The Beta Factor Method
Common Cause Failures (CCFs) are single faults that result in the failure
of multiple components. Typical examples include impact, vibration, temperature,
contaminants, miscalibration, improper maintenance, etc. There are different
methods to address CCFs, both qualitative and quantitative. In this article,
we discuss the β factor method and provide an example of an application
of this method
using BlockSim 7.
The β factor method is an approximation method used for the quantitative
evaluation of CCFs. In this method, the likelihood of the CCF is evaluated in
relation to the random failure rate for the component. A β factor is
estimated such that β% of the failure rate is attributed to the CCF and
(1 β)% to the random failure rate of the component. Ideally, this factor is
obtained through historical data by determining the percentage of all the
component failures in which multiple similar components failed. In the absence of
this information, it may also be obtained qualitatively (refer to
[1] for a partial list of sources on this subject).
In the following example, a redundant array of independent disks (RAID) is
modeled. In this system, the data is written identically to two disks, thus
providing redundancy. However, failures due to overheating have been identified
due to the location where the system operates. Analyzing the available historical
data provides an estimate of the β factor where β is found to be 0.08.
In other words, 8 out of 100 disk failures can be attributed to overheating that
resulted in the failure of both disks. In addition, the failure rate of each disk
(including all failures) is 0.017 failures per year.
The first step is to adjust the disk failures by a factor of (1 β);
that is, the failure rates for the events Disk 0 fails and Disk 1
fails need to be multiplied by (1 β). To model this
in BlockSim 7, a factor called the duty cycle is used. Some
common applications for the duty cycle involve components that do not operate
continuously or experience changes in environmental stress. For example, consider
a CDROM drive in a computer that accumulates only 10 minutes of
operating time for every 60 minutes the computer
operates. The duty cycle in this case would be 0.167. (For more information on
the duty cycle refer to [2].)
If t^{'} = d_{c} x t
(where d_{c} is the duty cycle), then:
In the case of an exponential model, we also have:
The failure rate of the disks can then be adjusted by (1β) in
BlockSim 7 by setting the following values in the General and
Reliability tabs of the Block Properties window:
The next step is to similarly model the common cause event (the RAID
CC block) by setting the failure rate of the disk to 0.017 and
the duty cycle value to 0.08.
We can obtain the probability of occurrence of a system failure at any time
by using the Quick Calculation Pad. For example, the probability of
failure after one year is 0.0016, as shown below.
Note that if the common cause failure had been ignored (that is, if only the
two disks in redundancy had been taken into account), the probability of the
failure of the system would have been calculated as 0.0003, largely
underestimating the probability of failure.
Conclusions
This article briefly illustrated how the β factor method can be applied
for common cause failure analysis in BlockSim 7. Although failure rates
can be manually adjusted to implement this method, inputting the β factor
separately as the duty cycle allows for easy access and modification.
References
[1]
Summers, Angela E., Kimberly A. Ford, and Glenn Raney,
"Estimation and Evaluation of Common Cause Failures in SIS."
Presented at the 1999 Loss Prevention Symposium, Houston, Texas, March 1999.
http://www.iceweb.com.au/sis/e_and_e.htm.
[2] ReliaSoft Corporation, Life Data Analysis
Reference, Tucson, AZ: ReliaSoft Publishing, 2007.
