A Hidden Semi-Markov Model with Duration-Dependent State Transition Probabilities for Prognostics

<table class="table-group" id="tab5"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td align="left">System state</td><td align="center">Normal 0</td><td align="center">Degradation level 1</td><td align="center">Degradation level 2</td><td align="center">Failure 3</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td align="left">Mean</td><td align="center">7.9577</td><td align="center">5.3105</td><td align="center">7.1435</td><td align="center">3.3435</td></tr><tr><td align="left">Variance</td><td align="center">1.3953</td><td align="center">1.1328</td><td align="center">0.7924</td><td align="center">0.5452</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mean and variance of duration in each state <svg height="16.450001" id="M196" style="vertical-align:-3.21404pt" version="1.1" viewbox="0 0 73.5 16.450001" width="73.5" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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Mathematical Problems in Engineering

tab5

Table 5

Table 5: A Hidden Semi-Markov Model with Duration-Dependent State Transition Probabilities for Prognostics 