The perturbation method, the Edgeworth series, the reliability-based optimization, the reliability sensitivity technique, and the robust design are employed to present a practical and effective approach for the robust reliability design of the Banjo flange with arbitrary distribution parameters on the condition of known first four moments of original random variables. The theoretical formulas of robust reliability design for the Banjo flange with arbitrary distribution parameters are obtained. The respective program can be used to obtain the robust reliability design parameters of the Banjo flange with arbitrary distribution parameters accurately and quickly.

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