PROPOSAL OF AN OPTIMAL REDUNDANCY AND RELIABILITY ALLOCATION APPROACH FOR DESIGNING COMPLEX SYSTEMS

Garcia, P. A. A.; Neves, T. A.; Jacinto, C. M. C.; Alvarez, G. B.; Garcia, V. S.; Motta, G. S.

doi:10.1590/0101-7438.2022.042nspe1.00263499

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ARTICLES • Pesqui. Oper. 42 (spe1) • 2022 • https://doi.org/10.1590/0101-7438.2022.042nspe1.00263499 copy

PROPOSAL OF AN OPTIMAL REDUNDANCY AND RELIABILITY ALLOCATION APPROACH FOR DESIGNING COMPLEX SYSTEMS

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

Problems of optimal reliability and redundancy allocation are not new. However, the literature describes two isolated situations, either when redundancy allocation is the target and the reliability metrics of the components are known, or focusing on the reliability allocation, that demands the metrics to be known in advance and the use of some optimization approach. In the present paper, we consider a combined situation, i.e., when both situations must be considered together. To guide the allocation process, we developed a cost function that considers the costs of acquisition, development and/or improvement as a function of monetary effort, along with the reliability target and expected failure costs. The results considering two classical test problems in the literature demonstrated the efficacy of the proposed approach to deal with similar situations.

Keywords:
optimal reliability allocation; optimal redundancy allocation; reliability optimization

Component	R(t) ⁽¹⁾	R0(t) ⁽¹⁾	c ₀	c _a	CF	m	ρ
1	0.90	-	-	1	0.7	3	-
2	-	0.81	1	-	0.7	3	0.1054
3	0.85	-	-	2	0.7	3	-
4	0.83	-	-	3	0.7	3	-
5	-	0.83	2	-	1	3	0.0675

Solution	Rs(t)	Total Cost	(n1, n2, n3, n4, n5)	(R2, R5)
1	0.998574	50.4589	(3, 3, 2, 3, 3)	(0.941272, 0.83)
2	0.998114	46.5611	(3, 3, 3, 1, 3)	(0.941272, 0.83)
3	0.994864	44.5744	(3, 3, 2, 1, 3)	(0.941272, 0.83)
4	0.993781	30.8609	(3, 3, 2, 3, 3)	(0.941272, 0.83)
5	0.991304	36.7169	(3, 3, 1, 3, 3)	(0.81, 0.951594)
6	0.991304	36.7169	(3, 3, 1, 3, 3)	(0.81, 0.951594)
7	0.990089	24.9764	(3, 3, 2, 1, 3)	(0.941272, 0.83)
8	0.983497	13.1452	(3, 3, 2, 1, 3)	(0.81, 0.83)
9	0.963603	12.1329	(3, 3, 1, 1, 3)	(0.825589, 0.83)
10	0.95343	10.2407	(2, 3, 1, 1, 3)	(0.81, 0.83)
11	0.868111	10.2022	(1, 3, 1, 1, 3)	(0.825589, 0.83)
12	0.866755	9.30371	(1, 3, 1, 1, 3)	(0.81, 0.83)

Solution	Rs(t)	Total Cost	(n1, n2, n3, n4, n5)	(R2, R5)
1	0.999996	48.5528	(3, 3, 3, 1, 3)	(0.993801, 0.83)
2	0.999989	48.5527	(3, 2, 3, 1, 3)	(0.993801, 0.83)
3	0.999977	46.5661	(3, 3, 2, 1, 3)	(0.993801, 0.83)
4	0.999963	21.0162	(3, 3, 3, 3, 3)	(0.81, 0.83)
5	0.999963	21.0162	(3, 3, 3, 3, 3)	(0.81, 0.83)
6	0.999811	17.1189	(3, 3, 1, 3, 3)	(0.81, 0.83)
7	0.999767	17.0393	(2, 3, 3, 2, 3)	(0.81, 0.83)
8	0.998911	16.0909	(3, 2, 2, 2, 2)	(0.81, 0.83)
9	0.997996	13.2016	(2, 3, 1, 1, 3)	(0.85711, 0.83)
10	0.997325	10.2407	(2, 3, 1, 1, 3)	(0.81, 0.83)
11	0.983777	9.30371	(1, 3, 1, 1, 3)	(0.81, 0.83)
12	0.983777	9.30371	(1, 3, 1, 1, 3)	(0.81, 0.83)

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[1] *Corresponding author