Summarize example 1.2 of the example applications of experimental design by determining the statement of the problem, objectives, choice of the response, variable, factors, design process. EXAMPLE 1.2Optimizing a Processat 145°F and 2.1 hours of reaction time, producing yieldsof around 80 percent. Figure 1.9 shows a view of thetime-temperature region from above. In this graph, thelines of constant yield are connected to form responsecontours, and we have shown the contour lines for yieldsof 60, 70, 80, 90, and 95 percent. These contours are pro-In a characterization experiment, we are usually interestedin determining which process variables affect the response.A logical next step is to optimize, that is, to determine theregion in the important factors that leads to the best possi-ble response. For example if the response is yield, wewould look for a region of maximum yield, whereas if theresponse is variability in a critical product dimension, we jections on the time-temperature region of cross sectionswould seek a region of minimum variability.Suppose that we are interested in improving the yieldof a chemical process. We know from the results of a char-acterization experiment that the two most importantprocess variables that influence the yield are operatingtemperature and reaction time. The process currently runsof the yield surface corresponding to the aforementionedpercent yields. This surface is sometimes called aresponse surface. The true response surface in Figure 1.9is unknown to the process personnel, so experimentalmethods will be required to optimize the yield withrespect to time and temperature.FIGURE 1.9 Contour plot of yield as afunction of reaction time and reaction temperature,illustrating experimentation to optimize a processSecond optimization experiment200Path leadingto region ofhigher yieldTo locate the optimum, it is necessary to perform anexperiment that varies both time and temperature together,that is, a factorial experiment. The results of an initial facto-rial experiment with both time and temperature run at twolevels is shown in Figure 1.9. The responses observed at thefour corners of the square indicate that we should move inthe general direction of increased temperature and decreasedreaction time to increase yield. A few additional runs wouldbe performed in this direction, and this additional experimen-tation would lead us to the region of maximum yield.Once we have found the region of the optimum, a secondexperiment would typically be performed. The objective ofthis second experiment is to develop an empirical model ofthe process and to obtain a more precise estimate of the opti-mum operating conditions for time and temperature. Thisapproach to process optimization is called response surfacemethodology, and it is explored in detail in Chapter 11. Thesecond design illustrated in Figure 1.9 is a central compos-ite design, one of the most important experimental designsused in process optimization studies.190180-95%17016090% Bo%15078Initialoptimizationexperiment80140 -Currentoperatingconditions707560%0.51.01.52.02.5Time (hours)Temperature ("F)

Statement of the problem: Identifying the process variables which are affecting the response.…

Answered: Summarize example 1.2 of the example…

Summarize example 1.2 of the example applications of experimental design by determining the statement of the problem, objectives, choice of the

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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