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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Probability and Statistics".

Deadline for manuscript submissions: closed (20 November 2023) | Viewed by 8899

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Prof. Dr. Don Wardell

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Guest Editor

David Eccles School of Business, University of Utah, Salt Lake City, UT, USA
Interests: statistical process control; six sigma; service operations management

Special Issue Information

Dear Colleagues,

Statistical process control (SPC) is a proven method that employs statistical methods to monitor and control a process in a proactive way. Proper use of SPC allows process operators and owners to reduce variation and stabilize processes, which in turn leads to process improvement and reduction of waste such as rework and scrap. SPC can be applied to any process where critical-to-quality variables can be measured. Because processes are a part of all facets of our society, it can be implemented in manufacturing, services, healthcare, education, government and more. Key tools used in SPC include run charts, control charts and design of experiments.

Because of its continuing importance, we invite submissions for our special issue on SPC and its applications. Through the special issue, we wish to extend our knowledge of SPC tools and applications. We therefore welcome submissions that emphasize new methodologies for monitoring processes, especially those with unique characteristics that may not meet the assumptions of traditional tools. Submissions that focus on applications in various contexts, especially novel contexts such as healthcare, not-for-profit organizations, etc., are also encouraged. Finally, review articles will also be considered, especially those that identify gaps in past and current research and suggest directions for new studies.

Prof. Dr. Don Wardell
Guest Editor

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Keywords

statistical process control
control charts
design of experiments
six sigma
process improvement

Published Papers (6 papers)

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Research

30 pages, 6368 KiB

Open AccessArticle

Use of Statistical Process Control for Coking Time Monitoring

by Marta Benková, Dagmar Bednárová, Gabriela Bogdanovská and Marcela Pavlíčková

Mathematics 2023, 11(16), 3444; https://doi.org/10.3390/math11163444 - 8 Aug 2023

Cited by 1 | Viewed by 1069

Abstract

Technical and technological developments in recent decades have stimulated the rapid development of methods and tools in the field of statistical process quality control, which also includes control charts. The principle of control charts defined by Dr. W. Shewhart has been known for more than 100 years. Since then, they have been used in many industries to monitor and control processes. This paper aims to assess the possibilities of use and the selection of the most suitable type of control chart for monitoring the quality of a process depending on its nature. This tool should help operators in monitoring coking time, which is one of the important control variables affecting the quality of coke production. The autoregressive nature of the variable being monitored was considered when selecting a suitable control chart from the group of options considered. In addition to the three traditional types of control charts (Shewhart’s, CUSUM, and EWMA), which were applied to the residuals of individual values of different types of ARIMA models, various statistical tests, and plots, a dynamic EWMA control chart was also used. Its advantage over traditional control charts applied to residuals is that it works with directly measured coking time data. This chart is intended to serve as a method to monitor the process. Its role is only to alert the process operator to the occurrence of problems with the length of the coking time. Full article

(This article belongs to the Special Issue Statistical Process Control and Application)

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20 pages, 1514 KiB

Open AccessArticle

A Study on the Laney p′ Control Chart with Parameters Estimated from Phase I Data: Performance Evaluation and Applications

by Pei-Wen Chen, Chuen-Sheng Cheng and Ching-Wen Wang

Mathematics 2023, 11(15), 3411; https://doi.org/10.3390/math11153411 - 4 Aug 2023

Viewed by 1137

Abstract

The Laney p′ control chart is a new type of attribute control chart that can be applied in situations where the process exhibits either overdispersion or underdispersion. While it has gained acceptance in the industry, there is still limited knowledge about its effectiveness in detecting process variation. It is well known that before applying a control chart, understanding its performance is crucial, especially when the parameters of the control chart need to be estimated from historical data. In this study, we used simulations to investigate the ability of the Laney p′ control chart to detect process variations when the parameters are estimated. We designed appropriate experiments to assess the impact of overdispersion on the average run length (ARL) performance. In this study, we assumed that the overdispersion comes from the variation in the mean fraction nonconforming of each sample. The mean value varies according to a uniform distribution. This study evaluated the performance of the Laney

p^{'}

control chart using the average of the ARL (AARL) and the standard deviation of the ARL (SDARL). Additionally, real-world data were utilized to illustrate the practical applications of the Laney

p^{'}

control chart in the PCB and IC substrate industries. The research findings can serve as valuable guidance for practical implementation. Full article

(This article belongs to the Special Issue Statistical Process Control and Application)

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32 pages, 2544 KiB

Open AccessArticle

Control Chart T2Qv for Statistical Control of Multivariate Processes with Qualitative Variables

by Wilson Rojas-Preciado, Mauricio Rojas-Campuzano, Purificación Galindo-Villardón and Omar Ruiz-Barzola

Mathematics 2023, 11(12), 2595; https://doi.org/10.3390/math11122595 - 6 Jun 2023

Cited by 1 | Viewed by 1559

Abstract

The scientific literature is abundant regarding control charts in multivariate environments for numerical and mixed data; however, there are few publications for qualitative data. Qualitative variables provide valuable information on processes in various industrial, productive, technological, and health contexts. Social processes are no exception. There are multiple nominal and ordinal categorical variables used in economics, psychology, law, sociology, and education, whose analysis adds value to decision-making; therefore, their representation in control charts would be useful. When there are many variables, there is a risk of redundant or excessive information, so the application of multivariate methods for dimension reduction to retain a few latent variables, i.e., a recombination of the original and synthesizing of most of the information, is viable. In this context, the T2Qv control chart is presented as a multivariate statistical process control technique that performs an analysis of qualitative data through Multiple Correspondence Analysis (MCA), and the Hotelling T2 chart. The interpretation of out-of-control points is carried out by comparing MCA charts and analyzing the

