1.1 N UNIT RELIABILITYWISE SERIES SYSTEM

A system is said to have units which are reliabilitywise in series when the failure of any one or more units before the mission is completed results in the failure of that system. Conversely, for a series system to succeed for the duration of the intended mission, all of its units have to succeed. The reliability block diagram of a series system is as shown in Fig. 1.1. Probabilistically, the reliability of this system is the probability that Unit 1 succeeds, or does not fail, during the mission, and Unit 2 succeeds, or does not fail, during the mission, ..., and that Unit n succeeds, or does not fail, during the mission. Mathematically, the reliability of this series system, R _ss, is given by

(1.1)

where R _1,R ₂, _,R _n are the reliabilities of Unit 1, Unit 2, ..., Unit n, respectively. This expression assumes that the R _i ' s are independent. If they are dependent, then the parameters in the pdf of each unit should be adjusted to reflect the effects, if any, of the application and operation stresses imposed thereupon by all units in the series system. Then Eq. (1.1) will apply.

Figure 1.1: The reliability block diagram of a reliabilitywise series system.

1.2 EXPONENTIAL UNITS

If the distribution of the times to failure of such units is the exponential, then each has a constant failure rate, ? _i, and...