surfaces and some contour plots are given.
81. Zeng, X.M., Martin, G.P. and Marriott, C. (1994). Tetrandrine delivery to the lung: the optimisation of albumin microsphere preparation by central composite design. International Journal of Pharmaceutics 109, 135–145.
Average responses froma three factor CCD with 6 centre points, the ÿtted equation and several response surface plots are given.
82. Abuzarur-Aloul, R., Gjellan, K., Sjolund, M. and Gra ner, C. (1998). Critical dissolution tests of oral systems based on statistically designed experiments. II. In vitro optimization of screened variables on ER-coated spheres for the establishment of an in vitro=in vivo correlation. Drug Development and Industrial Pharmacy T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 IV +4 centre points design was used to gain knowledge about “how a solid systemreleases its drug content in the gastrointestinal tract”. Percent dissolved remoxipride was measured for each experiment at 30, 60, 120, 360, and 720 minutes but is not given. The observed dissolution proÿles in vitro and in vivo are presented. Lastly an in vitro=in vivo correlation was established.
83. Alves, L.A., Felipe, M.G.A., Silva, J.B.A.E., Silva, S.S. and Prata, A.M.R. (1998).
Pretreatment of sugarcane bagasse hemicellulose hydrolysate for xylitol produc- tion by Candida Guilliermondii. Applied Biochemistry and Biotechnology 70, Average responses of two replicates of a 25−1 design are given. The two active factors were used in a 22 design with a centre face and three replicates at the centre point, and the data are given. Coe cients for response surfaces are given 84. Araujo, P.W. and Brereton, R.G. (1996). Experimental Designs.1. Screening.
TRAC—Trends In Analytical Chemistry 15, 26–31.
A general introduction written for chemists with references to uses of de- signs in chemical experiments in the literature. Includes the results of one 27−3 85. Bafna, S.S. and Beall, A.M. (1997). A design of experiments study on the factors a ecting variability in the melt index measurement. Journal of Applied Polymer design with three replicates, one for High Melt Index and one for Low Melt Index, are given.
86. Bauer, C. and Rombke, J. (1997). Factors in uencing the toxicity of two pesticides on three lumbricid species in laboratory tests. Soil Biology and Biochemistry 29, For each of 9 scenarios, a 25−1 design was used and three response variables observed but are not given. Some plots on % di erence to initial weight are given.
No ANOVAs or equations are given. Tests were done at day 14 and day 28.
87. Cestari, A.R., Bruns, R.E. and Airoldi, C. (1996). A fractional factorial design applied to organofunctionalized silicas for adsorption optimization. Colloids and Surfaces A-Physicochemical and Engineering Aspects 117, 7–13.
Results of two replicates of a 24−1 are presented, as well as a discussion of how the levels for the factors were determined.
88. Chen, G.Q. and Gouaux, E. (1997). Overexpression of a glutamate receptor (GluR2) ligand binding domain in Escherichia coli: application of a novel protein folding screen. Proceedings of the National Academy of Sciences of the United States of America 94, 13431–13436.
Three response variables froma 212−8 89. Chien, T.W., Lin, C.H. and Sphicas, G. (1997). A systematic approach to de- termine the optimal maintenance policy for an automated manufacturing system.
Quality and Reliability Engineering International 13, 225–233.
A thorough discussion of the steps involved in determining the factors and levels for a FFD. The results of a 25−1 are presented and discussed.
T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 90. Choueiki, M.H., Mountcampbell, C.A. and Ahalt, S.C. (1997). Building a quasi optimal neural network to solve the short-term load forecasting problem. IEEE Transactions on Power Systems. 12, 1432–1439.
A ‘quasi optimal’ neural network was built from the analysis of a 210−4 sign used to solve the aforementioned problem. Only signiÿcant e ects and their 91. Cohen, D. (1997). In uence, of ÿlament winding parameters on composite vessel quality and strength. Composites Part A—Applied Science and Manufacturing Seven response variables froma 25−2 design with one replicated run are given.
Excellent discussion of all phases of the experiment.
92. Dauneau, P. and Perezmartinez, G. (1997). Fractional factorial design and multiple linear regression to optimise extraction of volatiles from a lactobacillus plantarumbacterial suspension using purge and trap. Journal of Chromatography.
