Optimal tolerance design for products with non-normal distribution based on asymmetric quadratic quality loss

Due to the effect of various factors, the product quality characteristics are sometimes non-normal distribution. In this paper, two most commonly used non-normal distributions, triangular distribution and trapezoidal distribution, are studied based on asymmetric quadratic quality loss. With asymmetric quality loss, it is necessary to optimize the process mean in order to reduce the expected quality losses. In order to optimize the process mean of the triangular distribution, the different distances between the target value and the process mean are considered, and two mathematical models are proposed to calculate the expected quality loss. Because the probability density function of the trapezoidal distribution is a three-segment function, in order to optimize the process mean of the trapezoidal distribution, three models are established. Solving the proposed models, analytical solutions for the optimal process mean are obtained, and equations for the minimum quality loss are established. Considering the sum of manufacturing cost and the minimum quality loss as the objective function, tolerance model is established to calculate the optimal tolerances. Therefore, the optimal process mean and optimal tolerances are obtained for triangular distribution and trapezoidal distribution. At last, an example is used to illustrate the validity of the established model.