Mathematical Problems in Engineering / 2015 / Article / Tab 3

Research Article

Hidden Semi-Markov Models for Predictive Maintenance

Table 3

Average absolute prediction error () of the RUL estimation using the state duration estimator of (16) introduced by Azimi et al. [3032].
(a) of the RUL estimation for the continuous observation test cases

Test case Duration distribution
Gaussian Gamma Weibull
avguplowavguplowavguplow

1 57.8 51.0 66.8 26.2 9.7 52.7 25.9 28.4 64.6
2 50.2 44.4 57.7 21.3 17.0 46.9 29.0 19.2 70.8
3 50.3 44.7 57.3 27.1 8.7 56.5 34.5 13.9 73.4
4 51.8 46.0 60.4 21.3 14.3 45.9 34.9 17.1 78.7
5 59.4 53.7 66.2 29.0 9.5 55.4 33.4 15.6 74.9
6 58.0 51.7 67.1 25.8 8.3 54.1 23.1 25.8 66.5
7 59.4 53.6 66.9 18.2 12.5 47.7 36.0 17.1 74.4
8 63.4 55.6 72.3 19.4 15.7 44.1 34.8 17.8 77.0
9 49.1 43.5 57.0 14.5 17.1 43.2 25.1 26.7 67.0
10 54.4 48.4 62.8 23.2 7.9 52.7 24.1 24.5 67.4
Average 55.4 49.3 63.5 22.6 12.1 49.9 30.1 20.6 71.5

(b) of the RUL estimation for the discrete observation test cases

Test case Duration distribution
Gaussian Gamma Weibull
avguplowavguplowavguplow

1 51.4 41.0 62.4 42.4 31.8 53.0 32.6 26.4 73.6
2 49.6 39.9 60.4 59.5 48.3 70.8 31.3 27.6 69.3
3 50.2 38.6 62.3 46.5 35.7 57.4 32.4 25.7 70.2
4 42.2 31.5 53.8 50.1 40.5 60.6 23.7 36.1 60.3
5 44.3 33.9 55.8 47.8 37.4 59.1 36.0 25.6 76.5
6 52.2 43.2 62.7 55.2 44.3 66.9 27.2 31.6 64.3
7 55.0 43.9 66.8 56.0 45.7 67.0 34.7 23.2 74.4
8 50.3 39.0 62.0 60.4 50.5 71.0 35.1 26.4 72.4
9 55.5 47.4 64.0 48.0 37.2 59.5 31.8 22.2 73.6
10 49.0 38.2 60.7 52.1 41.2 63.1 29.4 28.9 68.7
Average 50.0 39.7 61.1 51.8 41.3 62.9 31.4 27.4 70.4

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