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Weibull Analysis and Advantages by Carl Tarum, Director of Software Research, Fulton Findings

What is Weibull Analysis?

When you test parts to failure, this is called Life Data. There will be variation. For example, if you test a drone while flying in a hover mode, the flight time will vary.

In the 1950’s Dr. Weibull proposed the Weibull equation that is a useful tool for estimating life data behavior.

  • F(t)=1−exp[−(t/h)b], where
  • F(t)      cumulative distributionfunction
  • exp      exponentialfunction
  • t           time tofailure
  • h          “Eta”, Characteristic life
  • b           “Beta”, WeibullSlope

Sample Tests

Suppose you test a drone with fresh batteries, and get times of 375, 381, and 400 seconds. Then test 6 flights that have been 3 weeks from charging. Times are 262, 280, 304, 308, 321, and 356 seconds. Next you test with

extra weight, and get times of 246, 255, 287, and 290. (These are actual test data from this author’s testing.)

You expect that time after charge and extra weight will affect flight time. These data can answer the following questions:

  • Is flight time affected by time sincecharge?
  • How does weight impact flighttime?
  • Are there enough data?
  • Is Weibull a good fit for the data? SuperSMITH® software provides a Weibull plot of the data (Figure 1) Reading from the chart, 10% of flights with fresh batteries would only last 363 seconds, and 90% will end before 402

Analysis

Flight Time affected: From Figure 1, the average flight time for freshly charged batteries is 386 seconds, while flights 3 weeks since charge have 308 seconds. Extra weight reduces time to 271 seconds.

Further data can produce a model for change in flight duration with respect to time since charge, and extra weight.

Data Sufficiency: A likelihood ratio test and contour plot (Figure 3) show that tests with extra weight or time since charge are significantly different from the tests with freshly charged batteries.  Read More

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