Deriving and Allocating Reliability Requirements

If we refer again to Section 8.6.8, we see a requirement for a mean time between failures (MTBF) of 500 hours for the overall system. Let us assume that the overall system has four major subsystems, as shown in Figure 8.3. The requirements document specifies only the overall system MTBF requirement of 500 hours and not the subordinate MTBF requirements for the subsystems. It therefore becomes a task of the systems engineer to derive and allocate MTBF requirements for the four subsystems. Based on analysis of the subsystem technical information and requirements, as well as data from previous programs and experience, the systems engineer might derive a set of MTBF requirements as illustrated in Figure 8.3. The four subsystem MTBF-derived requirements are

• Subsystem

1:

MTBF =

2500

hours

• Subsystem

2:

MTBF =

2000

hours

• Subsystem

3:

MTBF =

1667

hours

• Subsystem

4:

MTBF =

2000

hours

Figure 8.3. Derived and allocated reliability requirements.

Note that all of these MTBFs are larger than the system requirement of 500 hours. In order to develop this set of subsystem-derived requirements, however, the systems engineer must understand the basic relationship between MTBF and failure rate for a given system, given the assumption of an exponential failure law. The relationship is

Mean time between failures (MTBF) = 1

failure rate

Also, the failure rates are additive under these circumstances, so that the overall system failure rate is the sum of the subsystem failure rates. The resultant MTBFs and failure rates for the system and its subsystems are shown in Figure 8.3. We leave it as an exercise at the end of the chapter to verify the compatibility between the stated MTBFs and failure rates.

Through this example, we see how requirements may be derived and also how they are allocated to lower levels of indenture for the system. We also note that this process cannot be accomplished without an understanding of the specific relationships between MTBFs and failure rates. This is true for all situations of derived requirements and allocation of these requirements, namely, that the algorithms that apply to the situation at hand must be known to the systems engineer.

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