How to Use Confidence Intervals in Selecting a Suitable Time-Dependent Distribution Model for the Process

Milan Terek (1)
(1) School of Management, Bratislava, Slovakia

Abstract

Purpose: This paper proposes the possibility of using confidence intervals for the mean and variance in selecting a suitable time-dependent distribution model for the process.


Methodology/Approach: The approach describes a characteristic under consideration by the distribution, the location, the dispersion, and the shape, all of which are functions of time. The values of the characteristics under consideration are determined by taking samples from the process flow. Time-dependent distribution models are classified into four groups based on whether the location and dispersion moments remain constant or vary over time.


Findings: The paper explains a method for creating random samples, along with the calculation, presentation, and interpretation of the confidence intervals for the mean and variance in choosing the appropriate time-dependent distribution model of the process.


Research Limitation/Implication: The methods described in this document pertain exclusively to continuous quality characteristics. They can be applied to analyse processes across various industrial and economic sectors. The presented procedures assume that all instantaneous distributions are normal.


Originality/Value of paper: Confidence intervals can improve decision-making when selecting a suitable time-dependent distribution model.

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References

Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., Cochran, J. J., Fry, M. J. and Ohlmann, J. W., 2020. Statistics for Business and Economics.

e Edition. Boston: Cengage Learning, Inc.

Bartlett's Test, 2024. Definition and Examples. [online] Available at https://www.statisticshowto.com/bartletts-test/ [21 May 2024].

Chakraborty, S., Graham, M. A., 2019. Nonparametric Statistical Process Control. Hoboken: John Wiley & Sons Ltd.

Ghasemi, A., Zahediasl, S., 2012. Normality Tests for Statistical Analysis: A Guide for Non-Statisticians. International Journal of Endocrinology and Metabolism, 10 (2). https://doi.org/10.5812/ijem.3505.

ISO, 2017. ISO 22514-2 Statistical methods in process management – Capability and performance – Part 2: Process capability and performance of time-dependent process models. Electronic documents. Geneva: ISO.

Jarošová, E., Noskievičová, D., 2015. Pokročilejší metody statistické regulace procesu. Praha: Grada Publishing.

Montgomery, D. C., 2013. Introduction to Statistical Quality Control. Seventh edition. Hoboken: J. Wiley and Sons.

Montgomery, D. C., Peck, E. A., Vining, G. G., 2021. Introduction to linear regression analysis. Sixth edition. Hoboken: John Wiley & Sons.

Nussbaum, E. M., 2024. Categorical and nonparametric data analysis: choosing the best statistical technique. Second edition. New York: Routledge.

Oakland, J., Oakland, R., 2019. Statistical Process Control. 7th Edition. New York: Routledge.

Statistics How To, 2024. Bartlett’s Test for Homogeneity of Variances: Definition and Examples. [online] Available at https://www.statisticshowto.com/bartletts-test/ [21 May 2024].

Terek, M., 2017. Interpretácia štatistiky a dát. 5. doplnené vydanie [Interpretation of statistics and data. 5th revised ed.]. Košice: Equilibria.

Terek, M., 2023. How to Estimate the Sigma Level of the Process. Quality Innovation Prosperity, 27(3).

Thode, H.C. Jr., 2002. Testing for Normality. New York: Marcel Dekker.

Zgodavová, K., Bober, P., Majstorovič, V., Monková, K., Santos, G., Juhászová, D., 2020. Innovative Methods for Small Mixed Batches Production System Improvement: The Case of a Bakery Machine Manufacturer. Sustainability 2020, 12, 6266. https://doi.org/10.3390/su12156266.

Authors

Milan Terek
milan.terek1@gmail.com (Primary Contact)
Author Biography

Milan Terek, School of Management, Bratislava

Milan Terek, PhD. works from 2018 as a full professor at the School of Management in Bratislava (course leader on Introduction to Statistics, Statistics, Mathematics for Managers II, Quantitative Methods for Managers, Quantitative Methods in Business Management Research). Prior to this, he worked at the University of Economics in Bratislava (course leader on Statistics, Statistical Quality Control, Decision Analysis, Data Mining, Survey Sampling, Linear Programming, Nonlinear Programming, Operations Research, and System Modelling). His research activities are focused on the applications of statistical methods in economics and management. 

 

School of Management in Bratislava, Panónska cesta 17
851 04 Bratislava, Slovakia

 

e-mail: milan.terek1@gmail.com; mterek@vsm.sk

Terek, M. (2025). How to Use Confidence Intervals in Selecting a Suitable Time-Dependent Distribution Model for the Process . Quality Innovation Prosperity, 29(1), 25–38. https://doi.org/10.12776/qip.v29i1.2095

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