BlockSim Example RC2 - Optimized Reliability Allocation
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File (*.rbp)In this example, a system is defined using subdiagrams. A reliability target is set for the entire system and reliability is then allocated to the subsystems, assemblies and components using an optimized allocation methodology.
Consider the following system composed of two subsystems, A and B, as shown below:
Subsystem A is composed of two assemblies, A and B. Assembly B is in a 2-out-of-3 redundant configuration.
Subsystem B is composed of two assemblies, C and D.
Assembly A is made up of components 0 and 1.
Assembly B is made up of components 3, 4 and 5.
Assembly C is made up of components 6 and 7.
Assembly D is made up of components 8 and 9.
Furthermore, assume the following life characteristics for each component:
| Component | Life (Failure) Distribution | ||
| Comp. 0 : | Weibull | Beta = 2 | Eta = 5,000 |
| Comp. 1 : | Weibull | Beta = 2 | Eta = 4,500 |
| Comp. 3 : | Weibull | Beta = 1.5 | Eta = 8,965 |
| Comp. 4 : | Weibull | Beta = 1 | Eta = 8000 |
| Comp. 5 : | Lognormal | Log Mean = 10 | Log Sigma = 1.4 |
| Comp. 6 : | Weibull | Beta = 3 | Eta = 10,000 |
| Comp. 7 : | Weibull | Beta = 3 | Eta = 6,000 |
| Comp. 8 : | Exponential | Mean = 10,000 | |
| Comp. 9 : | Weibull | Beta = 2.2 | Eta = 7,000 |
The system reliability for this configuration at 500 hr is R(t) = 0.925656. Let's assume
that the target reliability for this system is R(t = 500) = 0.95.
Determine an optimum reliability allocation strategy assuming that the cost/difficulty of increasing an item's reliability is defined by the following function.
(1)
Where:
(
) is the penalty (or cost)
function as a function of component reliability.- f is the feasibility (or cost index) of improving a component's reliability relative to the other components in the system.
-
is the current reliability at the time at which the optimization is to be performed. -
is the maximum achievable reliability at the time at which the optimization is to be
performed.
At the system level, we'll set Subsystem 1 to f = 0.9 and Subsystems 2 to f = 0.7. Rmax for both subsystems is 0.99999 at 500 hrs.
Then the optimum allocation scheme for each subsystem is the one that satisfies:
While minimizing:
Solving this yields an optimum allocation for each subsystem. Specifically, the new target reliability for Subsystem A is 0.986137 and for Subsystem B is 0.963344.
Figure 1: Solution calculated using BlockSim 7.
The process can then be repeated for each assembly and component in the system. The results are given in the next table.
