The failure rate of a series system is equal to the sum of the failure rates of its components. This is true

regardless of the failure distributions of the components.

the system capability to successfully accomplish mission objectives. The mission reliability model may

be series, parallel, standby redundant, or complex.

(1) *Parallel system model*. In a parallel system, the system fails only when all of the components

fail. Such a system is represented in Figure 7. In this configuration, the system will still perform if at

least one of the components is working.

The reliability for the system is given by

(12)

or,

∏

[*1 - R*i(t)]

(13)

1-

A more general form of a parallel system is the "*r *out of *n*" system. In this type of system, if any

combination of *r *units out of *n independent *units arranged in parallel work, it guarantees the success of

the system. If all units are *identical*, which is often the case, the reliability of the system is a binomial

summation represented by

*n*

∑

R(*t*)j [1 - *R*(*t*)]n-j

(14)

*j*

where

*n*

=

(15)

*j*

The hazard rate for parallel systems can be determined by using

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