Causes of Non-normality of Monitored Quality Characteristics in Process Capability Analysis
Abstract
Purpose: In process capability analysis, violation of the normality assumption is considered a non-standard situation. This paper defines and categorises causes of non-normality in manufacturing processes, which are essential for quality planning, control, and selecting appropriate analytical procedures. Based on a literature review and systematic investigation, four main categories have been identified. Each category is analysed in detail with practical implications for capability analysis. The paper provides a comprehensive framework for identifying non-normality causes and guiding further analysis steps.
Methodology/Approach: Systematic literature review and expert synthesis of causes, supported by practical examples and categorisation into four key areas
Findings: four categories of non-normality causes identified; each requires a specific analytical approach before capability analysis can proceed
Research Limitation/Implication: Focuses on categorisation; future work should develop automated detection methods and validate solutions across diverse industries
Originality/Value of paper: Provides the first comprehensive framework for identifying non-normality causes in manufacturing, bridging theory and industrial practice
Full text article
References
Ag-Yi, D.; Aidoo, E. N. 2022. A comparison of normality tests towards convoluted probability distributions. Online. Research in Mathematics. Roč. 9, č. 1. Available from: https://doi.org/10.1080/27684830.2022.2098568. [cit. 2025-03-31].
AIAG, 2005. Statistical Process Control (SPC). 2nd ed. AIAG. ISBN 1605341088.
Alevizakos, V.; Koukouvinos, Ch. 2020. Evaluation of process capability in gamma regression profiles. Online. Communications in Statistics - Simulation and Computation. Roč. 51, č. 9, s. 5174-5189. Available from: https://doi.org/10.1080/03610918.2020.1758941. [cit. 2023-10-10].
Alevizakos, V.; Koukouvinos, Ch.; Castagliola, P. 2018. Process capability index for Poisson regression profile based on the Spmk index. Online. Quality Engineering. Roč. 31, č. 3, s. 430-438. Available from: https://doi.org/10.1080/08982112.2018.1523426. [cit. 2023-10-10].
Alexopoulos, C.; Brimeers, J.; Bergs, T. 2023. Model for tool wear prediction in face hobbing plunging of bevel gears. Online. Wear. S. 524-525. Available from: https://doi.org/https://doi.org/10.1016/j.wear.2023.204787. [cit. 2025-08-07].
Arellano-Valle, R.; Azzalini, A.; Ferreira, C.; Santoro, K. 2020. A two-piece normal measurement error model. Online. Computational Statistics & Data Analysis. Roč. 144, article 106863. Available from: https://doi.org/https://doi.org/10.1016/j.csda.2019.106863. [cit. 2025-07-28].
Avram, C.; Marusteri, M. 2022. Normality assessment, few paradigms and use cases. Online. Revista Romana de Medicina de Laborator. Roč. 30, č. 3, s. 251-260. Available from: https://doi.org/10.2478/rrlm-2022-0030. [cit. 2025-03-31].
Bae, I.; Ji, U. 2019. Outlier Detection and Smoothing Process for Water Level Data Measured by Ultrasonic Sensor in Stream Flows. Online. Water. Roč. 11, č. 5, s. 951. Available from: https://doi.org/https://doi.org/10.3390/W11050951. [cit. 2025-06-01].
Borucka, A.; Kozłowski, E.; Antosz, K.; Parczewski, R. 2023. A New Approach to Production Process Capability Assessment for Non-Normal Data. Online. Applied Sciences. Roč. 13, č. 11, s. 6721. Available from: https://doi.org/https://doi.org/10.3390/app13116721. [cit. 2025-08-19].
Cabral, C.; De Souza, N.; Leão, J. 2020. Bayesian measurement error models using finite mixtures of scale mixtures of skew-normal distributions. Online. Journal of Statistical Computation and Simulation. Roč. 92, s. 623-644. Available from: https://doi.org/https://doi.org/10.1080/00949655.2021.1969397. [cit. 2025-07-28].
