Example for Probit Analysis

An engineer of aircraft windshields wants to investigate how well the windshields can withstand projectile impacts at a range of velocities. The engineer subjects a random sample of windshields to projectiles at one of eight velocities and records whether the windshields withstood the impact.

The engineer performs probit analysis to determine the range of velocities at which a certain percentage of the windshields will break when subjected to the projectile impact.

  1. Open the sample data, WindshieldStress.MTW.
  2. Choose Stat > Reliability/Survival > Probit Analysis.
  3. Select Response in event/trial format.
  4. In Number of events, enter Breaks.
  5. In Number of trials, enter N.
  6. In Stress (stimulus), enter Stress.
  7. From Assumed distribution, select Normal.
  8. Click OK.

Interpret the results

To evaluate the distribution fit, the engineer uses a significance level of 0.1. The goodness-of-fit p-values (0.977 and 0.975) are greater than the significance level, and the points on the probability plot fall along an approximate straight line. Therefore, the engineer can assume that the normal distribution model provides a good fit for the data.

To evaluate significant effects, the engineer uses a significance level of 0.05. Because the p-value for Stress (0.000) is less than the significance level (0.05), the engineer concludes that the velocity of the projectile does have a statistically significant effect on whether or not the windshield breaks.

The table of percentiles indicates that the engineer can be 95% confident that 1% of the windshields will fail at a velocity between 300.019 mph and 501.649 mph.

Probit Analysis: Breaks, N versus Stress

Distribution: Normal

Response Information Variable Value Count Breaks Event 37 Non-event 52 N Total 89 Estimation Method: Maximum Likelihood
Regression Table Standard Variable Coef Error Z P Constant -6.20376 1.06565 -5.82 0.000 Stress 0.0089596 0.0015615 5.74 0.000 Natural Response 0 Log-Likelihood = -38.516
Goodness-of-Fit Tests Method Chi-Square DF P Pearson 1.19972 6 0.977 Deviance 1.22858 6 0.975 Tolerance Distribution
Parameter Estimates Standard 95.0% Normal CI Parameter Estimate Error Lower Upper Mean 692.416 18.3649 656.421 728.410 StDev 111.612 19.4518 79.3167 157.058
Table of Percentiles 95.0% Fiducial Standard CI Percent Percentile Error Lower Upper 1 432.767 45.8542 300.019 501.649 2 463.192 41.0355 345.266 525.291 3 482.496 38.0450 373.838 540.427 4 497.018 35.8391 395.242 551.902 5 508.830 34.0781 412.585 561.304 6 518.884 32.6067 427.289 569.364 7 527.699 31.3403 440.133 576.480 8 535.592 30.2277 451.589 582.896 9 542.771 29.2352 461.967 588.771 10 549.379 28.3398 471.482 594.217 20 598.480 22.4304 540.595 636.280 30 633.886 19.4337 587.639 669.400 40 664.139 18.1881 624.815 700.723 50 692.416 18.3649 656.409 733.152 60 720.692 19.8068 685.039 768.545 70 750.945 22.4716 713.104 808.979 80 786.351 26.5977 743.723 858.524 90 835.453 33.3805 783.926 929.497 91 842.060 34.3538 789.210 939.174 92 849.239 35.4233 794.925 949.712 93 857.132 36.6126 801.183 961.326 94 865.948 37.9558 808.140 974.328 95 876.002 39.5048 816.041 989.192 96 887.814 41.3455 825.280 1006.70 97 902.335 43.6350 836.585 1028.27 98 921.639 46.7171 851.535 1057.03 99 952.065 51.6465 874.954 1102.50

Probability Plot for Breaks

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