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Weibull Analysis


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Below is an explanation of how to use Weibull analysis to help diagnose equipment breakdowns.  The example utilizes the Reliability & Maintenance Analyst softwareClick here to download a free demo version of this software.

Weibull analysis is a powerful tool that can be used to classify failures and to model failure behavior. Weibull analysis involves fitting a time to fail distribution to failure data. There are several methods for doing this, and the software provides 4 methods:

  1. Maximum likelihood estimation (MLE),
  2. Probability plotting,
  3. Hazard plotting, and
  4. Modified moment estimation.

After Weibull analysis is completed, the value of the shape parameter, b , can be used to classify failures. A shape parameter of less than 1.0 indicates infant mortality failures. The causes of infant mortality failures are:

  • Improper use,
  • Improper installation
  • Improper setup
  • Inadequate training
  • Poor quality control
  • Defective materials
  • Power surges
  • Improper testing

In this case, there are two approaches for improving reliability. The equipment or component can be "burned-in" (burn-in refers to running the component for a period of time to weed out items with short lives. This is common for manufacturers of electronic devices). Or, personnel can be trained on proper setup, installation, inspection, etc.

A shape parameter equal to 1.0 indicates random failures. The only way to increase the reliability of the equipment in this case is by redesign.

A shape parameter greater than 1.0 indicates wearout failures. In this case, reliability and cost performance can be improved by optimizing the preventive maintenance schedule.

Example 1

Failure data for a bearing has been collected and is contained in the computer file "BEARING.DAT" (The demo version of the Reliability & Maintenance Analyst includes this file). A check in the "Censored" box indicates the bearing was removed from service without failing. This is called censored data, and cannot be ignored without creating severe errors.

This data can be entered into the software by opening the "BEARING.DAT" file. To analyze the data, selecting Parameter Estimation, Weibull, and then Maximum Likelihood Estimation menu. A shape parameter of 0.524 is calculated. Ninety percent confidence limits for this value are 0.4346 and 0.6317 (Confidence limits are important to distinguish values from 1.0. Is 0.97 equal to 1.0? What about 0.91 or 1.03? If the confidence interval includes 1.0, then the parameter should be considered equal to 1.0).

This information tells the maintenance engineer or technician that the bearings are not being properly installed, or the bearing manufacturer is shipping defective bearings. This analysis was used on a coating line, and it was found that by using laser alignment to install bearings, the bearing life was extended by over a factor of 10.

The MLE 3- Parameter routine also calculates a location parameter. In some cases, there is an extremely low probability of failing for some period of time. A location parameter is used to model this. The location parameter can also be negative. This means there is a probability of failure before the item was put into use. This is used to model failures caused by transportation and shelf-life failures.

The probability plotting and hazard plotting routines do not give confidence limits, but allow the user to visually determine how well the proposed distribution fits the data.

Example 2

Failure data for a bearing has been collected and is contained in the computer file "BEARING2.DAT" (The demo version of the Reliability & Maintenance Analyst includes this file). Again, a check mark in the "Censored" box indicates the bearing was removed from service without failing. A production manager familiar with Example 1, immediately began training the mechanics responsible for installation of the bearings. After several weeks passed with no change in failure rates, this manager asked for help in explaining why there was no improvement.

A Weibull analysis was performed using the following steps.

  1. Select File from the main menu.
  2. Select Open and select the file "BEARING2.DAT".
  3. Select Parameter Estimation from the menu.
  4. Select Weibull.
  5. Select Maximum Likelihood Estimation.

The software returns an estimate of 1.094 for the shape parameter. The lower 90% confidence limit for the estimated shape parameter is 0.9088, and the upper 90% limit is 1.317. This means that given the failure data, we are 80% confident (10% on each tail) that the true value of the shape parameter is between 0.9088 and 1.317. In this case, it should be assumed that the failure rate is constant (the shape parameter is equal to 1.0). There is no way to improve performance other than redesign. Training and preventive maintenance increase costs and have no effect on reliability.


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