Analysis of means approach for random factor analysis

Jayalath, Kalanka P.; Ng, Hon Keung Tony

doi:10.1080/02664763.2017.1375083

Cited by 7 publications

(10 citation statements)

References 14 publications

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“…The studied literature highlighted the relevance of studies that adopted alternative measures to improve the capacity of generating better practical decisions. The alternative measures include the use of practical variables, such as the time to reset the process and the increase in production costs (Wan et al, 2018); the use of complementary and simplified statistics methods, such as: analysis of means for comparing means and variances in fixed-effects models ( Jayalath and Ng, 2018); the use of PCI (C p and C pk ) jointly with process control (Subramani and Balamurali, 2012) and the satisfaction of customer requirements, considering the capability indices (Oprime and Mendes, 2017).…”

Section: Discussionmentioning

confidence: 99%

“…Recent literature discusses the importance of avoiding the exclusive use of statistical significance and adopting complementary analysis based on variables of practical significance ( Jayalath and Ng, 2018;Oprime and Mendes, 2017;Ramírez, 2018;Wan et al, 2018). Wan et al (2018) highlight that practical issues such as process restart time, increase in production costs and other causes must be observed, since they can improve the analytical capacity of the control charts, instead of considering only the statistical significance.…”

Section: Introductionmentioning

confidence: 99%

“…Oprime and Mendes (2017) also agree that practical implications should be considered in the decisions related to process stopping. Jayalath and Ng (2018) provided examples in the livestock industry, regarding animal weight gain, suggesting that, instead of only rejecting the null hypothesis, it may be important to analyze the practical situations that can cause the differences, in order to assess the practical significance.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Acceptance X-bar chart considering the sample distribution of capability indices, C ˆ p and C ˆ p k

Oprime

Lizarelli

Pimenta

et al. 2019

IJQRM

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Purpose The traditional Shewhart control chart, the X-bar and R/S chart, cannot give support to decide when it is not economically feasible to stop the process in order to remove special causes. Therefore, the purpose of this paper is to propose a new control chart design – a modified acceptance control chart, which provides a supportive method for decision making in economic terms, especially when the process has high capability indices. Design/methodology/approach The authors made a modeling expectation average run length (ARL), which incorporates the probability density function of the sampling distribution of Cpk, to compare and analyze the efficiency of the proposed design. Findings This study suggested a new procedure to calculate the control limits (CL) of the X-bar chart, which allows economic decisions about the process to be made. By introducing a permissible average variation and defining three regions for statistical CL in the traditional X-bar control chart, a new design is proposed. Originality/value A framework is presented to help practitioners in the use of the proposed control chart. Two new parameters (Cp and Cpk) in addition to m and n were introduced in the expected ARL equation. The Cpk is a random variable and its probability function is known. Therefore, by using a preliminary sample of a process under control, the authors can test whether the process is capable or not.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Acceptance X-bar chart considering the sample distribution of capability indices, C ˆ p and C ˆ p k

Oprime

Lizarelli

Pimenta

et al. 2019

IJQRM

View full text Add to dashboard Cite

show abstract

“…As Jayalath and Ng 14 indicated, to test the hypotheses

H_{0} : σ_{τ}^{2} = 0

H_{a} : σ_{τ}^{2} > 0

, one may adapt the ANOMQ procedure. Let

{\overline{τ}}_{[i]} = {\overline{y}}_{[i] •}

be the i th ordered treatment average and

{\hat{σ}}_{\overline{τ}} = \hat{σ} / \sqrt{n}

, where

\hat{σ} = \sqrt{\sum_{i = 1}^{t} s_{i}^{2} / t}

.…”

Section: Analysis Of Means Approachmentioning

confidence: 99%

“…A recent work by Jayalath and Ng 14 proposed an analysis of means procedure using the Studentized‐range (or q ) distribution (ANOMQ procedure), which allows the ANOM approach to test the random factor effects in completely randomized, randomized complete block, and factorial designs. In this article, we focus on developing a complete graphical procedure to test both random and fixed factor effects in advanced designs that use both ANOM and ANOMQ.…”

Section: Introductionmentioning

confidence: 99%

Analysis of means approach in advanced designs

Jayalath

2020

Appl Stoch Models Bus & Ind

Self Cite

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Analysis of means (ANOM), similar to Shewhart control chart that exhibits individual mean effects on a graphical display, is an attractive alternative mean testing procedure for the analysis of variance (ANOVA). The procedure is primarily used to analyze experimental data from designs with only fixed effects. Recently introduced, the ANOM procedure based on the q‐distribution (ANOMQ procedure) generalizes the ANOM approach to random effects models. This article reveals that the application of ANOM and ANOMQ procedures in advanced designs such as hierarchically nested and split‐plot designs with fixed, random, and mixed effects enhances the data visualization aspect in graphical testing. Data from two real‐world experiments are used to illustrate the proposed procedure; furthermore, these experiments exhibit the ANOM procedures' visualization ability compared with ANOVA from the point of view of the practitioner.

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A graphical alternative for multiple group comparisons in analysis of covariance

Jayalath

2022

Appl Stoch Models Bus & Ind

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Analysis of means (ANOM) is a graphical alternative for the analysis of variance (ANOVA) that was primarily developed for multiple mean comparisons. The ANOM is a simple graphical display that provides a visualization of statistically significant results and it allows validating their practical significance without deep statistics knowledge. The classical ANOM has been developed to analyze fixed mean effects, and its recent developments allow testing random and mixed effects. On the other hand, analysis of covariance (ANCOVA) is an extension of ANOVA that applies to test means in the presence of uncontrollable concomitant/nuisance variables. To effectively communicate the statistical findings from ANCOVA to a general audience on some public interest issue areas such as COVID-19, visualization of statistically significant results is a practical approach. This paper provides a graphical alternative for multiple group comparisons in ANCOVA as an extension of the ANOM. The proposed graphical alternative is validated and compared with the ANCOVA using a Monte Carlo simulation study. The simulation results indicated that the proposed method stands strong for practical ANCOVA problems. In addition, a COVID-19 application and two additional applications related to toxicology and business are used to exhibit the value of the proposed graphical procedure in practice.

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Analysis of means approach for random factor analysis

Cited by 7 publications

References 14 publications

Acceptance X-bar chart considering the sample distribution of capability indices, C ˆ p and C ˆ p k

Acceptance X-bar chart considering the sample distribution of capability indices, C ˆ p and C ˆ p k

Analysis of means approach in advanced designs

A graphical alternative for multiple group comparisons in analysis of covariance

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