Dynamic Time Series Reliability Analysis for Long-Life Mechanic Parts with Stress-Strength Correlated Interference Model

doi:10.23940/ijpe.19.01.p6.5666

Abstract

Abstract:

Based on data of the equivalent stress from the ANSYS for a loaded hollow shaft, the correlation between a mechanical part’s elastic modulus and the corresponding Von Mises stress is statistically verified in this paper. Using the Copula correlation theory, a static reliability model involving stress-strength interference is built. According to the performance degradation data of mechanical parts with long-life and high-reliability, deterministic time series models are used to extract the characteristic information of the distribution of degradation variables, and then a method is proposed for estimating the characteristic parameters of degradation strength and integrated stress. Two-stage maximum likelihood estimation is applied to determine the scalar degree of correlation between both, and then a reliability assessment of long-life mechanical parts is completed.

Key words: stress-strength interference model, time series, correlation, copula, reliability, statistical analysis

Bin Suo. Dynamic Time Series Reliability Analysis for Long-Life Mechanic Parts with Stress-Strength Correlated Interference Model [J]. Int J Performability Eng, 2019, 15(1): 56-65.

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No.	Material	Modulus of elasticity/GPa
1	Cl60 steel	205
2	B-wheel steel	192
3	45# steel	206
4	Aluminum	71.7
5	Porcelain	55
6	Lead	17
7	Gray cast iron	130
8	Cast aluminum bronze	105
9	Cold-drawing brass	95
10	Rolling zinc	84
11	Cast iron	100
12	Stainless steel	190
13	Magnesium	44.8
14	Nickel	207
15	Glass	46.2
16	Graphite	36.5
17	Titanium	102.04
18	Tungsten	344.7
19	Wood	11
20	Rubber	0.00784

No.	Material	Von Mises/MPa
1	Cl60 steel	13.98746
2	B-wheel steel	12.9309
3	45# steel	13.83837
4	Aluminum	4.94067
5	Porcelain	3.64025
6	Lead	1.20912
7	Gray cast iron	8.84996
8	Cast aluminum bronze	7.0457
9	Cold-drawing brass	6.22824
10	Rolling zinc	5.66791
11	Cast iron	6.62864
12	Stainless steel	12.95731
13	Magnesium	3.09795
14	Nickel	14.06966
15	Glass	3.08982
16	Graphite	2.5808
17	Titanium	6.94558
18	Tungsten	23.39905
19	Wood	0.75896
20	Rubber	0.00284

	Modulus of elasticity	Von Mises stress
N	20	20
Mean	112.15	7.59346
Std. Deviation	87.665	5.94303
Minimum	0	0.00284
Maximum	345	23.39905

The fitting of exponential distribution		Modulus of elasticity	Von Mises stress
N		20	20
Exponential parameter	Mean	112.15	7.5935
Most extreme differences	Absolute	.129	.138
	Positive	.108	.107
	Negative	-.129	-.138
Kolmogorov-smirnov z		.578	.618
Asymp. Sig. (2-tailed)		.892	.840