One response variable froma 24−1 with 3 centre points is given and 93. Davis, B.L., Cavanagh, P.R., Sommer, H.J. and Wu, G. (1996). Ground reaction forces during locomotion in simulated microgravity. Aviation Space and Environ- Describes a 4 × 3 × 3 × 2 fractionated design. Results are given as averages or 94. Donahue, D.W., Sowell, R.S. and Bengtson, N.M. (1996). Simulation of alterna- tive agricultural marketing systems. Agricultural Systems 51, 395–406.
Several marketing systems were developed and the e ect of a number of factors on the systems was determined using a FFD. Neither responses nor parameter 95. Eilamo, M., Kinnunen, A., Latvakala, K. and Ahvenainen, R. (1998). E ects of packaging and storage conditions on volatile compounds in gas-packed poultry meat. Food Additives and Contaminants 15, 217–228.
Ten response variables froma 21×36−4 FFD are given. Seven replicate samples were packed for each experiment. “Two of these were tested for microbial content, three for sensory quality and the other two for volatiles contents after the storage interval determined by the experimental design”.
96. Ekblad, A., Wallander, H., Carlsson, R. and Huss-danell, K. (1995). Fungal biomass in roots and extramatrical mycelium in relation to macronutrients and plant biomass of ectomycorrhizal. Pinus sylvestris and Alnus incana. New Phyto- Six macronutrients were arranged in a 26−2 FFD in pots and each combination replicated 12 times. Half of the pots were non-mycorrhizal and half inoculated with P. involutus. The pots were paired and arranged in a climate chamber in randomised blocks. Results are presented graphically.
97. Ellekjaer, M.R., Ilseng, M.A. and Naes, T. (1996). A case study of the use of ex- perimental design and multivariate analysis in product improvement. Food Quality T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 Compares design results to results of a principal components analysis on the same data set. The FFD was a 27−2 and some centre points and reference samples were also included. Results are given in normal plots and in tables indicating signiÿcant e ects. Plots of scores and loading are also given.
98. Fallman, A.M. (1997). Performance and design of the availability test for mea- surement of potentially leachable amounts from waste materials. Environmental Science and Technology 31, 735–744.
design was initially used but a foldover to a 26−2 sary. Forty-four di erent response variables were evaluated in these experiments.
Evaluations were based on a multiplicative model and the models parameters are given. Normality was assumed. The data are not given.
99. Feldman, H.A., McKinlay, J.B., Potter, D.A., Freund, K.M., Burns, R.B., Moskowitz, M.A. and Kasten, L.E. (1997). Nonmedical in uences on medical decision making: an experimental technique using videotapes, factorial design and survey sampling. Health Services Research 32, 343–366.
64 videos were made according to a 28−2 FFD and then paired to be shown to physicians who were asked to say what further diagnostic evaluation they would recommend and what options they would o er to the patients. Results are given 100. Garea, A., Fernandez, I., Viguri, J.R., Ortiz, M.I. Fernandez, J., Renedo, M.J. and Irabien J.A. (1997). Fly-ash calciumhydroxide mixtures for SO2 removal: struc- tural properties and maximum yield. Chemical Engineering Journal 66, Three response variables froma 25−1 design with 5 centre points are given.
101. Gates, T.K. and Alzahrani, M.A. (1996). Spatiotemporal stochastic open-channel ow.2. Simulation experiments. Journal of Hydraulic Engineering 122, 652–661.
Discusses the use of a 29−2 FFD in doing Monte Carlo simulation experiments.
Results are discussed and some parameter estimates given.
102. Glaser, R.A. and Shulman, S.A. (1996). Study of variables a ecting extraction of organic solvents from solid sorbent sampling media using supercritical carbon dioxide. Chromatographia 42, 665–674.
Some responses for a non-orthogonal FFD where collection was limited by instrument are given, as well as parameter estimates for some of the ÿtted poly- 103. Henderson-Sellers, B. and Henderson-Sellers, A. (1996). Sensitivity evaluation of environmental models using fractional factorial experimentation. Ecological Mod- Discusses the beneÿts of FFD over the designs traditionally used for sensitivity testing. Includes three references to earlier studies.
104. Joo, H.K., Hool, J.N. and Curtis, C.W. (1998). ANOVA Analysis of two-stage coprocessing of low-density polyethylene, coal, and petroleumresid. Energy and A 3 × 23−1 design was used to evaluate reaction parameters used in two-stage co-processing. A 33−1 design with duplication after one week for four of the experiments was used to determine the e ect of H2 pressure and coal content.
T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 The aliasing structure was given for both designs. Data are given along with some of the ANOVAs for a subset of the response variables measured.
