Construction of fuzzy X¯−S control chart using trapezoidal fuzzy number with unbalanced data

Ahmad, Mohammad Nazir; Cheng, Weihu; Haq, Ahteshamul; Shah, Sayed Kifayat

doi:10.1080/00949655.2022.2116437

Cited by 3 publications

(4 citation statements)

References 13 publications

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“…For the j th random sample, there are n fixed values for the explanatory variable. When the process is in statistical control, a SLP can be defined as Equation (2).…”

Section: -Simple Linear Profilesmentioning

confidence: 99%

“…where 𝐴 0𝑗 , 𝐴 1𝑗 are the slope and intercept, respectively, and the error terms 𝜀 𝑖𝑗 are assumed to be normally and independently distributed with mean zero and variance 𝜎 𝑗 and 𝑆𝑆𝐸 𝑗 = (𝑌 𝑖𝑗 − 𝑎 0𝑗 − 𝑎 1𝑗 𝑋 𝑖 ) 2 . 𝑀𝑆𝐸 𝑗 is the unbiased estimator of 𝜎 2 for sample j and 𝑒 𝑖𝑗 denotes residuals and is defined as 𝑒 𝑖𝑗 = 𝑌 𝑖𝑗 − 𝑌 ̂𝑖𝑗 .…”

Section: -Simple Linear Profilesmentioning

confidence: 99%

“…In this method, coded 𝑋-values are used which make the intercept and slope of each profile independent. Equation ( 16) presents the coded form of the model given in Equation (2).…”

Section: -Pcis For Parametersmentioning

confidence: 99%

“…2 = 1. The explanatory variable with four fixed 𝑋 𝑖 -values of 2, 4, 6, and 8 are used in the simulation study.…”

mentioning

confidence: 99%

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Process Capability Analysis for Simple Linear Profiles in Multistage Processes

Adibfar,

Noorossana

2024

Pak.j.stat.oper.res.

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When a process is statistically under control, one may be interested in assessing the process performance based on the specification limits provided by the customer. This evaluation is referred to as process capability analysis. Manufacturing operations are often involved with multistage processes, in which the output of a stage is the input of its subsequent stage. This property is known as the cascade property. Existing methods in capability analysis studies are not applicable when a process or product is represented by profiles. This study presents a method to conduct process capability analysis in a multistage process when quality of a product or process is characterized by a simple linear profile. The performance of the proposed method for a two-stage process is evaluated by numerical simulation using an example from the literature. The results indicate that the proposed method eliminates the effect of the cascade property for different shift sizes and autocorrelations.

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“…For the j th random sample, there are n fixed values for the explanatory variable. When the process is in statistical control, a SLP can be defined as Equation (2).…”

Section: -Simple Linear Profilesmentioning

confidence: 99%

Section: -Simple Linear Profilesmentioning

confidence: 99%

“…In this method, coded 𝑋-values are used which make the intercept and slope of each profile independent. Equation ( 16) presents the coded form of the model given in Equation (2).…”

Section: -Pcis For Parametersmentioning

confidence: 99%

“…2 = 1. The explanatory variable with four fixed 𝑋 𝑖 -values of 2, 4, 6, and 8 are used in the simulation study.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Process Capability Analysis for Simple Linear Profiles in Multistage Processes

Adibfar,

Noorossana

2024

Pak.j.stat.oper.res.

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A nonparametric adaptive EWMA control chart for monitoring multivariate time-between-events-and-amplitude data

Xue,

An,

Feng

et al. 2024

Computers & Industrial Engineering

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Fuzzy Method to Improve Products and Processes Considering the Approach of Sustainable Development (FQE-SD Method)

2023

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Assumptions of the concept of sustainable development should include actions towards the development of modern, well-managed enterprises. However, making decisions in this area is difficult as it often results from subjective assessments of environmental problems. Hence, there is a motivation to develop a method of analysing the search for solutions to environmental problems that supports decisions in the area of improving the quality of products or processes while considering their impacts on the natural environment. In view of the specification of this problem, it was considered that this method should be conducted in a fuzzy decision environment. This method is called FQE-SD (fuzzy qualitatively environmentally sustainable development). This method integrated, in a hybrid way, the selected tools or elements of qualitative and multi-criteria decision methods, i.e., using the SMARTER method, brainstorming (BM), a method to select the team of experts, the Pareto-Lorenz analysis, the fuzzy QE-FMEA method, and the fuzzy AHP method. The main contribution of the FQE-SD method is its hybrid methodology, which supports: (i) a coherent and objective approach during the identification, analyses, and ranking of the causes of incompatibility of products or processes and (ii) the realization of the sustainable development of products or processes. The method was tested using the magnetic-powder test (MT). This control was carried out for producers of an outer bearing made fromAMS6470 steel. The results of this work confirmed the practical possibilities of applying the FQE-SD method. This method can also be applied to other production situations, if appropriate assumptions are made.

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Construction of fuzzy X¯−S control chart using trapezoidal fuzzy number with unbalanced data

Cited by 3 publications

References 13 publications

Process Capability Analysis for Simple Linear Profiles in Multistage Processes

Process Capability Analysis for Simple Linear Profiles in Multistage Processes

A nonparametric adaptive EWMA control chart for monitoring multivariate time-between-events-and-amplitude data

Fuzzy Method to Improve Products and Processes Considering the Approach of Sustainable Development (FQE-SD Method)

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