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Competing Failure Modes Analysis

For many products, there are multiple failure modes that can result in the failure of an individual unit. When performing reliability analysis on this type of product, you can take the view that each individual unit could fail due to any one of the possible failure modes and, since an item cannot fail more than one time in a non-repairable system, that there can only be one failure mode for each failed unit. With this approach, the failure modes “compete” as to which one causes the failure for each particular unit. This can be represented in a reliability block diagram as a series system in which a block represents each failure mode.

Competing failure modes analysis, which segregates the analysis of failure modes and then combines the results to provide an overall reliability model for the product in question, can be used to analyze data of this type. This article presents an overview of competing failure modes analysis and an example to illustrate the techniques. ReliaSoft’s Weibull++ software (with the “Intermediate” default settings) will be used to perform the analysis.

Performing Competing Failure Modes Analysis
The first step in analyzing data sets with more than one competing failure mode is to perform a separate analysis for each failure mode. In the analysis for each failure mode, the failure times for the mode being analyzed are considered to be failures and the failure times for all other modes are considered to be suspensions. These are suspension times because the units would have continued to operate for some unknown amount of time if they had not been removed from the test when they failed due to another mode.

Once the analysis for each individual failure mode has been completed in this manner, the resulting reliability equation for all modes is the product of the reliability equation for each individual failure mode. This is given by the following equation:

where n is the total number of failure modes under consideration. This is the product rule for the reliability of a series system with statistically independent components, which states that the reliability for a series system is equal to the product of the reliability values of the components that compose the system. An example to demonstrate these techniques is presented next.

Example of Competing Failure Modes Analysis
Table 1 presents failure times for an air conditioning compressor that has two competing failure modes. One failure mode is due to reed valve breakages, which cause failure by overloading the system (denoted as an R in the table). The other failure mode is due to seal and gasket wear-out failures, which usually happen only after the system has run for many cycles (denoted as a G).

You can use competing failure modes analysis to determine the overall reliability for the component at 100 million cycles. The first step is to perform an analysis for the reed valve (R) failure mode. For this analysis, all failures that occurred due to the reed valve failure mode are considered to be failures. The failures that occurred due to the gasket (G) failure mode are considered to be suspended at the gasket failure times. The eight units that did not fail during the test are also considered to be suspensions. When you use the maximum likelihood estimation (MLE) analysis method and assume a Weibull distribution, the estimated parameters for the reed valve failure mode are calculated as:

Beta = 0.6492
Eta = 417.6668

The reliability for the reed valve failure mode at 100 million cycles is RR = 0.6735.

The next step is to perform an analysis for the gasket (G) failure mode. In this case, all failures that occurred due to the gasket failure mode are considered to be failures and the failures that occurred due to the reed valve (R) failure mode as well as the eight units that did not fail are considered to be suspensions. The estimated parameters for this data set with the Weibull distribution and the MLE analysis method are:

Beta = 4.1215
Eta = 313.0839

The reliability for the gasket failure mode at 100 million cycles is RG = 0.9910.

Finally, you can use the following equation to determine the overall reliability at 100 million cycles:

Therefore, the reliability of the compressor for both failure modes at 100 million cycles is 66.74%.

You can perform this analysis automatically with the Weibull++ software. Simply use the Subset ID column to specify the failure mode for each data point and select CFM-Weibull, along with the MLE analysis method, on the control panel. When you calculate the data set, you will be prompted to define the competing failure modes in the analysis. The Weibull++ competing failure modes analysis for the reed valve failure mode is presented in Figure 1. The plot of the competing failure modes is presented in Figure 2. Finally, the QCP results for the reliability for both failure modes together at 100 million cycles is presented in Figure 3.

 Figure 1: Weibull++ Data Folio with competing failure modes analysis for the reed valve mode

 Figure 2: Competing failure modes plot from Weibull++

 Figure 3: Reliability for both modes at 100 million cycles

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