105. Khundker, S., Dean, J.R. and Jones, P. (1995). A comparison between solid phase extraction and supercritical uid extraction for the determination of ucona- zole fromanimal feed. Journal of Pharmaceutical and Biomedical Analysis 13, Results and discussion of two 24−1 FFDs.
106. Kinoshita, E., Sugimoto, T., Ozawa, Y. and Aishima, T. (1998). Di erentiation of soy sauce produced fromwhole soybeans and defatted soybeans by pattern recog- nition analysis of HPLC Proÿles. Journal of Agricultural and Food Chemistry 46, Results froma 25−1 design with 3 replicates of one point are given. Principal components were calculated separately for the two soy sauce data sets. Cluster analysis was performed on the HPLC proÿles.
107. Lenk, P.J., Desarbo, W.S., Green, P.E. and Young, M.R. (1996). Hierarchical Bayes conjoint analysis: recovery of partworth heterogeneity fromreduced exper- imental designs. Marketing Science 15, 173–191.
This paper compares the estimates obtained from a main e ects design and a subset of such a design. Parameter estimates are given for two sets of data.
108. Loukas, Y.L. (1997). 2(K−P) fractional factorial design via fold over: applica- tion to optimization of novel multicomponent vesicular systems. Analyst 122, Two response variables froma 26−2 design are given. An additive linear model in the main e ects was ÿtted for both sets of data. Diagnostic plots of residuals and Pareto charts of e ects are presented.
109. Loukas, Y.L. (1998). A computer-based expert system designs and analyzes a 2k−p fractional factorial design for the formulation optimization of novel multi- component liposomes. Journal of Pharmaceutical and Biomedical Analysis 17, Two response variables froma 24−1 and coe cients for the linear equations ÿtted to the two responses are given.
110. Loukas, Y.L. (1998). Experimental studies for screening the factors that in u- ence the e ectiveness of new multicomponent and protective liposomes. Analytica One response variable froma 26−3 FFD and its foldover are given. A discussion of the choice of factors and factor levels is given and an analysis and discussion 111. Moon, H.S. and Na, S.J. (1997). Optimum design based on mathematical model and neural network to predict weld parameters for ÿllet joints. Journal of Man- Five responses froma 25−1 design are given. On the basis of the results, a systemwas developed to estimate the welding process variables’ “e ect on the ÿllet welded joint shape using the neural network and optimum design”.
112. Nascimento, I.C., Deoliveira, A.E. and Bruns, R.E. (1998). A statistical approach of density functional e ects on the vibrational frequencies and infrared T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 intensities of Ch3F. Spectrochimica Acta Part A—Molecular and Biomolecular Six response variables froma 25−1 FFD are given and used to determine more accurate wave functions. Results obtained for all frequency and intensity values were analysed using principal components analysis.
113. Oles, P.J. (1998). Fractional factorial experimental design as a teaching tool for quantitative analysis. Journal of Chemical Education 75, 357–359.
The application presented is gravimetric determination of chloride by precipi- tation with Ag+ ion and results froma 25−2 design are given.
114. Oppewal, H., Louviere, J.J. and Timmermans, J.P. (1994). Modeling hierarchi- cal conjoint processes with integrated choice experiments. Journal of Marketing This paper describes the use of fractional factorial designs to describe travel options and shopping centre options to consumers, and hence to establish the e ect of each of various factors on their choices.
115. Osborne, L.M. and Miyakawa, T.W. (1997). Use of experimental design in the optimization of hplc methodology for the separation of stereoisomers. Journal of Liquid Chromatography and Related Technologies 20, 501–509.
Four response variables froma 24−1 design with 3 centrepoints are given.
116. Renard, C.M.G.C., Lemeunier, C. and Thibault, J.F. (1995). Alkaline extraction of xyloglucan from depectinised apple pomace—optimisation and characterisation.
Carbohydrate Polymers 28, 209–216.
Gives the results of a 25−2 design with 2 centre points. A discussion of why a 117. Rustom, I.Y.S., Foda, M.I. and Lopezleiva, M.H. (1998). Formation of oligosac- charides from whey UF-permeate by enzymatic hydrolysis—analysis of factors.
Four response variables froma 24−1 design for each of three di erent enzymes 118. Slaveykova, V.I. and Hoenig, M. (1997). Electrothermal atomic absorption spec- trometric determination of lead and tin in slurries. Optimization study. Analyst Four response variables froma 27−3 design are given. Some interaction dia- grams are presented for confounded terms and estimated e ects also given.
