Control chart for exponential individual samples with adaptive sampling interval method based on economic statistical design: an extension of costa and Rahim’s model

2021 ◽  
pp. 1-17
Author(s):  
Masoud Tavakoli ◽  
Ali Akbar Heydari
Keyword(s):  
Control Chart ◽  
Adaptive Sampling ◽  
Statistical Design ◽  
Sampling Interval ◽  
Interval Method

Comparison Between the Economic-Statistical Design of Double and Triple Sampling X ¯ \bar{X} Control Charts

2017 ◽  
Vol 32 (1) ◽  
Author(s):  
Azamsadat Iziy ◽  
Bahram Sadeghpour Gildeh ◽  
Ehsan Monabbati
Keyword(s):  
Optimal Control ◽  
Quality Control ◽  
Control Chart ◽  
Control Charts ◽  
Statistical Design ◽  
Sampling Interval ◽  
Point Of View ◽  
Double Sampling ◽  
Control Limits

AbstractControl charts have been established as major tools for quality control and improvement in industry. Therefore, it is always required to consider an appropriate design of a control chart from an economical point of view before using the chart. The economic design of a control chart refers to the determination of three optimal control chart parameters: sample size, the sampling interval, and the control limits coefficient. In this article, the double sampling (DS)

scholarly journals Economic Statistical Design of Variable Sampling Interval X¯ $\overline X $ Control Chart Based on Surrogate Variable Using Genetic Algorithms

2016 ◽  
Vol 7 (4) ◽  
pp. 54-64
Author(s):  
Tae-Hoon Lee ◽  
Sung-Hoon Hong ◽  
Hyuck-Moo Kwon ◽  
Minkoo Lee
Keyword(s):  
Genetic Algorithms ◽  
Control Chart ◽  
Statistical Design ◽  
Sampling Interval ◽  
Performance Variable ◽  
Variable Sampling Interval ◽  
Surrogate Variable ◽  
Variable Sampling ◽  
Proposed Model ◽  
A Performance

Abstract In many cases, a $\overline X $ control chart based on a performance variable is used in industrial fields. Typically, the control chart monitors the measurements of a performance variable itself. However, if the performance variable is too costly or impossible to measure, and a less expensive surrogate variable is available, the process may be more efficiently controlled using surrogate variables. In this paper, we present a model for the economic statistical design of a VSI (Variable Sampling Interval) $\overline X $ control chart using a surrogate variable that is linearly correlated with the performance variable. We derive the total average profit model from an economic viewpoint and apply the model to a Very High Temperature Reactor (VHTR) nuclear fuel measurement system and derive the optimal result using genetic algorithms. Compared with the control chart based on a performance variable, the proposed model gives a larger expected net income per unit of time in the long-run if the correlation between the performance variable and the surrogate variable is relatively high. The proposed model was confined to the sample mean control chart under the assumption that a single assignable cause occurs according to the Poisson process. However, the model may also be extended to other types of control charts using a single or multiple assignable cause assumptions such as VSS (Variable Sample Size) $\overline X $ control chart, EWMA, CUSUM charts and so on.

scholarly journals Economic and Economic-Statistical Design of Multivariate Bayesian Control Chart with Variable Sampling Intervals

2020 ◽  
pp. 737-750
Author(s):  
Masoud Tavakoli ◽  
Reza Pourtaheri
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Fixed Ratio ◽  
Statistical Design ◽  
Sampling Interval ◽  
Design Parameters ◽  
Variable Sampling ◽  
Sampling Intervals ◽  
Bayesian Control ◽  
T2 Control Chart

Due to the proper performance of Bayesian control chart in detecting process shifts, it recently has become the subject of interest. It has been proved that on Bayesian and traditional control charts, the economic and statistical performances of the variable sampling interval (VSI) scheme are superior to those of the fixed ratio sampling (FRS) strategy in detecting small to moderate shifts. This paper studies the VSI multivariate Bayesian control chart based on economic and economic-statistical designs. Since finding the distribution of Bayesian statistic is t complicated, we apply Monte Carlo method and we employ artificial bee colony (ABC) algorithm to obtain the optimal design parameters (sample size, sampling intervals, warning limit and control limit). In the end, this case study is compared with VSI Hotelling’s T2 control chart and it is shown that this approach is more desirable statistically and economically.

scholarly journals Statistical Design of an Adaptive SyntheticX-Control Chart with Run Rule on Service and Management Operation

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Shucheng Yu ◽  
Qiang Wan ◽  
Zhenghong Wei ◽  
Tianbo Tang
Keyword(s):  
Control Chart ◽  
Statistical Design ◽  
Sampling Interval ◽  
Cusum Chart ◽  
Process Mean ◽  
Markov Chain Approach ◽  
Variable Sampling ◽  
Proposed Model ◽  
Adaptive Schemes ◽  
Management Operation

An improved syntheticX-control chart based on hybrid adaptive scheme and run rule scheme is introduced to enhance the statistical performance of traditional syntheticX-control chart on service and management operation. The proposed scientific hybrid adaptive schemes consider both variable sampling interval and variable sample size scheme. The properties of the proposed chart are obtained using Markov chain approach. An extensive set of numerical results is presented to test the effectiveness of the proposed model in detecting small and moderate shifts in the process mean. The results show that the proposed chart is quicker than the standard syntheticX-chart and CUSUM chart in detecting small and moderate shifts in the process of service and management operation.

Adaptive Shewhart Control Charts Under Fuzzy Parameters with Tuned Particle Swarm Optimization Algorithm

2021 ◽  
pp. 1-36
Author(s):  
Amirhossein Amiri ◽  
Ali Salmasnia ◽  
Meraj Zarifi ◽  
Mohammad Reza Maleki
Keyword(s):  
Particle Swarm Optimization ◽  
Control Chart ◽  
Adaptive Sampling ◽  
Control Charts ◽  
Particle Swarm ◽  
Design Parameters ◽  
Swarm Optimization ◽  
Inference System ◽  
Scale Parameters ◽  
Adaptive Control Charts

In recent years, adaptive control charts in which the design parameters depend on the observed samples have been successfully used as efficient alternatives for traditional control charts with constant parameters. In crisp run control rules, the process state may change very sharply from in-control to out-of-control conditions which increase the rate of false alarms. To overcome this drawback, this paper presents an adaptive Shewhart-type control chart, where the design parameters (sample size ([Formula: see text]), sampling interval ([Formula: see text]), and control limit coefficients ([Formula: see text] and [Formula: see text])) are defined with linguistic variables. To accomplish that, the chart parameters are determined based on the location of eight previous chart statistics using a set of fuzzy rules in a continuous environment. In order to improve the sensitivity of the proposed control chart in detecting small shifts in both location and scale parameters, the adaptive procedure is designed by integration of fuzzy Western Electric rules and fuzzy adaptive sampling rules. After designing the control charts using a fuzzy inference system (FIS), in order to provide an economic design of the proposed control chart, a tuned Particle Swarm Optimization (PSO) algorithm is employed to determine the optimal values corresponding to membership functions of the control chart parameters. Finally, using simulation studies, the capability of the proposed control chart is analyzed and compared with common charts in the literature. The results confirm that under different shifts in location and scale parameters, the proposed control chart outperforms other charts in terms of both economic and statistical criteria.

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