Cavus, M.; Yaizici, B.; Sezer, A. 2023. Penalized power properties of the normality tests in the presence of outliers. Online. Communication in Statistics- Simulation and Computation. Roč. 52, č. 8, s. 3568-3580. Available from: https://doi.org/10.1080/03610918.2021.1938124. [cit. 2025-03-31].
CONSENSUS, 2025. Online. Consensus AI. AI nástroj pro rešerši vědeckých článků. Available from: https://consensus.app/. [cit. 2025-07-28].
Demir, S. 2022. Comparison of Normality Tests in Terms of Sample Sizes under Different Skewness and Kurtosis Coefficients. Online. International journal of assessment tools in education. Roč. 9, č. 2, s. 397-409. Available from: https://doi.org/10.21449/ijate.1101295. [cit. 2025-03-31].
Gai, X.; CHeng, Y.; Guan, R.; Jin, Y. a Lu, M. 2022. Tool wear state recognition based on WOA-SVM with statistical feature fusion of multi-signal singularity. Online. The International Journal of Advanced Manufacturing Technology. Roč. 123, s. 2209 - 2225. Available from: https://doi.org/https://doi.org/10.1007/s00170-022-10342-9. [cit. 2025-07-28].
Hao, L.; Bian, L.; Gebraeel, N.; Shi, J. 2017. Residual Life Prediction of Multistage Manufacturing Processes With Interaction Between Tool Wear and Product Quality Degradation. Online. IEEE Transactions on Automation Science and Engineering. Roč. 14, s. 1211-1224. Available from: https://doi.org/https://doi.org/10.1109/TASE.2015.2513208.
Herrera-Granados, G.; Misaka, T.; Herwan, J.; Komoto, H.; Furukawa, Y. 2024. An experimental study of multi-sensor tool wear monitoring and its application to predictive maintenance. Online. The International Journal of Advanced Manufacturing Technology. Roč. 133, s. 3415–3433. Available from: https://doi.org/https://doi.org/10.1007/s00170-024-13959-0. [cit. 2025-07-28].
Hosseinifard, S.; Abbasi, B. 2012. Process Capability Analysis in Non Normal Linear Regression Profiles. Online. Communications in Statistics - Simulation and Computation. Roč. 41, s. 1761 - 1784. Available from: https://doi.org/https://doi.org/10.1080/03610918.2011.611313. [cit. 2025-08-19].
Hosseinifard, S.; Abbasi, B.; Ahmad, S.; Abdollahian, M. 2009. A transformation technique to estimate the process capability index for non-normal processes. Online. The International Journal of Advanced Manufacturing Technology. Roč. 40, č. 5, s. 512-517. Available from: DOI: 10.1007/s00170-008-1376-x. [cit. 2023-10-10].
Huang, Z.; Shao, J.; Zhu, J.; Zhang, W. a Li, X. 2024. Tool wear condition monitoring across machining processes based on feature transfer by deep adversarial domain confusion network. Online. Journal of Intelligent Manufacturing. Roč. 35, s. 1079-1105. Available from: https://doi.org/https://doi.org/10.1007/s10845-023-02088-2. [cit. 2025-07-28].
Chen, C. 2018. The determination of product and process parameters under the non-normal distribution. Online. Journal of Information and Optimization Sciences. Roč. 40, s. 29-36. Available from: https://doi.org/https://doi.org/10.1080/02522667.2017.1406581. [cit. 2025-06-22].
Cheng, Y.; Gai, X.; Guan, R.; Jin, Y.; Lu, M. et al. 2023. Tool wear intelligent monitoring techniques in cutting: a review. Online. Journal of Mechanical Science and Technology. Roč. 37, s. 289-303. Available from: https://doi.org/https://doi.org/10.1007/s12206-022-1229-9. [cit. 2025-07-28].
