Journal of Quality Engineering and Management

Abstract Purpose: The main goal of this study is to propose a realistic and practical model for the economic-statistical design of control charts in the presence of multiple independent assignable causes under the Burr Type XII shock model. The model aims to minimize the underestimation of the actual cost per unit time of the quality cycle.
Methodology: This research utilizes the Burr Type XII distribution as a shock model to develop the RED model for optimal design of control charts. The Lorenz and Van cost function is also extended to account for multiple assignable causes, and a numerical example is provided to demonstrate the solution approach.
Findings: Numerical results reveal that the proposed model outperforms existing models in accurately estimating the real cost per unit time of the quality cycle. Furthermore, an increase in the shock probability leads to a non-decreasing trend in the average cost, underscoring the importance of accounting for this probability in E(A) calculations.
Originality/Value: This is the first study to employ the Burr Type XII distribution as a shock model in the economic-statistical design of control charts. By extending existing cost models, the paper introduces a novel and realistic approach to designing control charts in the presence of multiple independent shocks.

Abstract Modelling and estimating the intensity function of a point pattern is one of the preliminary and fundamental issues in inference of point processes, and it considered as a prerequisite for many other problems. It has been addressed from different perspectives. With the rapid development of data-collection technologies, a wide range of data has been produced, and considering covariates has been a big step forward in the theory of point processes, which has mainly been addressed from a parametric perspective.

In this paper, we introduce a novel approach for nonparametrically estimating the intensity of an inhomogeneous Poisson point process, which is an unknown function of several independent spatial covariates. In the proposed method, using the approximation technique of radial basis function for unknown multivariate functions, the nonparametric model of the intensity function is transformed into a log-linear model. Since the accuracy of the multivariate function approximation directly affects the accuracy of the intensity function estimate, we enhance the nonparametric estimation quality of the intensity function in spatial Poisson point processes by optimizing the shape parameter of the radial basis function through minimizing the Bayesian information criterion.

Abstract This paper for the first time in the statistical design of adaptive control charts, deals with the statistical design of univariate control chart X ̅ under the Weibull shock model. practically, the use of shock models with more flexible risk rate functions in the statistical design of adaptive control charts is closer to reality. This study shows that diagram X ̅-VRS under Weibull shock model with non-uniform sampling intervals and variable sample size, compared to diagram X ̅ under Weibull shock model with non-uniform sampling intervals and fixed sample size (FRS), Detecting average changes is faster and performs better.
In this model, with increasing changes in the mean, the rate of detection of changes in the mean increases and the value of h_1 increases and the ANF decreases. Also relatively large changes (𝛅≥2), lead to a relatively small sample size (n_2≤ 10) and smaller changes (2 ≤ 𝛅 <0.25) lead to a larger optimal sample size (〖"11≤n" 〗_2 "≤14" ).