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. [30–32].

(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	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
	avg	up	low	avg	up	low	avg	up	low
	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