Journal of Data Science and Modeling

Minimum Loss Design of X Control Chart for Correlated Data Under Weibull In-Control Times with Multiple Assignable Causes

Document Type : Research Manuscript

Authors

mohammad hossein naderi 1
Mohammad Bameni Moghadam 2
asghar Seif 3

1 PhD candidate in statistics, Allameh Tabataba'i University, Tehran, Iran.

2 Department of Statistics, Faculty of Mathematical Sciences and Computer, Allameh Tabataba'i University

3 Assistant professor of statistics, Bu-Ali Sina University, Hamedan, Iran.

https://doi.org/10.22054/jcsm.2018.36532.1014
Abstract
A proper method of monitoring a stochastic system is to use the control charts of statistical
process control in which a drift in characteristics of output may be due to one or several assignable causes. In the establishment of X charts in statistical process control, an assumption is made that there is no correlation within the samples. However, in practice, there are many cases where the correlation does exist within the samples. It would be more appropriate to assume that each sample is a realization of a multivariate
normal random vector. Using three di erent loss functions in the concept of quality control charts with economic and economic statistical design leads to better decisions in the industry. Although some research works have considered the economic design of control charts under single assignable cause and correlated data, the economic statistical design of X control chart for multiple assignable causes and correlated data under Weibull shock model with three di erent loss functions have not been presented yet. Based on the
optimization of the average cost per unit of time and taking into account the di erent combination values
of Weibull distribution parameters, optimal design values of sample size, sampling interval and control limit
coecient were derived and calculated. Then the cost models under non-uniform and uniform sampling
scheme were compared. The results revealed that the model under multiple assignable causes with correlated
samples with non-uniform sampling integrated with three di erent loss functions has a lower cost than the
model with uniform sampling.

Keywords

Economic statistical design
X control chart
Multiple assignable causes
Subjects
Journal of Data Science and Modeling
Volume 1, Issue 1 - Serial Number 1
December 2022
Pages 99-127

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