Combining Reliabilities (No Repair)
Having established the functional relationship between the items in a system, the system reliability can be predicted by combining the reliabilities of the individual items.
Expressions for predicting the system reliabilities from the individual reliabilities of items in a system can be carried out in many ways. However, two particularly useful ways are based on the following:
• If P(X) and P(Y)are two independent events with probabilities and of occurring, then the probability that both events will occur, P(X,Y) , is the product:
• If two events X and Yare mutually exclusive (when one occurs the other cannot occur), the probability that either X or Y will occur is:
• If the events X and Y are independent (not mutually exclusive), the probability that X or Y, or both X and Y, will occur is:
Clearly, these rules may be extended to any number of events. However, the standby redundancy situation is an exception to the use of these rules. In a standby redundancy case, dependency must be considered because the failure time distribution of the standby element depends on the state of another element. RBDs cannot deal with sequential failures.
 | This guide does not discuss common mode failures. Except in the case of standby redundancy, it is not necessary to assume constant failure rates in order that the expressions for combining reliabilities are valid. Expressions for combining reliabilities can become complicated. The aim here is simply to introduce general principles. Thus, the expressions are concerned only with simple series and redundancy configurations (see also Reliability Modelling) and do not relate to systems containing complex redundancy. As a general rule, a system should always be broken down into the simplest independent groups of items. The reliabilities of these groups can then be progressively combined to provide the system reliability. |