Reliability Distribution for an Aircraft Launch System

Build a reliability model for an aircraft launch system using exponential component failure rates

In the following, boolean variables are used to represent the functioning of components of a particular aircraft launch system. The overall ability to launch is formed from a logical combination of the individual component variables.

Model the launch of an aircraft. The hangar door can be opened electronically or manually:

In[1]:=

hangarDoor=power∨manual;

Two fuel pumps (labelled A2 and B2) require power to run:

In[2]:=

fuelTransferA2=power∧pumpA2;fuelTransferB2=power∧pumpB2;

Two more pumps (A1 and B1) run on reliable batteries. Assuming that fuel transfer requires either pump A1 or A2, as well as either pump B1 or B2, to be functioning gives the following overall fuel transfer structure:

In[3]:=

fuelTransfer=(pumpA1∧(pumpB1∨fuelTransferB2))∨(fuelTransferA2∧(pumpB1∨fuelTransferB2));

The aircraft launch requires successful operation of the fuel storage, fuel transfer, hangar door, and deicing systems:

In[4]:=

launch=fuelStorage∧fuelTransfer∧hangarDoor∧deicing;

List the component variables used in the launch logic:

In[5]:=

vars={deicing,fuelStorage,manual,power,pumpA1,pumpB1,pumpA2,pumpB2};

Attach an exponential model to each component with the given failure rates per hour. Note that the electrical power failure rate is left as a free parameter

In[6]:=

lifetimes=ExponentialDistribution/@{

-7

-8

-3

,λ,5×

-4

,5×

-4

,5×

-4

,5×

-4

};dists=Transpose[{vars,lifetimes}];

Build the overall system lifetime distribution using the launch success logic:

In[7]:=

ℛ=ReliabilityDistribution[launch,dists];

Compute the survival function (probability the system is still operating at time t) and the mean time to failure:

In[8]:=

sf=SurvivalFunction[ℛ,t]

Out[8]=

1	t<0
-11t/100000000   -t/500  + -tλ  - -t/500  + 2 1- 2 (1- -t/2000  )  	True

In[9]:=

μ=Mean[ℛ]

Out[9]=

100000000

200011

100011

100000000

+λ

150011

100000000

+λ

Study how the reliability varies for three different values of the power failure rate

In[10]:=

PlotEvaluateTableLegended[sf,Row[{"λ","=",λ}]],λ,λVals=N@12×

-3

,2×

-4

,12×

-4

,{t,0,5000}

Out[10]=

	λ=0.0005
	λ=0.0002
	λ=0.00005

Compute the mean times to failure for each value of λ:

In[11]:=

Table[μ/.λf,{f,λVals}]

Out[11]=

{1166.55,1480.21,1728.64}

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Contributed by: Wolfram Staff

Reliability Distribution for an Aircraft Launch System

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