A 16-run fractional factorial experiment in 10 factors on sand-casting of engine

Question

A 16-run fractional factorial experiment in 10 factors on sand-casting of engine manifolds was conducted by engineers at the Essex Aluminum Plant of the Ford Motor Company the purpose was to determine which of 10 factors has an effect on the proportion of defective castings. the design and the resulting proportion of nondefective castings p observed on each run are shown below. This is a resolution III fraction with generators E=CD, F=BD, G=BC, H=AC, J=AB, and K=ABC. Assume that the number of castings made at each run in the design is 1000. Analyze the data and make your conclusions both with respect to mean and variance. What would be your final recommendation?

Explanation / Answer

Finding the defining relation and the alias relationships in this design: I=CDE=BDF=BCG=ACH=ABJ=ABCK=BCEF=BDEG=ADEH=ABCDEJ=ABDEK=CDFG=ABCDFH = ADFJ=ACDFK=ABGH=ACGJ=AGK=BCHJ=BHK=CKJ Estimating the factor effects and use a normal probability plot to tentatively identify the important factors design expert output model term intercept Effect SumSqr % Contribtn Error A -0.011875 0.000564063 0.409171 Error B 0.006625 0.000175562 0.127353 Error C 0.017625 0.00124256 0.901355 Error D -0.052125 0.0108681 7.88369 Error E 0.036375 0.00529256 3.83923 Model F 0.107375 0.0461176 33.4537 Error G -0.050875 0.0103531 7.51011 Error H 0.028625 0.00327756 2.37754 Error J -0.012875 0.000663062 0.480986 Model K 0.099625 0.0397006 28.7988 Error AB Aliased Error AC Aliased Error AD 0.004875 9.50625E-005 0.0689584 Error AE -0.034625 0.00479556 3.4787 Error AF 0.024875 0.00247506 1.79541 Error BE -0.053125 0.0112891 8.18909 Error DK 0.015375 0.000945563 0.685911 Lenth's ME 0.103145 Lenth's SME 0.209399

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