Failures in aircraft gas turbine engines due to high cycle fatigue is a pervasive problem. The article "Effect of Crystal Orientation on Fatigue Failure of Single Crystal Nickel Base Turbine Blade Superalloys" (J. of Engineering for Gas Turbines and Power, 2002: 161-176) gave the accompanying data and fit a nonlinear regression model in order to predict strain amplitude from cycles to failure. Fit an appropriate model, investigate the quality of the fit, and predict amplitude when cycles to failure = 5000.

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Obs Cycfail Strampl Obs Cvcfail Strampl 1326 .01495 1593 .01470 4414.01100 5673 .01190 5 29516 .00873 26 .01819 843 .00810 1016 00801 3410 00600 10 710100575 735600576 7904 00580 79 01212 4175 .00782 15 34676 .00596 16 114789 .00600 2672 00880 7532 00883 19 30220 .00676 12 13 14 17 18