CHou, C.; Chen, C. 2017. Optimum process mean, standard deviation and specification limits settings under the Burr distribution. Online. Engineering Computations. Roč. 34, s. 66-76. Available from: https://doi.org/https://doi.org/10.1108/EC-10-2015-0321. [cit. 2025-06-22].
ISO, 2017. ISO 22514-2, ISO 22514-2: Statistical methods in process management – Capability and performance. Part 2: Process capability and performance of time-dependent process models.
Jain, S.; Shukla, S. a Wadhvani, R. 2018. Dynamic selection of normalization techniques using data complexity measures. Online. Expert Systems with Applications. Roč. 106, s. 252-262. Available from: https://doi.org/https://doi.org/10.1016/j.eswa.2018.04.008. [cit. 2025-07-29].
Jäntschi, L. a Bolboacă, S. 2018. Computation of Probability Associated with Anderson–Darling Statistic. Online. Mathematics. Roč. 6, č. 88, s. 103-105. Available from: https://doi.org/https://doi.org/10.3390/MATH6060088. [cit. 2025-08-13].
Karakaya, K. 2024. A general novel process capability index for normal and non-normal measurements. Online. Ain Shams Engineering Journal. Roč. 15, č. 6. Available from: https://doi.org/https://doi.org/10.1016/j.asej.2024.102753. [cit. 2025-08-19].
Kitani, M.; Murakami, H. 2024. Modified two-sample Anderson-Darling test statistic. Online. Communications in Statistics - Theory and Methods. Roč. 54, s. 4575 - 4599. Available from: https://doi.org/https://doi.org/10.1080/03610926.2024.2425733. [cit. 2025-08-21].
Lavrač, S.; Turk, G. 2024. A Power Transformation for Non-Normal Processes Capability Estimation. Online. IEEE Access. Roč. 12, s. 93020-93032. Available from: https://doi.org/https://doi.org/10.1109/ACCESS.2024.3423488. [cit. 2025-08-19].
Lee, W.; Mendis, G.; Triebe, M.; Sutherland, J. 2019. Monitoring of a machining process using kernel principal component analysis and kernel density estimation. Online. Journal of Intelligent Manufacturing. Roč. 31, s. 1175 - 1189. Available from: https://doi.org/https://doi.org/10.1007/s10845-019-01504-w.
Leone, C.; D´Addona, D.; Teti, R. 2011. Tool wear modelling through regression analysis and intelligent methods for nickel base alloy machining. Online. Cirp Journal of Manufacturing Science and Technology. Roč. 4, č. 3, s. 327-331. Available from: https://doi.org/https://doi.org/10.1016/J.CIRPJ.2011.03.009. [cit. 2025-08-07].
Li, Z.; Liu, R. ; Wu, D. 2019. Data-driven smart manufacturing: Tool wear monitoring with audio signals and machine learning. Online. Journal of Manufacturing Processes. Roč. 48, s. 66-76. Available from: https://doi.org/https://doi.org/10.1016/j.jmapro.2019.10.020. [cit. 2025-07-28].
Liao, H.; Xiao, Y.; Wu, X.; Baušys, R. 2024. Z-DNMASort: A double normalization-based multiple aggregation sorting method with Z-numbers for multi-criterion sorting problems. Online. Information Sciences. Roč. 653, article 119782. Available from: https://doi.org/https://doi.org/10.1016/j.ins.2023.119782. [cit. 2025-07-29].
Mandić-Rajčević, S.; Colosio, C. 2019. Methods for the Identification of Outliers and Their Influence on Exposure Assessment in Agricultural Pesticide Applicators: A Proposed Approach and Validation Using Biological Monitoring. Online. Toxics. Roč. 7, č. 3, s. 37. Available from: https://doi.org/https://doi.org/10.3390/toxics7030037. [cit. 2025-06-01].
Munaro, R.; Attanasio, A.; Del Prete, A. 2023. Tool Wear Monitoring with Artificial Intelliegence Methods: A review. Online. Journal of Manufacturing and Materials Processing. Roč. 7, č. 4, s. 129. Available from: https://doi.org/https://doi.org/10.3390/jmmp7040129. [cit. 2025-08-07].
