Metal fatigue. The following plot shows fatigue life data (log base 10 cycles to failure) on specimens from 27 blends of a metal alloy, tested at the same stress, temperature, etc. The basic question is: are the blends consistent? The following analyses assess this. Visually examine the plot.
(a) Assess whether the blends are similar or different with respect to typical life. Mark the sample median of each blend as an aid
(b) Identify any blends with significantly longer or shorter life.
(c) How do the blends compare with respect to scatter in (log) fatigue life? Take into account the differing sample sizes.
(d) How do the blends compare in the lower tail, say. at roughly the 10 or 1% point. Early failures are important in fatigue work, and components are retired before they fail. Design life is cycles to usually
0.1% failure divided by 3. Estimate it.
(e) The blends are plotted in order of manufacture. Are there any time trends in fatigue life?
The following computer output shows a chi-square contingency table analysis to compare the 27 blends with respect to the (binomial) proportion failing by 7000 cycles, denoted by LE7K. Those surviving 7000 cycles are
denoted by GT7K.
( f ) Are there convincing differences among the blends?
(g) Which blends have a large chi-square contribution and differ from the others? Add the two chi-square contributions (LE7K and GT7K) to get the total chi-square contribution of a blend. How d o those blends
differ (better or worse)?
(h) If the blends that clearly differ are removed from the data, how do the remaining blends compare (subjective evaluation based on the contingency table analysis)?
The following computer output shows a one-way analysis of variance to compare the mean log life of the blends.
( i ) Are there convincing differences among the blends? Are the sample sizes large enough so the F test is accurate enough? Explain.
(j) Examine the blend means. Which blends differ significantly from the others (better or worse)?
( k ) Use the analysis of variance table to get an estimate of the standard deviation of the pooled data, ignoring blends. Compare this with the pooled estimate of the standard deviation within blends. Are the two
estimates the same for practical purposes? I f so, the alloy can be treated as a single homogeneous population. and blends can be ignored.
(I) Explain why Bartlett's test to compare (log) standard deviations of the blends is not suitable.
(m) In nonstatistical terms, write up all your conclusions in a form suitable for a department general manager.
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