Example for Regression with Life Data

Engineers want to assess the reliability of a redesigned compressor case of jet engines. To test the design, the engineers use a machine to throw a single projectile into each compressor case. After the projectile impact, engineers inspect the compressor every twelve hours for failure.

The engineers perform regression with life data to evaluate the relationship between the case design, the projectile weight, and the failure time. They also want to estimate the failure times at which they can expect 1% and 5% of the engines to fail. The engineers use a Weibull distribution to model the data.

  1. Open the sample data, JetEngineReliability.MTW.
  2. Choose Stat > Reliability/Survival > Regression with Life Data.
  3. Select Responses are uncens/arbitrarily censored data.
  4. In Variables/Start variables, enter Start.
  5. In End variables, enter End.
  6. In Model, enter Design and Weight.
  7. In Factors (optional), enter Design.
  8. Click Estimate. In Enter new predictor values, enter New Design New Weight.
  9. In Estimate percentiles for percents, enter 1 5, then click OK.
  10. Click Graphs. Select Probability plot for standardized residuals.
  11. Click OK in each dialog box.

Interpret the results

In the regression table, the p-values for design and weight are significant at an α-level of 0.05. Therefore, the engineers conclude that both the case design and the projectile weight have a statistically significant effect on the failure times. The coefficients for the predictors can be used to define an equation that describes the relationship between the case design, the projectile weight, and the failure time for the engines.

The table of percentiles shows the 1st and 5th percentiles for each combination of case design and projectile weight. The time that passes before 1% or 5% of the engines fail is longer for the new case design than the standard case design, at all the projectile weights. For example, after being subject to a 10-pound projectile, 1% of the engines with a standard case design can be expected to fail after approximately 101.663 hours. With the new case design, 1% of the engines can be expected to fail after approximately 205.882 hours.

The probability plot of the standardized residuals shows that the points follow an approximate straight line. Therefore, the engineers can assume that the model is appropriate.

Regression with Life Data: Start versus Design, Weight

Response Variable Start: Start End: End Censoring Information Count Right censored value 25 Interval censored value 23 Estimation Method: Maximum Likelihood Distribution: Weibull Relationship with accelerating variable(s): Linear
Regression Table Standard 95.0% Normal CI Predictor Coef Error Z P Lower Upper Intercept 6.68731 0.193766 34.51 0.000 6.30754 7.06709 Design Standard -0.705643 0.0725597 -9.72 0.000 -0.847857 -0.563428 Weight -0.0565899 0.0212396 -2.66 0.008 -0.0982187 -0.0149611 Shape 5.79286 1.07980 4.02001 8.34755 Log-Likelihood = -88.282
Anderson-Darling (adjusted) Goodness-of-Fit Standardized Residuals = 26.470
Table of Percentiles Standard 95.0% Normal CI Percent Design Weight Percentile Error Lower Upper 1 Standard 5.0 134.911 17.6574 104.385 174.363 1 Standard 7.5 117.113 16.0279 89.5591 153.144 1 Standard 10.0 101.663 16.3830 74.1295 139.423 1 New 5.0 273.214 36.8022 209.819 355.763 1 New 7.5 237.171 32.6878 181.028 310.726 1 New 10.0 205.882 32.8675 150.568 281.518 5 Standard 5.0 178.749 16.9676 148.404 215.300 5 Standard 7.5 155.168 14.1107 129.836 185.443 5 Standard 10.0 134.698 15.4568 107.568 168.670 5 New 5.0 361.994 36.0778 297.761 440.084 5 New 7.5 314.239 28.8741 262.450 376.247 5 New 10.0 272.783 30.6102 218.928 339.887

Probability Plot for SResids of Start

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