Applied Statistics and Probability for Engineers

run at two levels each at 10F and 0.5 hours above and below the current operating condi-

tions. This two-factor factorial design is shown in Fig. S14-2. The average responses

observed at the four points in the experiment (145F, 1.2 hours; 145F, 2.2 hours; 165F, 1.2

hours; and 165F, 2.2 hours) indicate that we should move in the general direction of

increased temperature and lower reaction time to increase yield. A few additional runs could

be performed in this direction to locate the region of maximum yield.

A Product Design Example

We can also use experimental design in the development of new products. For example, suppose

that a group of engineers are designing a door hinge for an automobile. The product characteris-

tic is the check effort, or the holding ability, of the latch that prevents the door from swinging

closed when the vehicle is parked on a hill. The check mechanism consists of a leaf spring and a

roller. When the door is opened, the roller travels through an arc causing the leaf spring to be com-

pressed. To close the door, the spring must be forced aside, and this creates the check effort. The

engineering team thinks that check effort is a function of the following factors:

1. Roller travel distance


2. Spring height from pivot to base


3. Horizontal distance from pivot to spring


4. Free height of the reinforcement spring


5. Free height of the main spring
   The engineers can build a prototype hinge mechanism in which all these factors can be varied
   over certain ranges. Once appropriate levels for these five factors have been identified, an ex-
   periment can be designed consisting of various combinations of the factor levels, and the pro-
   totype can be tested at these combinations. This will produce information concerning which
   factors are most influential on the latch check effort, and through analysis of this information,
   the latch design can be improved.
   These examples illustrate only three applications of experimental design methods. In the
   engineering environment, experimental design applications are numerous. Some potential areas
   of use are


6. Process troubleshooting


7. Process development and optimization


8. Evaluation of material and alternatives


9. Reliability and life testing


10. Performance testing


11. Product design configuration


12. Component tolerance determination
    Experimental design methods allow these problems to be solved efficiently during the early
    stages of the product cycle. This has the potential to dramatically lower overall product cost
    and reduce development lead time.

14-6 FACTORIAL EXPERIMENTS WITH RANDOM FACTORS

(CD ONLY)

In this chapter, we focus primarily on the case where all the factors are fixed; that is, the experi-

menter specifically chose the levels, and the conclusions from the experiment are confined to

14-3

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