Cumulative Sum Schemes for Monitoring the Ratio of Two Correlated Normal Variables in Short Production Runs with Fixed and Variable Sampling Interval Strategies: Application in Wheat Seed Processing

Short-run production is frequently used in manufacturing due to technological advancements, and it is integral to Agriculture 4.0. In addition, monitoring multiple variables in short production runs (SPR) is often essential. For example, balancing the ratio of coating components of wheat seeds is cr...

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Main Authors: Wei Yang, Xueting Ji, Hongxing Cai, Jiujun Zhang
Format: Article
Language:English
Published: MDPI AG 2025-02-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/4/657
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author Wei Yang
Xueting Ji
Hongxing Cai
Jiujun Zhang
author_facet Wei Yang
Xueting Ji
Hongxing Cai
Jiujun Zhang
author_sort Wei Yang
collection DOAJ
description Short-run production is frequently used in manufacturing due to technological advancements, and it is integral to Agriculture 4.0. In addition, monitoring multiple variables in short production runs (SPR) is often essential. For example, balancing the ratio of coating components of wheat seeds is crucial for the growth and yield of wheat. Therefore, in this paper, two one-sided cumulative sum (CUSUM) schemes for monitoring the ratio of two correlated normal variables in SPR are proposed. Furthermore, performance metrics are evaluated, and the effects of various parameters on the schemes are analyzed through Monte Carlo simulations. To improve the detection efficiency of the proposed schemes, variable sampling interval (VSI) strategy is considered. The performance of these schemes under different sampling intervals is simulated. The results indicate that the monitoring performances of the schemes utilizing the VSI strategy surpass that of both the system without the VSI strategy and the Shewhart scheme. A comprehensive sensitivity analysis was conducted on the VSI strategy scheme to ensure its robustness. The analysis examined the effects of parameter variations, data contamination, and data correlation on the scheme’s performance. The proposed schemes were applied to the experiment of monitoring the nutrient composition ratio of wheat seed coating, and the results show that the schemes achieved the anticipated monitoring performance and possess practical application value.
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spelling doaj-art-1f11bebbd3fa44688b70fd1be62c8de42025-08-20T03:12:09ZengMDPI AGMathematics2227-73902025-02-0113465710.3390/math13040657Cumulative Sum Schemes for Monitoring the Ratio of Two Correlated Normal Variables in Short Production Runs with Fixed and Variable Sampling Interval Strategies: Application in Wheat Seed ProcessingWei Yang0Xueting Ji1Hongxing Cai2Jiujun Zhang3School of Mathematics and Statistics, Liaoning University, Shenyang 110036, ChinaSchool of Economics and Law, University of Science and Technology Liaoning, Anshan 114051, ChinaSchool of Mathematics and Statistics, Liaoning University, Shenyang 110036, ChinaSchool of Mathematics and Statistics, Liaoning University, Shenyang 110036, ChinaShort-run production is frequently used in manufacturing due to technological advancements, and it is integral to Agriculture 4.0. In addition, monitoring multiple variables in short production runs (SPR) is often essential. For example, balancing the ratio of coating components of wheat seeds is crucial for the growth and yield of wheat. Therefore, in this paper, two one-sided cumulative sum (CUSUM) schemes for monitoring the ratio of two correlated normal variables in SPR are proposed. Furthermore, performance metrics are evaluated, and the effects of various parameters on the schemes are analyzed through Monte Carlo simulations. To improve the detection efficiency of the proposed schemes, variable sampling interval (VSI) strategy is considered. The performance of these schemes under different sampling intervals is simulated. The results indicate that the monitoring performances of the schemes utilizing the VSI strategy surpass that of both the system without the VSI strategy and the Shewhart scheme. A comprehensive sensitivity analysis was conducted on the VSI strategy scheme to ensure its robustness. The analysis examined the effects of parameter variations, data contamination, and data correlation on the scheme’s performance. The proposed schemes were applied to the experiment of monitoring the nutrient composition ratio of wheat seed coating, and the results show that the schemes achieved the anticipated monitoring performance and possess practical application value.https://www.mdpi.com/2227-7390/13/4/657statistical process monitoringshort production runscumulative sumvariable sampling intervalcorrelated normal variables
spellingShingle Wei Yang
Xueting Ji
Hongxing Cai
Jiujun Zhang
Cumulative Sum Schemes for Monitoring the Ratio of Two Correlated Normal Variables in Short Production Runs with Fixed and Variable Sampling Interval Strategies: Application in Wheat Seed Processing
Mathematics
statistical process monitoring
short production runs
cumulative sum
variable sampling interval
correlated normal variables
title Cumulative Sum Schemes for Monitoring the Ratio of Two Correlated Normal Variables in Short Production Runs with Fixed and Variable Sampling Interval Strategies: Application in Wheat Seed Processing
title_full Cumulative Sum Schemes for Monitoring the Ratio of Two Correlated Normal Variables in Short Production Runs with Fixed and Variable Sampling Interval Strategies: Application in Wheat Seed Processing
title_fullStr Cumulative Sum Schemes for Monitoring the Ratio of Two Correlated Normal Variables in Short Production Runs with Fixed and Variable Sampling Interval Strategies: Application in Wheat Seed Processing
title_full_unstemmed Cumulative Sum Schemes for Monitoring the Ratio of Two Correlated Normal Variables in Short Production Runs with Fixed and Variable Sampling Interval Strategies: Application in Wheat Seed Processing
title_short Cumulative Sum Schemes for Monitoring the Ratio of Two Correlated Normal Variables in Short Production Runs with Fixed and Variable Sampling Interval Strategies: Application in Wheat Seed Processing
title_sort cumulative sum schemes for monitoring the ratio of two correlated normal variables in short production runs with fixed and variable sampling interval strategies application in wheat seed processing
topic statistical process monitoring
short production runs
cumulative sum
variable sampling interval
correlated normal variables
url https://www.mdpi.com/2227-7390/13/4/657
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