A new perspective on fuzzy process capability indices: Robustness

Kaya, İ̇hsan; Kahraman, Cengiz

doi:10.1016/j.eswa.2009.12.049

Cited by 31 publications

(12 citation statements)

References 36 publications

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“…Moameni et al (2012) considered fuzzy numbers for problems that can be caused by measurement errors, and these fuzzy numbers taken into account for true X ¯ -R control charts. Kaya and Kahraman (2010) described process capability indexes as triangular and trapezoidal fuzzy numbers.…”

Section: Introductionmentioning

confidence: 99%

Different methods to fuzzy X¯-R control charts used in production

Ercan-Teksen

Anagün

2018

JEIM

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Purpose The control charts are used in many production areas because they give an idea about the quality characteristic(s) of a product. The control limits are calculated and the data are examined whether the quality characteristic(s) is/are within these limits. At this point, it may be confusing to comment, especially if it is slightly below or above the limit values. In order to overcome this situation, it is suitable to use fuzzy numbers instead of crisp numbers. The purpose of this paper is to demonstrate how to create control limits of X ¯ -R control charts for a specified data set of interval type-2 fuzzy sets. Design/methodology/approach There are methods in the literature, such as defuzzification, distance, ranking and likelihood, which may be applicable for interval type-2 fuzzy set. This study is the first that these methods are adapted to the X ¯ -R control charts. This methodology enables interval type-2 fuzzy sets to be used in X ¯ -R control charts. Findings It is demonstrated that the methods – such as defuzzification, distance, ranking and likelihood for interval type-2 fuzzy sets – could be applied to the X ¯ -R control charts. The fuzzy control charts created using the methods provide similar results in terms of in/out control situations. On the other hand, the sample points depicted on charts show similar pattern, even though the calculations are different based on their own structures. Finally, the control charts obtained with interval type-2 fuzzy sets and the control charts obtained with crisp numbers are compared. Research limitations/implications Based on the related literature, research works on interval type-2 fuzzy control charts seem to be very limited. This study shows the applicability of different interval type-2 fuzzy methods on X ¯ -R control charts. For the future study, different interval type-2 fuzzy methods may be considered for X ¯ -R control charts. Originality/value The unique contribution of this research to the relevant literature is that interval type-2 fuzzy numbers for quantitative control charts, such as X ¯ -R control charts, is used for the first time in this context. Since the research is the first adaptation of interval type-2 fuzzy sets on X ¯ -R control charts, the authors believe that this study will lead and encourage the people who work on this topic.

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Section: Introductionmentioning

confidence: 99%

Different methods to fuzzy X¯-R control charts used in production

Ercan-Teksen

Anagün

2018

JEIM

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“…In the literature, in order to merge PCIs and the fuzzy set theory, various studies have been conducted for developing fuzzy PCIs [1,[4][5][6][7][8]25]. The concept of a type-2 fuzzy set was introduced by [14] as an extended version of the original concept of an ordinary fuzzy set, which is also known as a type-1 fuzzy set.…”

Section: Introductionmentioning

confidence: 99%

Type-2 fuzzy process capability indices for non-normal processes

Şenvar

Kahraman

2014

Journal of Intelligent &Amp; Fuzzy Systems

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We developed type-2 fuzzy percentile-based standard PCIs for non-normal data via Clements' method. For modeling uncertainty and imprecision of data, interval type-2 fuzzy sets are utilized. To prove usefulness and applicability of the proposed type-2 fuzzy percentile-based standard PCIs, a numerical illustration is performed for the data randomly generated from Lognormal distribution. The results show that in comparison with their crisp types, the proposed type-2 fuzzy percentile-based standard PCIs for non-normal processes are more informative, sensitive and flexible to evaluate the process performance of the industrial processes.

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“…The main outputs of PCA are PCIs which provide a numerical measure of whether a production process is capable of producing items within the SLs predetermined by the designer or consumer. Several PCIs such as C p , C pk , C pm , and C pmk are used to estimate the capability of a process [1][2][3][4][5]. These PCIs have been proposed to provide unitless measures of process potential and performance for processes with symmetric tolerances.…”

Section: Introductionmentioning

confidence: 99%

A process capability index with asymmetric tolerances under fuzzy environment

Kahraman

Kaya

Çebı

2010

2010 IEEE International Conference on Intelligent Systems and Knowledge Engineering

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Process capability indices (PCIs) are summary statistics to depict the process location and dispersion successfully and they can be used to show the process performance by producing PCIs. Although PCIs are generally used for a process which has a symmetric tolerance, it is a necessity to analyze some processes where the target value (T) cannot be defined at the midpoint of the specification interval (m). If the T does not locate on m which is called asymmetric tolerances, PCIs have some disadvantages in the casual use and interpretation of PCIs. For these cases, PCIs with asymmetric tolerances have been developed and applied successfully. In this paper one of the most used PCIs with asymmetric tolerances pmk C′′ is analyzed and the fuzzy set theory is used to provide deep and flexible analysis. The fuzzy formulations of the index pmk C′′ , which is one of the most used PCI with asymmetric tolerances, are developed. Then a real case application from an automotive company is given.

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A new perspective on fuzzy process capability indices: Robustness

Cited by 31 publications

References 36 publications

Different methods to fuzzy X¯-R control charts used in production

Different methods to fuzzy X¯-R control charts used in production

Type-2 fuzzy process capability indices for non-normal processes

A process capability index with asymmetric tolerances under fuzzy environment

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