119. Smith, B.C., Penrod, S.D., Otto, A.L. and Park, R.C. (1996). Jurors use of prob- abilistic evidence. Law and Human Behavior 20, 49–82.
Sixteen videos of a simulated rape trial were made according to a 27−3 although one factor could not be orthogonally confounded. The responses were mock jurors’ assessment of the guilt of the defendent at ÿve time points. Raw results are not available but analyses at each time point and across the time points are given.
120. Thorsteinsdottir, M., Westerlund, D., Andersson, G. and Kaufmann, P. (1998).
Chemometric evaluation of the band broadening in micellar electrokinetic chro- matography of peptides. Journal of Chromatography A 809, 191–201.
One response variable fromeach of three 25−2 FFD with centre points, as well as various estimated parameters and response surface plots, are given.
T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 121. Vepa, T.S. and George, K.P. (1997). De ection response models for cracked rigid pavements. Journal of Transportation Engineering—ASCE 123, 377–384.
This paper discusses the development of a model for describing the de ection of cracked rigid pavements. Eight factors are identiÿed as being important and a 24−3 × 34 design is used to determine a database of results from which a regression model is developed. The results from the regression model are then compared with actual results from two test pavements. The estimated parameters are given as are graphs which indicate the agreement between the predicted and 122. Woodside, A.G., Breaux, R. and Briguglio, E. (1998). Testing care-giver accep- tance of new syringe technologies. IJTM Special Issue on Management of Tech- This paper describes the use of fractional factorial designs to establish options to present to care-givers to establish which syringe types they prefer.
123. Yang, G.C.C. and Tsai, C.M. (1998). A study on heavy metal extractability and subsequent recovery by electrolysis for a municipal incinerator y ash. Journal of Hazardous Materials 58, 103–120.
One response variable froma 24−1 and froma 23−1 are given. E ect estimates, normal probability plots and some results plots are all given.
124. Yang, H.J. and Yang, C.H. (1998). Statistical experimental strategies approach to emulsion copolymerization of styrene and n-butyl acrylate. Journal of Applied Six response variables froma 25−1 experiment are given. Univariate analyses of each response are given and discussed.
125. Zhang, H., Lunsford, S.K., Marawi, I., Rubinson, J.F. and Mark, H.B. (1997).
Optimization of preparation of poly(3-Methylthiophene)-modiÿed pt microelec- trodes for detection of catecholamines. Journal of Electroanalytical Chemistry A 25−1 design was used for two di erent experiments and the data are given.
Each experiment has two response variables, one being dichotomous.
126. ∗Zhang, S. and Forssberg, E. (1998). Optimization of electrodynamic separation for metals recovery from electronic scrap. Resources Conservation and Recycling One response variable froma 24−4 signiÿcant interaction e ect was clariÿed by conducting 4 additional runs.
127. Zhu, Y., Knol, W., Smits, J.P. and Bol, J. (1996). Medium optimization for nu- clease p1 production by penicilliumcitrinumin solid-state fermentation using polyurethane foamas inert carrier. Enzyme and Microbial Technology 18, One response variable fromeach of two 27−4 experiments are given. The second experiment uses di erent levels, based on the results of the ÿrst experiment.
128. Zipper, P., Janosi, A., Wrentschur, E., Geymayer, W., Ingolic, E. Friesenbichler, W. and Eigl, F. (1997). Wide-angle X-Ray, densitometric and microscopical stud- ies on injection molded Polypropylene disks. International Polymer Processing T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 One response variable froma 25−3 design is given.
129. Boonkerd, S., Detaevernier, M.R., Heyden, Y.V., Vindevogel, J. and Michotte, Y. (1996). Determination of the enantiomeric purity of dexfen uramine by capil- lary electrophoresis: use of a Plackett–Burman design for the optimization of the separation. Journal of Chromatography 736, 281–289.
Four responses from2 ÿve-factor, 8 run PBDs are given, as well as the esti- mated e ects. The repeatability of the optimal settings was determined.
130. Bullington, R.G., Lovin, S., Miller, D.M. and Woodall, W.H. (1993). Improve- ment of an industrial thermostat using designed experiments. Journal of Quality This is a case study of an eleven-factor, 12-run PBD. The responses are given and some possible analyses discussed.
131. Castro, P.M.L., Ison, A.P., Hayter, P.M. and Bull, A.T. (1996). CHO cell growth and recombinant interferon- production: e ects of BSA, Pluronic and lipids.
