Journal of Quality Engineering and Management

Abstract In many statistical process control applications, the relationship between a response variable and one or more control variables is evaluated by a function called a profile. Profiles are divided into different types according to the nature of the response variable, such as linear and nonlinear profiles. In this research, a new control diagram based on the generalized linear test approach and fractional regression is presented to monitor multiple linear profiles with interactions in phase 2. The simulation results of the proposed control diagram show its much better performance than the control diagram based on the least squares error method.

Abstract Curve fitting is an important tool in data analysis, geometric modeling, and other engineering applications. When the shape of the measured data function is complex, estimating the curve using a polynomial function becomes difficult. In such cases, spline functions are generally preferred due to their higher accuracy and smoother approximation compared to other approximation functions. Often, for proper spline fitting, the number and locations of knots are unknown. Therefore, this paper presents a genetic algorithm to simultaneously determine the number and positions of knots based on a minimum error objective function without any restrictive assumptions. The proposed algorithm employs both the maximum likelihood estimation and least squares error methods for curve fitting. The performance of the proposed algorithm is evaluated using numerical examples with both methods. Simulation results indicate that when observations follow a normal distribution, the least squares method performs better. However, the main advantage of the maximum likelihood-based approach is its applicability to all statistical distributions. Finally, the effectiveness of the proposed approach is demonstrated through a practical case study.