Nepraš, K.; Plura, J. 2015. Possibilities of data non-normality solving at process capability analysis in terms of part symmetry. In: Metal 2015: conference proceedings. Ostrava: Tanger, s. 2009-2014. ISBN 978-80-87294-62-8.
Nepraš, K.; Plura, J. 2016. Methodical Approaches to Process Capability Analysis in the Cases of Non-Normal Distribution of Monitored Quality Characteristic. In: Metal 2016: conference proceedings. Ostrava: Tanger, s. 1950-1955. ISBN 978-80-87294-67-3.
Peng, H.; Han, Q. 2024. Containing geometrical tolerances in concurrent optimal allocation of design and process tolerances. Online. The International Journal of Advanced Manufacturing Technology. Roč. 133, s. 1549–1562. Available from: https://doi.org/https://doi.org/10.1007/s00170-024-13860-w. [cit. 2025-07-28].
Rabatel, G.; Marini, F.; Walczak, B.; Roger, J. 2020. VSN: Variable sorting for normalization. Online. Journal of Chemometrics. Roč. 34, č. 2. Available from: https://doi.org/https://doi.org/10.1002/cem.3164. [cit. 2025-07-29].
Rao, G. S.; Albassam, M.; Aslam, M. 2019. Evaluation of Bootstrap Confidence Intervals Using a New Non-Normal Process Capability Index. Online. Symmetry. Roč. 11, č. 4, s. 484. Available from: https://doi.org/10.3390/sym11040484. [cit. 2023-10-10].
Razali, N.; Wah, Y. 2011. Power comparisons of Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors and Anderson-Darling tests. Online. Journal of Statistical Modeling and Analytics. Roč. 2, č. 1, s. 21-33. Available from: https://www.researchgate.net/publication/267205556_Power_Comparisons_of_Shapiro-Wilk_Kolmogorov-Smirnov_Lilliefors_and_Anderson-Darling_Tests#fullTextFileContent. [cit. 2025-08-13].
Ropinski, T.; Ritschel, T.; Singh, G.; Van Onzenoodt, C. 2021. Blue Noise Plots. Online. Computer Graphics Forum. Roč. 40, č. 2, s. 425-433. Available from: https://doi.org/https://doi.org/10.1111/cgf.142644. [cit. 2025-06-18].
Senvar, O.; Sennaroglu, B. 2016. Comparing performances of clements, box-cox, Johnson methods with weibull distributions for assessing process capability. Online. Journal of Industrial Engineering and Management. Roč. 9, č. 3, s. 634-656. Available from: https://doi.org/http://dx.doi.org/10.3926/jiem.1703. [cit. 2023-10-10].
Spicker, D.; Wallace, M.; Yi, G. 2021. Nonparametric simulation extrapolation for measurement‐error models. Online. Canadian Journal of Statistics. Roč. 52, č. 2, s. 477-499. Available from: https://doi.org/https://doi.org/10.1002/cjs.11777. [cit. 2025-07-28].
Subramaniam, M.; Chandra Umakantham, O. 2025. Cluster Sort: A Novel Hybrid Approach to Efficient In-Place Sorting Using Data Clustering. Online. IEEE Access. Roč. 13, s. 74359-74374. Available from: https://doi.org/https://doi.org/10.1109/ACCESS.2025.3564380. [cit. 2025-07-29].
Taib, H.; Alani, B. 2021. Estimation of Non-Normal Process Capability Indices. Online. Al-Rafidain Journal of Computer Sciences and Mathematics. Roč. 15, č. 1, s. 35-56. Available from: https://doi.org/https://doi.org/10.33899/CSMJ.2021.168260. [cit. 2025-08-19].