A four-factor 8 run PBD was used to construct 8 culture media. To each of these culture media di erent combinations of a lipid mixture and Pluronic F68 was added. The responses for these media are given.
132. Chehbouni, A., Chaouki, J., Guy, C. and Klvana, D. (1995). E ects of di erent parameters on the onset of uidization in a turbulent regime [French]. Canadian Journal of Chemical Engineering 73, 41–50.
One response froma four-factor 8 run PBD, and the corresponding analysis, are given. The authors compare the model that they have developed with other 133. Dung, N.V. (1995). Factors a ecting product yields and oil quality during retorting of Stuart oil shale with recycled shale: a screening study. Fuel 74, 623–627.
Seven response variables froma seven-factor, 8 run PB design are given. It is clear fromthe paper that some of the factors can not be held at exactly the levels determined and the actual levels observed are given. The signiÿcant factors for each of the responses are identiÿed.
134. Durig, T. and Fassihi, A.R. (1993). Identiÿcation of stabilizing and destabilizing e ects of excipient-drug interactions in solid dosage formdesign. International Journal of Pharmaceutics 97, 161–170.
Thirteen factors were investigated using a 24 run PB design. Responses are given as well as the estimated factor e ects.
135. Irvine, G.M. Clark, N.B. and Recupero, C. (1996). Extended deligniÿcation of mature and plantation eucalypt wood Part 2: the e ects of chip impregnation factors. Appita Journal 49, 347–352.
One response froma 14 factor, 16-run PBD is given.
136. Lavilla, I., Perez-Cid, B. and Bendicho, C. (1998). Optimization of digestion methods for sewage sludge using the Plackett–Burman saturated design. Fresenius Journal of Analytical Chemistry 361, 164–167.
T. Prvan, D.J. Street / Journal of Statistical Planning and Inference 106 (2002) 245–269 Five responses for three experiments, a six-factor, a ÿve-factor and a four-factor, PBD are given, as are the estimated e ects. The accuracy of the method was conÿrmed using a sample of known composition.
137. Poorna, V. and Kulkarni, P.R. (1995). A study of inulinase production in Aspergillus niger using fractional factorial design. Bioresource Technology 54, One response variable froma 15-factor, 16-run PB is given.
138. Rogan, M.M., Altria, K.D. and Goodall, D.M. (1994). Plackett–Burman experi- mental design in chiral analysis using capillary electrophoresis. Chromatographia Three response variables froma four-factor, three-level, 15-run PBD are given, as are the estimated percentage main e ects for each of the responses.
139. Srinivas, M.R.S., Chand, N. and Lonsane, B.K. (1994). Use of Plackett–Burman design for rapid screening of several nitrogen sources, growth product promoters, minerals and enzyme inducers for the production of alpha-galactosidase by As- pergillus niger MRSS-234 in solid state fermentation system. Bioprocess Longitudinal results for three responses froma nineteen-factor, 20 run PBD are presented. The estimated coe cients for one of the responses, at each of four 140. Stevens, T.O. (1995). Optimization of media for enumeration and isolation of aerobic heterotrophic bacteria fromthe deep terrestrial subsurface. Journal of Microbiological Methods 21, 293–303.
A twelve-factor 16-run PBD was used and the estimated e ects of each of the factors, for each of 10 samples, are given.
141. Taillandier, P., Gilis, F., Portugal, F.R., Laforce, P. and Strehaiano, P. (1996).
In uence of medium composition, pH and temperature on the growth and viability of Lactobacillus acidophilus. Biotechnology Letters 18, 775–780.
Three response variables froma seven-factor 8-run PBD, augmented with 4 centre points, are given. Estimated equations are given, as well as Pareto charts 142. Van Driessche, I., Persyn, F., Fiermans, L. and Hoste, S. (1996). A statistical Plackett–Burman design of the thermal process in the synthesis of the Bi-2223 HTSC. Superconductor Science & Technology 9, 843–848.
Four response variables froma 10 factor, 16-run PBD are given. Large values for some dummy factors suggest signiÿcant two factor interactions so a larger design was used but only summary results for this are given.
143. Veress, T. (1993). Study of the extraction of LSD fromillicit blotters for HPLC determination. Journal of Forensic Sciences 38, 1105–1110.
One response varible froma four factor, 8-run PBD is given.
The authors thank Dr. R.J. Ritchie for helping to classify the papers by area. D.J.
Street gratefully acknowledges support froma UTS Incentive Grant.
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