Empirical distribution function as a tool in quality control

Jevremović, Vesna; Avdović, Atif

doi:10.5937/spsunp2001037j

Cited by 4 publications

(8 citation statements)

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“…The research suggests that both the Quantile-Zone distribution and Zone distribution hold significant potential for applications in quality control. This recognition aligns with the growing importance of quality control as a notable research topic, both in theory and practical application [11][12][13][14][15][16][17].…”

Section: Introductionsupporting

confidence: 67%

“…The outcomes of this research have broader implications for improving quality control achieved by control charts. The relevance of these innovations is underscored by the findings reported in recent publications [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]19,21,26,29].…”

Section: Introductionmentioning

confidence: 99%

“…This difficulty arises from its connection to the empirical distribution function (EDF), making it impractical or extremely complicated to determine functional and numerical characteristics [4]. The idea for such an approach was derived from research in quality control that the authors have also been working on [11,12]. Essentially, the concept of the X-bar chart has been modified to give new approaches in control charts, Quantile-Zone distribution, and normality testing.…”

Section: Introductionmentioning

confidence: 99%

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Discrete Parameter-Free Zone Distribution and Its Application in Normality Testing

Avdović,

Jevremović

2023

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In recent research endeavors, discrete models have gained considerable attention, even in cases where the observed variables are continuous. These variables can often be effectively approximated by a normal distribution. Given the prevalence of processes requiring robust quality control, models associated with the normal distribution have found widespread applicability; nevertheless, there remains a persistent need for enhanced accuracy in normality analysis, prompting the exploration of novel and improved solutions. This paper introduces a discrete parameter-free distribution linked to the normal distribution, derived from a quality control methodology rooted in the renowned ‘3-sigma’ rule. The development of a novel normality test, based on this distribution, is presented. A comprehensive examination encompasses mathematical derivation, distribution tables generated through Monte Carlo simulation studies, properties, power analysis, and comparative analysis, all with key features illustrated graphically. Notably, the proposed normality test surpasses conventional methods in performance. Termed the ‘Zone distribution’, this newly introduced distribution, along with its accompanying ‘Zone test’, demonstrates superior efficacy through illustrative examples. This research contributes a valuable tool to the field of normality analysis, offering a robust alternative for applications requiring precise and reliable assessments.

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Section: Introductionsupporting

confidence: 67%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Discrete Parameter-Free Zone Distribution and Its Application in Normality Testing

Avdović,

Jevremović

2023

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“…Knuth has analyzed LCG and obtained results that show the optimal modulus for the multiplicator 2 k + 1 is a prime number even though the modulus 2 p (p > k) yields the fastest generating [13] (pp. [12][13][14][15]. Some issues concerning this choice of multiplicator and modulus are discussed in [17].…”

Section: Introductionmentioning

confidence: 99%

“…New random number generators, whether they are based on modular reduction or not [9] are still developed, discussed, tested and compared [10] to other known generators. In this sense the present paper offers an important improvement of a widely used and researched random number generator that is still of interest for application as well as further scientific research such as control charts performance analysis [11,12], goodness-of-fit tests power analysis [1,2], probabilistic topic modelling [18] etc.…”

Section: Introductionmentioning

confidence: 99%

Extension of Linear Congruential Generator

Avdović

2023

SPSUNP

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Random number generation is a significant research topic, even though there have already been a lot of papers published about it. Particularly detailed research has been made about the Linear Congruent Generator (LCG), which is still the most frequently used one. Research into the LCG has lead to the results in this paper in form of a new, extended LCG model. We have shown that the extended model has all the necessary features of randomness, but still a significantly larger period than the standard LCG.

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Quantile-Zone Based Approach to Normality Testing

Avdović

Jevremović

2022

Mathematics

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Normality testing remains an important issue for researchers, despite many solutions that have been published and in use for a long time. There is a need for testing normality in many areas of research and application, among them in Quality control, or more precisely, in the investigation of Shewhart-type control charts. We modified some of our previous results concerning control charts by using the empirical distribution function, proper choice of quantiles and a zone function that quantifies the discrepancy from a normal distribution. That was our approach in constructing a new normality test that we present in this paper. Our results show that our test is more powerful than any other known normality test, even in the case of alternatives, with small departures from normality and for small sample sizes. Additionally, many test statistics are sensitive to outliers when testing normality, but that is not the case with our test statistic. We provide a detailed distribution of the test statistic for the presented test and comparable power analysis with highly illustrative graphics. The discussion covers both the cases for known and for estimated parameters.

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Empirical distribution function as a tool in quality control

Cited by 4 publications

References 1 publication

Discrete Parameter-Free Zone Distribution and Its Application in Normality Testing

Discrete Parameter-Free Zone Distribution and Its Application in Normality Testing

Extension of Linear Congruential Generator

Quantile-Zone Based Approach to Normality Testing

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