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Robust design of processes and products using the mathematics of the stochastic frontier (SF)

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Abstract

The paper discusses a generic procedure for the parameter design of product and process development using planned and non-planned experiments. The method can predict the system sensitivity (robustness) against the stochastic stressful noises (e.g., unit-to-unit, stochastic chocks, environmental variation) and the non-natural sources of variation explaining the inability of the developed product/process to achieve its optimal functionality, beyond the pure random disturbances. The intrinsic and the extrinsic insensitivity components are isolated and evaluated using the stochastic frontier production methodology. The Cobb-Douglas and the TransLog, two accepted functional forms for the stochastic frontier model, are used to check the sample data adequacy and predictability. Hypothesis tests regarding the magnitude and the direction of the intrinsic and the extrinsic robustness components, the distributional form of the extrinsic insensitivity, and the estimation of the stochastic frontier parameters are performed using the maximum likelihood estimator. Finally, for the sake of completeness and applicability, the method has been demonstrated using three industrial case studies.

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Abbreviations

CD:

Cobb-Douglas

CRS:

Constant Return to Scale

DFSS:

Design for Six Sigma

DMU:

Decision Making Unit

DRS:

Decreasing Return to Scale

ENI:

Extrinsic Noise Insensitivity

INI:

Intrinsic Noise Insensitivity

IRS:

Increasing Return to Scale

LR-statistic:

Log Ratio-statistic

LTB:

the ‘Larger is The Better’

ML:

Maximum Likelihood

NTB:

the ‘Nominal is The Better’

OLS:

Ordinary Least Square

PCH:

Performance CHaracteristic

SF:

Stochastic Frontier

S/N:

Signal to Noise ratio

STB:

the ‘Smaller is The Better

STI:

System Total Insensitivity

TE:

Technical inEfficiency

TL:

TransLog

VRS:

Varying Return to Scale

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Acknowledgments

The authors would like to thank the IJAMPT editor and the anonymous reviewers for the contribution they made to this article.

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  1. Laboratoire, Mécanique, Productique et Energétique, LR18ES01, Ecole Nationale Supérieure d’Ingénieurs de Tunis, University of Tunis, 5 Avenue Taha Hussein, BP, 56, Bâb Manara, 1008, Tunis, Tunisia

    Ali Trabelsi & Mohamed Ali Rezgui

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Trabelsi, A., Rezgui, M.A. Robust design of processes and products using the mathematics of the stochastic frontier (SF). Int J Adv Manuf Technol 106, 2829–2841 (2020). https://doi.org/10.1007/s00170-019-04503-6

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