Optimized Reliability Allocation Case Study for BlockSim 7

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BlockSim 7 Case Studies

Case Study RC2 - Optimized Reliability Allocation

Software Used:
BlockSim 7

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:

System RBD

Subsystem A is composed of two assemblies, A and B. Assembly B is in a 2-out-of-3 redundant configuration.

Subsystem A RBD

Subsystem B is composed of two assemblies, C and D.

Subsystem B RBD

Assembly A is made up of components 0 and 1.

Assembly B is made up of components 3, 4 and 5.

Assembly B RBD

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.

equation (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.
$R_{min,i}$ is the current reliability at the time at which the optimization is to be performed.
$R_{max,i}$ 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. R_max for both subsystems is 0.99999 at 500 hrs.

Then the optimum allocation scheme for each subsystem is the one that satisfies:

equation

While minimizing:

equation

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 [Enlarge]