χ^{2}

distance between the categories of the concatenated table and those that represent out-of-control points. Sensitivity analysis determined that the T2Qv control chart performs well when working with high dimensions. To test the methodology, an analysis was performed with simulated data and with a real case applied to the graduate follow-up process in the context of higher education. To facilitate the dissemination and application of the proposal, a reproducible computational package was developed in R, called T2Qv, and is available on the Comprehensive R Archive Network (CRAN). Full article

(This article belongs to the Special Issue Statistical Process Control and Application)

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21 pages, 514 KiB

Open AccessArticle

Robust Surveillance Schemes Based on Proportional Hazard Model for Monitoring Reliability Data

by Moezza Nabeel, Sajid Ali, Ismail Shah, Mohammed M. A. Almazah and Fuad S. Al-Duais

Mathematics 2023, 11(11), 2480; https://doi.org/10.3390/math11112480 - 28 May 2023

Cited by 1 | Viewed by 1020

Abstract

Product reliability is a crucial component of the industrial production process. Several statistical process control techniques have been successfully employed in industrial manufacturing processes to observe changes in reliability-related quality variables. These methods, however, are only applicable to single-stage processes. In reality, manufacturing processes consist of several stages, and the quality variable of the previous stages influences the quality of the present stage. This interdependence between the stages of a multistage process is an important characteristic that must be taken into account in process monitoring. In addition, sometimes datasets contain outliers and consequently, the analysis produces biased results. This study discusses the issue of monitoring reliability data with outliers. To this end, a proportional hazard model has been assumed to model the relationship between the significant quality variables of a two-stage dependent manufacturing process. Robust regression technique known as the M-estimation has been implemented to lessen the effect of outliers present in the dataset corresponding to reliability-related quality characteristics in the second stage of the process assuming Nadarajah and Haghighi distribution. The three monitoring approaches, namely, one lower-sided cumulative sum and two one-sided exponentially weighted moving average control charts have been designed to effectively monitor the two-stage dependent process. Using Monte Carlo simulations, the efficiency of the suggested monitoring schemes has been examined. Finally, two real-world examples of the proposed control approaches are provided in the study. Full article

(This article belongs to the Special Issue Statistical Process Control and Application)

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14 pages, 3839 KiB

Open AccessArticle

Hotelling T² Control Chart for Detecting Changes in Mortality Models Based on Machine-Learning Decision Tree

by Suryo Adi Rakhmawan, M. Hafidz Omar, Muhammad Riaz and Nasir Abbas

Mathematics 2023, 11(3), 566; https://doi.org/10.3390/math11030566 - 20 Jan 2023

Cited by 3 | Viewed by 1833

Abstract

Mortality modelling is a practical method for the government and various fields to obtain a picture of mortality up to a specific age for a particular year. However, some information on the phenomenon may remain in the residual vector and be unrevealed from the models. We handle this issue by employing a multivariate control chart to discover substantial cohort changes in mortality behavior that the models still need to address. The Hotelling T² control chart is applied to the externally studentized deviance model, which is already optimized using a machine-learning decision tree. This study shows a mortality model with the lowest MSE, MAPE, and deviance, by accomplishing simulations in various countries. In addition, the model that is more sensitive in detecting signals on the control chart is singled out so that we can perform a decomposition to determine the attributes of death in the specific outlying age group in a particular year. The case study in the decomposition uses data from the country Saudi Arabia. The overall results demonstrate that our method of processing and producing mortality models with machine learning can be a solution for developing countries or countries with limited mortality data to produce accurate predictions through monitoring control charts. Full article

(This article belongs to the Special Issue Statistical Process Control and Application)

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21 pages, 2505 KiB

Open AccessArticle

Optimized np Attribute Control Chart Using Triple Sampling

by Jose Jorge Muñoz, Manuel J. Campuzano and Jaime Mosquera

Mathematics 2022, 10(20), 3791; https://doi.org/10.3390/math10203791 - 14 Oct 2022

Cited by 5 | Viewed by 1421

Abstract

This paper studies an attribute control chart for monitoring the number of nonconforming items using a triple sampling (TS-np) which has not yet been applied to attribute control charts. The chart design and procedure for the decision about the state of the process are given. Mathematical expressions for the average run length (ARL) for in-control and out-of-control processes and the average sample number (ASN) are given. A bi-objective genetic algorithm that seeks to minimize the ASN and the probability of type 2 error is implemented in order to optimize the design of the TS-np control chart. A comparison between TS-np, single sampling np (SS-np), double sampling np (DS-np), and multiple dependent state repetitive sampling (MDSRS) control charts is carried out in terms of the out-of-control average run length (

A R L_{1}

). Tables of

A R L_{1}

values for TS-np are presented in comparison with MDSRS and DS-np for various scenarios. The operation of the proposed control chart is shown through simulated data. Finally, it is concluded that the proposed TS-np chart has a better performance in terms of

A R L_{1}

detecting small and moderate shifts in the process nonconforming rate in-control (

p_{0}

) compared with MDSRS and DS-np. Full article

(This article belongs to the Special Issue Statistical Process Control and Application)

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