Tang, L.; Than, S. 1999. Computing process capability indices for non‐normal data: a review and comparative study. Online. Quality and Reliability Engineering International. Roč. 15, s. 339-353. Available from: https://doi.org/https://doi.org/10.1002/(SICI)1099-1638(199909/10)15:5<339::AID-QRE259>3.0.CO;2-A. [cit. 2025-08-19].
Thavron, E.; Sudasna-Na-Ayudthhya, P. 2022. The Effects of Weibull Distribution on Supplier Comparison using Lower Process Capability Index: A Case Study. Online. Trends in Sciences. Roč. 19, č. 3, s. 2158. Available from: https://doi.org/10.48048/tis.2022.2158. [cit. 2023-10-10].
Velyka, O. T.; Liaskovska, S. E.; Smotr, O. O.; Boyko, M. V. 2021. Simulation modeling of technological process of manufacturing in FlexSim environment. Online. Scientific Bulletin of UNFU. Roč. 31, č. 2, s. 108-113. Available from: https://doi.org/https://doi.org/10.36930/40310218. [cit. 2025-07-29].
Wang, S.; Chiang, J.-Y.; Tsai, T.-R.; Qin, Y. 2021. Robust process capability indices and statistical inference based on model selection. Online. Computers & Industrial Engineering. Č. 156, s. 1-17. ISSN 0360-8352. Available from: https://doi.org/10.1016/j.cie.2021.107265. [cit. 2023-11-15].
Yan, B.; Zhu, L. a Dun, Y. 2021. Tool wear monitoring of TC4 titanium alloy milling process based on multi-channel signal and time-dependent properties by using deep learning. Online. Journal of Manufacturing Systems. Roč. 61, s. 495-508. Available from: https://doi.org/https://doi.org/10.1016/j.jmsy.2021.09.017. [cit. 2025-07-28].
Yang, Q.; Pattipati, K.; Awasthi, U.; Bollas, G. 2022. Hybrid data-driven and model-informed online tool wear detection in milling machines. Online. Journal of Manufacturing Systems. Roč. 63, s. 329-343. Available from: https://doi.org/https://doi.org/10.1016/j.jmsy.2022.04.001. [cit. 2025-07-28].
Yang, Y. ; Zhu, H. 2018b. A Study of Non-Normal Process Capability Analysis Based on Box-Cox Transformation. Online. 2018 3rd International Conference on Computational Intelligence and Applications (ICCIA). S. 240-243. Available from: https://doi.org/https://doi.org/10.1109/ICCIA.2018.00053. [cit. 2025-08-19].
Yang, Y.; Li, D.; Qi, Y. 2018. An Approach to Non-normal Process Capability Analysis Using Johnson Transformation. Online. 2018 IEEE 4th International Conference on Control Science and Systems Engineering (ICCSSE). S. 495-498. Available from: https://doi.org/https://doi.org/10.1109/CCSSE.2018.8724679. [cit. 2025-08-19].
Yang, Y.; Zhu, H. 2018a. A study of non-normal process capability analysis based on box-cox transformation. Online. In: Proceedings – 3rd Internationl Conference on Computational Intelligence and Applications. Qingdao: Naval Aviation University, s. 240-243. Available from: https://doi.org/10.1109/ICCIA.2018.00053. [cit. 2023-10-10].
Yi, X.; Song, Y.; Zhang, H.; Cui, H.; Lu, W. et al. 2025. A workflow to select local tolerance limits by combining statistical process control and error curve model. Online. Medial Physics. Roč. 52, č. 6, s. 4815 - 4827. Available from: https://doi.org/https://doi.org/10.1002/mp.17715. [cit. 2025-07-28].
Authors
Copyright (c) 2025 Monika Sekaninová
This work is licensed under a Creative Commons Attribution 4.0 International License.
This is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. This is in accordance with the BOAI definition of open access. This journal is licensed under a Creative Commons Attribution 4.0 License - http://creativecommons.org/licenses/by/4.0.
Authors who publish with the Quality Innovation Prosperity agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.