Hidden Semi-Markov Models for Predictive Maintenance

Table 2

Average absolute prediction error () of the RUL estimation using the proposed state duration estimator of (20).

(a) of the RUL estimation for the continuous observation test cases

Test case	Duration distribution
	Gaussian			Gamma			Weibull
	avg	up	low	avg	up	low	avg	up	low
	1	5.1	17.0	6.7	14.0	29.0	0.91	4.5	17.0	8.1
2	7.6	19.0	5.0	6.1	21.0	8.5	6.6	19.0	6.1
3	7.7	5.4	19.0	2.9	12.0	17.0	16.0	29.0	3.0
4	9.0	21.0	2.9	7.5	22.0	6.8	6.0	19.0	6.7
5	7.3	19.0	4.7	2.2	14.0	14.0	3.9	17.0	8.7
6	6.5	18.0	5.6	5.1	18.0	10.0	14.0	27.0	2.7
7	4.7	16.0	7.5	4.8	17.0	11.0	1.2	13.0	12.0
8	10.0	22.0	2.9	5.2	18.0	10.0	9.2	22.0	3.9
9	3.1	9.2	14.0	2.0	16.0	13.0	8.2	21.0	4.9
10	6.4	18.0	5.6	7.5	22.0	6.9	3.3	12.0	13.0
Average	6.8	17.0	7.4	5.7	19.0	9.9	7.3	20.0	7.0

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

Test case	Duration distribution
	Gaussian			Gamma			Weibull
	avg	up	low	avg	up	low	avg	up	low
	1	2.1	11.0	14.0	3.1	8.8	14.0	2.4	12.0	13.0
2	2.1	11.0	13.0	11.0	22.0	3.3	19.0	32.0	7.1
3	5.1	17.0	7.6	6.6	18.0	5.1	2.3	14.0	11.0
4	5.9	6.5	18.0	5.2	17.0	6.7	4.2	16.0	9.0
5	3.2	14.0	10.0	8.3	19.0	3.4	12.0	24.0	2.9
6	12.0	24.0	2.7	6.2	18.0	5.2	4.1	8.4	16.0
7	2.9	15.0	9.7	9.3	21.0	2.3	19.0	31.0	6.6
8	15.0	27.0	7.0	7.4	18.0	4.3	4.3	17.0	9.4
9	5.9	18.0	7.7	11.0	23.0	5.5	3.9	16.0	8.8
10	3.5	11.0	14.0	5.5	6.0	16.0	5.2	17.0	7.1
Average	5.7	15.0	10.0	7.4	17.0	6.6	7.7	19.0	9.0