One-Factor-at-a-Time Versus Designed Experiments - imag.fr

1 One-Factor-at-a-Time Versus Designed Experiments Veronica CZITROM. helpful to use examples of real engineering OFAT experi- ments, and to compare the OFATs to Designed Experiments Many engineers and scientists perform One-Factor-at-a-Time to illustrate why the latter would have been better. It is (OFAT) Experiments . They will continue to do so until they important to describe the disadvantages of OFAT experi- understand the advantages of Designed Experiments over mentation early in an industrial workshop, so students do OFAT Experiments , and until they learn to recognize OFAT not drop out of the course to do more important things. Experiments so they can avoid them. A very effective way College textbooks, which present a fair amount of statis- to illustrate the advantages of Designed Experiments , and tics up front, often introduce OFAT Experiments later: Box, to show ways in which OFAT Experiments present them- Hunter, and Hunter (1978, pp.)

2 312 and 510); Montgomery selves in real life, is to introduce real examples of OFAT (1997, p. 201); and Mason, Gunst, and Hess (1989, p. 101). Experiments and then demonstrate why a Designed experi- The first morning of the three-day design of Experiments ment would have been better. Three engineering examples industrial workshop is an overview. The overview starts of OFAT Experiments are presented, as well as Designed ex- with a brief description of what Designed Experiments are, periments that would have been better. The three examples what they are used for, and how the rest of the industry uses have been successfully used in an industrial workshop and them. The core of the overview is a complete, real example can also be used in academic courses.

3 (23 with center points) that is used to introduce the basic KEY WORDS: Teaching statistics. concepts, including description of the process, planning the experiment , conducting the experiment , analyzing the data with main effect and interaction plots, and reaching conclu- sions and implementing recommendations. The example is followed by a section on Why DOE Works or Why it is 1. INTRODUCTION. Possible to Study Several factors Simultaneously and Still Engineers and scientists often perform one-factor-at-a- Get Useful Information. The overview ends with a sec- time (OFAT) Experiments , which vary only one factor or tion on the advantages of Designed Experiments over OFAT. variable at a time while keeping others fixed. However, sta- Experiments , which will be described in this article.

4 Tistically Designed Experiments that vary several factors si- The student reaction to the overview is very positive. The multaneously are more efficient when studying two or more material is stripped down to bare essentials, and is illus- factors . trated by real-life examples they can relate to. In the au- That is what statisticians know. But in industry, they need thor's experience, this goes a long way toward convincing to be able to convince adult, practicing engineers that what engineers (and managers) to use Designed Experiments . they have been doing for years can be improved upon. This Section 2 describes advantages of Designed Experiments is particularly true because engineers usually have higher over OFAT Experiments , and Section 3 gives three examples standing in the company than statisticians from the Qual- that illustrate these advantages.

5 Section 4 is a summary. The ity Assurance Department, and hence may be inclined to OFAT examples can be used in both academic and industrial discount the statisticians' advice unless they understand it. design of Experiments courses. The examples are semicon- Also, engineers need to learn to recognize OFAT experi- ductor industry Experiments , and they can easily be adapted ments in order to avoid them. When teaching an academic for use in other areas. course, it is important to convince engineering and science students that Designed Experiments are relevant to their ap- plications, and to give statistics students (some of whom 2. ADVANTAGES OF DOE OVER OFAT. will work in industry) a better understanding of practical Experiments . considerations.

6 A Designed experiment is a more effective way to deter- In teaching a three-day design of Experiments workshop mine the impact of two or more factors on a response than for engineers in industry, the author has found it extremely a OFAT experiment , where only one factor is changed at one time while the other factors are kept fixed, because: Veronica Czitrom is a Distinguished Member of Technical Staff at Bell It requires less resources ( Experiments , time , material, Laboratories, Lucent Technologies, 9333 S. John Young Parkway, Orlando, etc.) for the amount of information obtained. This can be FL 32819 (Email: The author thanks Osvaldo Ro- driguez, Juan Becerro, and Charles Storey for their contributions to the of major importance in industry, where Experiments can be article.)

7 Very expensive and time consuming. 126 The American Statistician, May 1999, Vol. 53, No. 2 c 1999 American Statistical Association Table 1. OFAT experiment in two factors in three runs, with Table 2. Full factorial Designed experiment in two factors at two levels 16 of the 48 wafers at each run each in four runs, with 12 of the 48 wafers at each run Temperature Temperature Pressure Standard New Pressure Standard New Standard 16 wafers 16 wafers Standard 12 wafers 12 wafers New 16 wafers New 12 wafers 12 wafers The estimates of the effects of each factor are more The interaction between temperature and pressure (differ- precise. Using more observations to estimate an effect re- ence between the effect of temperature on the response at sults in higher precision (reduced variability).)

8 For example, the standard pressure and the effect of temperature on the for full and fractional factorial designs, all the observations response at the new pressure) cannot be estimated because are used to estimate the effect of each factor and each inter- there is no information at the new pressure with standard action (property of hidden replication), while typically only temperature. two of the observations in a OFAT experiment are used to Table 2 shows a Designed experiment that could have estimate the effect of each factor. been performed, a 22 full-factorial with two factors (tem- The interaction between factors can be estimated sys- perature and pressure) at two levels each (standard and new). tematically. Interactions are not estimable from OFAT ex- in four runs.

9 Twelve of the 48 wafers are used for each run, periments. Engineers who are not using Designed experi- which allows 12 replications of the four-run 22 full fac- ments often perform a hit-and-miss scattershot sequence of Experiments from which it may be possible to estimate in- torial experiment . To study the effect of temperature, the teractions, but they usually do not estimate them. standard temperature is compared to the new temperature There is experimental information in a larger region using the 12 + 12 = 24 wafers at the standard pressure, and of the factor space. This improves the prediction of the re- the standard temperature is compared to the new temper- sponse in the factor space by reducing the variability of the ature using the 12 + 12 = 24 wafers at the new pressure.

10 Estimates of the response in the factor space, and makes The average of the two comparisons is the main effect of process optimization more efficient because the optimal so- temperature, and the difference between the two compar- lution is searched for over the entire factor space isons is the interaction between temperature and pressure. The interaction graph between temperature and pressure is These concepts are now illustrated using three examples. shown in Figure 2. All 48 wafers are used to study the ef- 3. EXAMPLES fect of temperature, and to estimate the interaction between temperature and pressure. Two factors in Three Runs An engineer planned an experiment to compare pressure and temperature for a standard gas anneal process and a new gas anneal process using three experimental runs: 1.