Multiple Failure Modes with the Weibull Distributions

Several leading consultants have stated that the Weibull distribution cannot be used to model multiple failure modes.  In some extreme cases this is true, but often it is not.  By definition the Weibull distribution is an extreme value distribution.  Click Here to download an Excel spreadsheet with simulated data for both single and multiple failure modes.

Sheet 2 of this spreadsheet, shown below, contains 3 failure modes:

1. A resistor with a shape parameter of 1 and a scale parameter of 100,
2. A hose with a shape parameter of 2 and a scale parameter of 200, and
3. A switch with a shape parameter of 0.9 and a scale parameter of 300.

If the three components are in series, the system fails when any one of the components fails.  The spreadsheet simulates this situation:

• Column B contains simulated data for the time to fail of the resistor,
• Column C contains simulated data for the time to fail of the hose,
• Column D contains simulated data for the time to fail of the switch, and
• Column E contains simulated data for the time to fail of the system.

Cell E9 is the theoretical reliability of the system at a time of 30.  If the Weibull distribution is used to model the time to fail for the system, the results will match the theoretical value, proving that it is possible to model multiple failure modes with the Weibull distribution.

The spreadsheet is set up to be flexible.  The theoretical reliability is computed at a time of 30; this can easily be changed.  The shape and scale parameters of each of the parameters are also easily changed.  Also, each pressing the "F9" key will provide a new set of random numbers.  Sheet one of the spreadsheet contains a 2 failure mode model, and Sheet 3 contains a 10 spreadsheet model.

The Reliability Engineering Handbook is an excellent reference for further review.