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Selection of optimal target reliability in RBDO through reliability-based design for market systems (RBDMS) and application to electric vehicle design

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Abstract

Reliability-based design optimization (RBDO) allows decision-makers to achieve target reliability in product performance under engineering uncertainties. However, existing RBDO studies assume the target reliability as a given parameter and do not explain how to determine the optimal target reliability. From the perspective of the market, designing a product with high target reliability can satisfy many customers and increase market demand, but it can generate a large cost leading to profit reduction of the company. Therefore, the target reliability should be a decision variable which needs to be found to maximize the company profit. This paper proposes a reliability-based design for market systems (RBDMS) framework by integrating RBDO and design for market system (DMS) approaches to find the optimal target reliability. The proposed RBDMS framework is applied to electric vehicle (EV) design problems to validate effect of the target reliability on company profit—or market share—and engineering performances of EV. Several observations about the optimal target reliability are presented from the case study with various scenarios. From the EV design case study, it is verified that the proposed RBDMS framework is an effective way of finding the optimal target reliability that maximizes the company profit, and the optimal target reliability varies depending on the situation of market and competitors.

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Abbreviations

SoC :

State of charge of battery

DoD :

Depth of discharge of battery

D :

DoD

F :

Additional fraction of nominal capacity

P :

Penalty factor for deeper DoD

A :

Capacity loss factor

σ :

1 − A

Π :

Profits

D :

Market demands

MC :

Manufacturing cost

C :

Compensation costs

X :

Deterministic decision variable vector

X power :

Powertrain design variable vector

R :

Target reliability

W :

Warranted battery lifetime

Price :

Price

\( {P}_F^{\mathrm{Target}} \) :

Target probability of failure for probabilistic constraints

g :

Inequality constraint functions

G :

Probabilistic constraint functions

N S :

Number of battery cells in series

N P :

Number of battery cells in parallel

FR :

Final gear ratio

RP e :

Random parameter vector of engineering model

P :

Matrix of probabilistic performances

P MPGe :

Vector of probabilistic MPGe

P range :

Vector of probabilistic driving range

P speed :

Vector of probabilistic top speed

P accel :

Vector of probabilistic acceleration

P Batt :

Vector of probabilistic battery lifetime

PR :

Vector of engineering performances that satisfy the target reliability

A :

Advertised attribute vector

A eng :

Vector of advertised attributes determined from engineering model

f engineering :

Engineering model

f attribute :

Attribute model

f marketing :

Marketing model

f X(x):

Joint probability density function

ΩF :

Failure set

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Acknowledgments

The authors would like to thank Alparslan Emrah Bayrak of the University of Michigan for his help in building the engineering model.

Funding

This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (No. 2017R1C1B2005266) and the development of thermoelectric power generation system and business model utilizing non-use heat of industry funded by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade Industry & Energy (MOTIE) of the Republic of Korea (No. 20172010000830).

Author information

Correspondence to Namwoo Kang or Ikjin Lee.

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Lee, U., Kang, N. & Lee, I. Selection of optimal target reliability in RBDO through reliability-based design for market systems (RBDMS) and application to electric vehicle design. Struct Multidisc Optim 60, 949–963 (2019). https://doi.org/10.1007/s00158-019-02245-3

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Keywords

  • Reliability-based design optimization (RBDO)
  • Design for market systems (DMS)
  • Electric vehicles
  • Target reliability
  • Uncertainty