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Reliability evaluation and big data analytics architecture for a stochastic flow network with time attribute

  • S.I.: Reliability Modeling with Applications Based on Big Data
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Abstract

A network with multi-state (stochastic) elements (arcs or nodes) is commonly called a stochastic flow network. It is important to measure the system reliability of a stochastic flow network from the perspective of operations management. In the real world, the system reliability of a stochastic flow network can vary over time. Hence, a critical issue emerges—characterizing the time attribute in a stochastic flow network. To solve this issue, this study bridges (classical) reliability theory and the reliability of a stochastic flow network. This study utilizes Weibull distribution as a possible reliability function to quantify the time attribute in a stochastic flow network. For more general cases, the proposed model and algorithm can apply any reliability function and is not limited to Weibull distribution. First, the reliability of every single component is modeled by Weibull distribution to consider the time attribute, where such components comprise a multi-state element. Once the time constraint is given, the capacity probability distribution of elements can be derived. Second, an algorithm to generate minimal component vectors for given demand is provided. Finally, the system reliability can be calculated in terms of the derived capacity probability distribution and the generated minimal component vectors. In addition, a big data architecture is proposed for the model to collect and estimate the parameters of the reliability function. For future research in which very large volumes of data may be collected, the proposed model and architecture can be applied to time-dependent monitoring.

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Abbreviations

MC:

Minimal cut

MP:

Minimal path

RSDP:

Recursive sum of disjoint products

a i :

ith arc

A :

{ai|i = 1, 2, …, n}: set of n arcs

N :

Set of nodes

G :

(A, N): a stochastic flow network

x i :

Number of (available) components in ai

C i :

Total number of identical components in ai

k i :

Capacity of a component

D :

(Total) demand amount

t * :

Required completion time

d t* :

Demand rate to process D in t*

y i(d t*):

Minimal number of components for ai to satisfy (D, t*)

\( \left\lceil \Delta \right\rceil \) :

Ceiling function to find the smallest integer no less than Δ

R i :

Reliability of ai to satisfy (D, t*)

r i(t):

Reliability of single component in ai

α :

Scale parameter (characteristic life) of Weibull distribution

β :

Shape parameter of Weibull distribution

R i(t, x i):

Probability that ai can provide at least xi components until time t

R i(t, y i(d t*)):

Time-dependent reliability of ai

h :

Number of minimal component vectors

Y(d t*):

(y1(dt*), y2(dt*), …, yn(dt*)): the minimal component vector

B μ :

Set of {X|X ≥ Y(dt*)μ}

R sys :

System reliability

g :

Number of minimal paths

P j :

jth MP

f j :

Flow on the jth MP

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Funding

This work was supported by the Ministry of Science and Technology, Taiwan, Republic of China [Grant Number MOST 106-2221-E-507-004-MY3].

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Authors and Affiliations

  1. Department of Industrial Engineering and Management, National Quemoy University, Kinmen County, 892, Taiwan, ROC

    Ping-Chen Chang

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Correspondence to Ping-Chen Chang.

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Chang, PC. Reliability evaluation and big data analytics architecture for a stochastic flow network with time attribute. Ann Oper Res 311, 3–18 (2022). https://doi.org/10.1007/s10479-019-03427-4

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