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A Guide for Using the Weibull Distribution in Failure Mode Analysis

The engine had numerous in-flight aborts (IFA), which is a direct safety-of-flight issue. This guide also demonstrates how to use Weibull in combining or merging different failure modes to form a new failure mode. The versatile distribution is very useful in root cause analysis (RCA), reliability-centered maintenance (RCM), reliability and availability (RAM), and other processes that lead to a solution for failure modes.

Users of this guide should have taken at least one class in Weibull analysis and several classes in theory and practical problem solving. Users also should be in the reliability field, have experience in using their Weibull software, and have good knowledge about their system(s) and components. It is also recommended that users review the Crow-AMSAA 101 and Weibull 101 basics by Paul Barringer at


In preparing to use the Weibull distribution in failure mode analysis, first create four folders in the directory containing the failure and failure mode data. Name these four folders:

  1. Lrr;
  2. Wrr;
  3. W3P;
  4. Not a Weibull.

When you separate all failure modes (217 in my case) and start the WFMA process, each failure mode will be classified in one of the four above categories. Weibull distributions depend on data; that is the data selects the distribution. Up until Dr. Weibull’s methodology was accepted, a distribution was selected, then data was found that matched the distribution. Today, the Weibull distribution is the leading method in the world for fitting and analyzing life data.1

The Weibull distribution is the choice for analysis of life-limited components’ failure modes, such as turbofan jet engines’ blade cracks, disk cracks and other life limits placed upon any component. In this guide, the x-axis is defined in engine flight hours (EFH). The x-axis is always engine flight hours; there are no changes or deviations in the x-axis definition. Each Weibull plot will have this notation on the x-axis: EFH(Hours).

It is very important to understand the data requirements for Weibull plots. To determine failure time precisely, there are three requirements:1

  • A time origin must be unambiguously defined.
  • A scale for measuring the passage of time must be agreed to.
  • The meaning of failure must be entirely clear.

As stated in The New Weibull Handbook, “ The age of each part is required, both failed and nonfailed. The units of age depend on the part usage and the failure mode.” Keep in mind the, “ both failed and nonfailed,” age for the part because there will be examples of this using various parts/components of a turbofan jet engine. No matter the time base selected or failed or nonfailed, age is a requirement. This will be demonstrated later in this article.

The 14-Step Weibull Failure Mode Process

First, I will provide my 14-step process, then use an actual turbofan jet engine component to show the software input/output. However, some caution when using Weibull software. There is only one software that complies with International Electrotechnical Commission (IEC) Weibull analysis and that is SuperSMITH (SS), which complies with IEC-61649. SS software greatly reduces the maximum-likelihood estimation (MLE) of small data bias.

In beginning the 14-step process using data from past analysis in Weibull failure mode analysis, I use two failure modes, 037-Fluctuations/Oscillations and 398-Oil Consumption Excessive, and perform these 14 steps:

    1. Organize each failure mode (FM) into Weibull input data format using Excel. Figure 1 shows input for engine in-flight abort failure mode 037-Fluctuations/Oscillations.

        2. Input data into the Weibull software, Figure 2.

          3. Perform outlier data test, remove any outlier data points. Figure 2 shows no outliers.

            4. Perform distribution analysis for failure mode 037. Figure 2shows this is a WrrWeibull.


              5. Check if the data is a true Weibull. Figure 3 shows the Wrr, Wmle and W/RBAmd with lines associated with the distribution.


                6. Use the Aggregate Cumulative Hazard (ACH), which is the best method for detecting batch problems. The New Weibull Handbook Appendix F describes this function and its optional use for the possibility of more than one failure mode. CAUTION: There are other methods for looking at the Weibull data plot. I use the ACH method, you may or may not elect to use ACH at this time. However, it is most imperative that a batch detection method be used after combining different failure modes data.The ACH plot for failure mode 037 is shown in Figure 4. Notice the data is close to the ACH line; we accepted this plot, so this failure mode will be used.


                  7. Select two failure modes from the same distribution family. Failure modes 037 and 398 will be chosen since both have been verified as true Weibull’s and are now ready for additional analysis, see Figure 5.


                    8. Perform set compare on the selected Weibulls. Figure 6 has the LRT.

                      9. Perform the likelihood contour plot (LCP). Figure 7 is the contour plot and we see a good intersection between the two failure modes. Based upon the LCP, the data from these two failure modes may be combined to form a new failure mode.


                        10. Merging the failure modes data produces failure mode 435, the Weibull is shown as in Figure 8.


                          11. Performing the outlier test. Figure 9 shows no outliers.

                            12. Distribution analysis proves it is a WrrWeibull, as shown in Figure 10.

                              13. Test for true Weibull: Figure 11 shows the proof. The Beta values are very close and the various lines have very little deviation, therefore, this failure mode is a true Weibull.


                                14. Use the ACH function on failure mode 435: Figure 12 is the ACH plot and the data is very close to the ACH plotted line. Failure mode 435 is acceptable to use for additional failure mode analysis.


                                  The absolute goal of the 14-step process is a reduction in many failure modes to those “few” that are major contributors to system failures. The 14-step process must be followed in the given order, otherwise you will incorrectly make errors in your system failures.

                                  If you have less than 20 data points, the data values will be above and below the ACH line, but do not discount these due to the plot. Always use best engineering and logistical practices. Out of 217 possible failure modes, the 14-step process reduced these to only five, with one major and one minor failure mode.

                                  Are these steps the only way to perform Weibull failure mode analysis? Absolutely not! But they are definitely worth considering.


                                  1. Abernethy, Dr. Robert B. The New Weibull Handbook. Houston: Gulf Publishing Company, 2008.

                                  Technical Adviser: Dr. Robert B. Abernethy reviewed this document for me; Thanks Dr. Bob. Technical Assistance: James W Fulton, Fulton Findings Paul Barringer, Barringer Associates

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