To assess the potential risks

To assess the potential risks associated with failure of a particular process, investigators often perform a failure modes and effects analysis (FMEA). An FMEA identifies opportunities for failure, known as failure modes, in a given process. Each mode is assessed with a numeric score based on (1) severity of the consequences of failure, (2) likelihood of failure occurrence, and (3) likelihood that failure would not be detected. The product of these scores is the risk priority number (RPN) for the mode. Modes having the highest RPN values are usually given the highest priority in carrying out further analyses.

The article “Continuous Quality Improvement in Investment Castings: An Experimental Study using a Modified FMEA Approach Called FEAROM” (Eur. J. of Sci. Res., 2012: 308–325) reported on a study that compared four design methods (M1, M2, M3, M4) in preproduction trials of the upper range for a particular casting valve. The design methods are applied by human operators, which introduces potential operatorto-operator variation in RPN values. To account for this, each of the four design methods was used (in random order) by all 21 individuals in the study.

The data was analyzed by the R software, giving the following output. Note that the format of the ANOVA table in R is very similar to the one we use, except R eliminates the row of “totals” and uses the word residuals instead of error. The column labeled ‘Pr(>F)’ represents P-value.

a. Fill in the missing values in the table above.

b. Using   .05, can it be concluded that there is a difference in the true average RPN among the four design methods?

c. Do the person-to-person differences in RPN seem to be confirmed by the data? Explain.

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