# Manual for Life Cost Based FMEA

4 2 2 1 1 k k k − ± − x_{1}, x_{2 }= 2

t x e x k t R + = 1 1 1 ) ( ) R(t) = (

t x e x k + − 2 1 2 ) (

=e

−λt

(12)

x_{1 }− x_{2 }

λ is the failure rate of the component, R is the reliability, t is 6480 hours which is the operation time for a one year period (Eberling, 1997).

Knowing the MTBF for the redundant set of components, availability of the redundant set can be calculated and the overall system availability can be calculated using Equation 10 and paying attention to the number of components in the system.

# Step 6 Calculate MTBF and Downtime

Knowing the availability of the entire system, the MTBF for the entire system can be calculated using Equation 7. The expected operating hours for the ILC is 6480

hours/year.

# Thus, the downtime of the accelerator can be predicted using the

following equation:

Downtime = (1-Availability) x 6480 hours

# Step 7 Calculate Frequency

Knowing downtime and the MTTR for the system, failure frequency per year can be calculated using the following equation:

# Frequency (Failure/year) =

Downtime MTTR

To predict specific types of failures as defined in the FMEA table, one can follow steps 4 through 7 for each individual failure modes or root causes. It is critical to find the root cause of each failure from the CATER system to conduct this analysis. This further analysis will result in creating several versions of table 6.

4.2.

# Reliability Estimation from Distributions

When a new design is being introduced and no field data exists, we have to rely on manufacturer’s reliability data or use time-to-failure distributions. The most popular failure distributions are the Weibull, normal, and exponential distributions.

The normal distribution is frequently used to model quality related characteristics and sampling measures. It is widely used for process behaviors for quality control purposes. It is symmetrical and has a single mode. Despite its popularity it is

FMEA MANUAL By S. Rhee and C.M. Spencer

20/26

January 2009