10.3 LED System Reliability
221
X2 is observed as e, which will propagate through the network to update the prior
probability. The probability of X1 and X3 posterior is.
P(x 1 , x 3 |e ) =
P(x 1 )P( e|x 1 )P( x 3 |x 1 )
x 1
P(x 1 )P( e|x 1 )
.
(10.18)
For a specific problem, the general steps of Bayesian network modeling are as
follows: (1) determine the key variables involved in the problem and the possible
values of the variables, and use one node to represent one variable in the Bayesian
network. (2) Judge the correlation or independence between different nodes, and use
graphs and directed arcs to represent them in Bayesian networks. (3) Determine the
probability parameters required for Bayesian network calculations and calculate the
probability. In general, detailed analysis about the key technologies and difficulties
of the problem to be solved is required to construct a reasonable Bayesian network
model. Only in this way can Bayesian networks effectively solve practical problems,
rather than just probabilistic calculations.
The reliability of semiconductor lighting systems depends on the individual
components. For example, the light output power of the LED chip is reduced to
80% of initial, and the light transmission performance of the optical material is
reduced to 80% of initial. That means the overall luminous performance is reduced
to 64%, which is less than 70%. Thus, the LED product is considered to have failed.
In addition, a sudden failure of a component, power module for example, can cause
the overall product to fail. Its Bayesian network can be represented by the following
figure (Fig. 10.10):
A dynamic Bayesian network (DBN) is an extended concept of a static Bayesian
network combined with (discrete) time. Therefore, a dynamic Bayesian network
is a model of discrete-time stochastic processes. A DBN represents a set of static
Bayesian networks which connect arc points between different time nodes in each
time tangent.
Markov chain
Fig. 10.10 Bayesian network in the reliability analysis of LED system products
221
X2 is observed as e, which will propagate through the network to update the prior
probability. The probability of X1 and X3 posterior is.
P(x 1 , x 3 |e ) =
P(x 1 )P( e|x 1 )P( x 3 |x 1 )
x 1
P(x 1 )P( e|x 1 )
.
(10.18)
For a specific problem, the general steps of Bayesian network modeling are as
follows: (1) determine the key variables involved in the problem and the possible
values of the variables, and use one node to represent one variable in the Bayesian
network. (2) Judge the correlation or independence between different nodes, and use
graphs and directed arcs to represent them in Bayesian networks. (3) Determine the
probability parameters required for Bayesian network calculations and calculate the
probability. In general, detailed analysis about the key technologies and difficulties
of the problem to be solved is required to construct a reasonable Bayesian network
model. Only in this way can Bayesian networks effectively solve practical problems,
rather than just probabilistic calculations.
The reliability of semiconductor lighting systems depends on the individual
components. For example, the light output power of the LED chip is reduced to
80% of initial, and the light transmission performance of the optical material is
reduced to 80% of initial. That means the overall luminous performance is reduced
to 64%, which is less than 70%. Thus, the LED product is considered to have failed.
In addition, a sudden failure of a component, power module for example, can cause
the overall product to fail. Its Bayesian network can be represented by the following
figure (Fig. 10.10):
A dynamic Bayesian network (DBN) is an extended concept of a static Bayesian
network combined with (discrete) time. Therefore, a dynamic Bayesian network
is a model of discrete-time stochastic processes. A DBN represents a set of static
Bayesian networks which connect arc points between different time nodes in each
time tangent.
Markov chain
Fig. 10.10 Bayesian network in the reliability analysis of LED system products