Razieh Seirani, Mohsen Torabian, Mohammad Hassan Behzadi and Asghar Seif
The purpose of this paper is to present an economic–statistical design (ESD) for the Bayesian
Abstract
Purpose
The purpose of this paper is to present an economic–statistical design (ESD) for the Bayesian
Design/methodology/approach
The design used in this study is based on determining the control chart of the predictive distribution and then its ESD. The new proposed cost model is presented by considering the conjugate and Jeffrey's prior distribution in calculating the expected total cycle time and expected cost per cycle, and finally, the optimal design parameters and related costs are compared with the fixed ratio sampling (FRS) mode.
Findings
Numerical results show decreases in costs in this Bayesian approach with both Jeffrey's and conjugate prior distribution compared to the FRS mode. This result shows that the Bayesian approach which is based on predictive density works better than the classical approach. Also, for the Bayesian approach, however, there is no significant difference between the results of using Jeffrey's and conjugate prior distributions. Using sensitivity analysis, the effect of cost parameters and shock model parameters and deviation from the mean on the optimal values of design parameters and related costs have been investigated and discussed.
Practical implications
This research adds to the body of knowledge related to quality control of process monitoring systems. This paper may be of particular interest to quality system practitioners for whom the effect of the prior distribution of parameters on the quality characteristic distribution is important.
Originality/value
economic statistical design (ESD) of Bayesian control charts based on predictive distribution is presented for the first time.
Details
Keywords
Salimeh Sadat Aghili, Mohsen Torabian, Mohammad Hassan Behzadi and Asghar Seif
The purpose of this paper is to develop a double-objective economic statistical design (ESD) of (
Abstract
Purpose
The purpose of this paper is to develop a double-objective economic statistical design (ESD) of (
Design/methodology/approach
The design used in this study is based on a double-objective economic statistical design of (
Findings
Numerical results indicate that it is not possible to reduce the second type of error and costs at the same time, which means that by reducing the second type of error, the cost increases, and by reducing the cost, the second type of error increases, both of which are very important. Obtained based on the needs of the industry and which one has more priority has the right to choose. These designs define a Pareto optimal front of solutions that increase the flexibility and adaptability of the
Practical implications
This research adds to the body of knowledge related to flexibility in process quality control. This article may be of interest to quality systems experts in factories where the choice between cost reduction and statistical factor reduction can affect the production process.
Originality/value
The cost functions for double-objective uniform and non-uniform sampling schemes with the Weibull shock model based on the Linex loss function are presented for the first time.
Details
Keywords
Mohammad Hosein Nadreri, Mohamad Bameni Moghadam and Asghar Seif
The purpose of this paper is to develop an economic statistical design based on the concepts of adjusted average time to signal (AATS) and ANF for
Abstract
Purpose
The purpose of this paper is to develop an economic statistical design based on the concepts of adjusted average time to signal (AATS) and ANF for
Design/methodology/approach
The design used in this study is based on a multiple assignable causes cost model. The new proposed cost model is compared with the same cost and time parameters and optimal design parameters under uniform and non-uniform sampling schemes.
Findings
Numerical results indicate that the cost model with non-uniform sampling cost has a lower cost than that with uniform sampling. By using sensitivity analysis, the effect of changing fixed and variable parameters of time, cost and Weibull distribution parameters on the optimum values of design parameters and loss cost is examined and discussed.
Practical implications
This research adds to the body of knowledge relating to the quality control of process monitoring systems. This paper may be of particular interest to practitioners of quality systems in factories where multiple assignable causes affect the production process.
Originality/value
The cost functions for uniform and non-uniform sampling schemes are presented based on multiple assignable causes with AATS and ANF concepts for the first time.
Details
Keywords
Aitin Saadatmeli, Mohamad Bameni Moghadam, Asghar Seif and Alireza Faraz
The purpose of this paper is to develop a cost model by the variable sampling interval and optimization of the average cost per unit of time. The paper considers an…
Abstract
Purpose
The purpose of this paper is to develop a cost model by the variable sampling interval and optimization of the average cost per unit of time. The paper considers an economic–statistical design of the X̅ control charts under the Burr shock model and multiple assignable causes were considered and compared with three types of prior distribution for the mean shift parameter.
Design/methodology/approach
The design of the modified X̅ chart is based on the two new concepts of adjusted average time to signal and average number of false alarms for X̅ control chart under Burr XII shock model with multiple assignable causes.
Findings
The cost model was examined through a numerical example, with the same cost and time parameters, so the optimal of design parameters were obtained under uniform and non-uniform sampling schemes. Furthermore, a sensitivity analysis was conducted in a way that the variability of loss cost and design parameters was evaluated supporting the changes of cost, time and Burr XII distribution parameters.
Research limitations/implications
The economic–statistical model scheme of X̅ chart was developed for the Burr XII distributed with multiple assignable causes. The correlated data are among the assumptions to be examined. Moreover, the optimal schemes for the economic-statistic chart can be expanded for correlated observation and continuous process.
Practical implications
The economic–statistical design of control charts depends on the process shock model distribution and due to difficulties from both theoretical and practical aspects; one of the proper alternatives may be the Burr XII distribution which is quite flexible. Yet, in Burr distribution context, only one assignable cause model was considered where more realistic approach may be to consider multiple assignable causes.
Originality/value
This study presents an advanced theoretical model for cost model that improved the shock model that presented in the literature. The study obviously indicates important evidence to justify the implementation of cost models in a real-life industry.