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Weibull Analysis

Tip: For a quick demonstration, select a test data set from the last pull-down in the Options area (#4) and click calculate.

The data input format (time-to-failure, box 1 below) is a failure time followed by either an "f" or an "s", indicating a failure or suspension (i.e., item did not fail), one record per line. Box #1 is prefilled with example input data for six test items. The first item was taken off test (suspended) at 42.1 hours and the final item failed at 139.1 hours.

The following provides an example for grouped, or interval data input. The columns are "time-to-failure", "f" or "s" indicating a failure or suspension, "g" indicating grouped data, followed by the number of items in the group. The following shows example input for 93 items placed on test. Between test start and 10 hours, one item failed. Between 10 and 20 hours 11 failures occurred. After 50 hours 8 items still did not fail and the test was stopped, indicated by an "s" in the second column of the final input line. The analysis results from this input assume that failures occur at the end of the interval. If failures can occur anytime during the interval, then a more accurate approach is to enter mid-point times for the interval (i.e., change the first four times to 5, 15, 25 and 35).

10 f g 1
20 f g 11
30 f g 28
40 f g 45
50 s g 8

Data entered into box #1 below can be separated by spaces, tabs (e.g., copy paste from Microsoft Excel), or no space at all (e.g., 10fg1). Because the Weibull plot starts at a minimum time value of one, if fractional time values less than 1.0 are being analyzed, such as a failure at 0.5 hours, all time values should first be scaled upward by converting to minutes (i.e., multiply all times by 60 minutes/hour).

For additional details, click here.

Example Excel template
Example Excel template, grouped data

Excel Warranty Data Analysis Template.xls

Calculation Inputs:

1. Time-to-failure input, one record per line.


Input is limited to approximately 1,600 lines for Weibull parameter analysis. Weibull probability plot is limited to approximately 300 points.
Remove commas from input data.


2. Location parameter (δ):

The location parameter is sometimes referred to as the "failure free life." The probability of failure is zero up to this time (δ). If there is any probability of failure during early life, then enter 0 for the location parameter. If entered, the maximum value must be less than the earliest failure time entered in box 1 above. A negative value can also be entered, indicating that some life is used up prior to the start of testing.


3. Decimal places:

Summary results
Table calculations

4. Options:

Plots RRY MLE RRX
     R(t) summary table
     F(t) summary table
Increment/order table
Equations
Raw input

Note: Least squares line fitting options: Rank Regression on Y (RRY), Rank Regression on X (RRX, uncommon). MLE = Maximum Liklihood Estimate.


Confidence level:

Time : Bubble text

Time field takes either a number (time) or an encoded number. Enter c to show characteristic life. Enter F5.5 to show the 5.5% life. Leave blank for no lines or shading.


Labels:
Chart title: Font size:
X-axis label:


Use a test data set or simulate failure times:

Simulation trials (n):
Simulation beta (β):
Simulation characteristic life (η):
Simulation location parameter (δ)

Selecting a test data set will overide any inputs in Box #1, Box #2 and least squares fitting options above.





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References:

  1. MIL-HDBK-338, Electronic Reliability Design Handbook.
  2. Nelson, Wayne, Applied Life Data Analysis (Wiley Series in Probability and Statistics)
  3. Dodson, Bryan, Weibull Analysis
  4. Dodson, Bryan, The Weibull Analysis Handbook
  5. Abernethy, Robert, The New Weibull Handbook Fifth Edition, Reliability and Statistical Analysis for Predicting Life, Safety, Supportability, Risk, Cost and Warranty Claims
  6. Bazovsky, Igor, Reliability Theory and Practice.
  7. O'Connor, Patrick, D. T., Practical Reliability Engineering.
  8. http://en.wikipedia.org/wiki/Weibull_distribution
  9. http://en.wikipedia.org/wiki/Maximum_likelihood
  10. Weibull Distribution, NIST Engineering Statistics Handbook .
  11. Khan Academy, Probability density functions for continuous random variables..
  12. Barringer, Paul, Typical beta (β) values: http://www.barringer1.com/wdbase.htm.
  13. http://www.weibull.com/LifeDataWeb/published_examples_using_the_weibull_distribution.htm
  14. Kececioglu, Dimitri, Reliability & Life Testing Handbook, Vol 1.