Loss-based process capability indices: a review

Abdolshah, Mohammad; Yusuff, Rosnah Mohd; Hong, Tang Sai; Ismail, Md Yusof

doi:10.1504/ijpqm.2011.037729

Cited by 10 publications

(5 citation statements)

References 44 publications

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“…It should also be noted that the cost tolerance can be employed along with the loss function. [53][54][55] Thus, the development of a robust 𝐶 𝑝𝑐 incorporating the Taguchi's loss function along with a cost tolerance parameter is warranted. The estimated PCI Ĉ𝑝𝑐 = 0.4757809 with LSL = 0.0052 and USL = 0.0092.…”

Section: Discussionmentioning

confidence: 99%

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Confidence intervals of the process capability index Cpc$C_{pc}$ revisited via modified bootstrap technique and ROC curves

Ouyang

Dey²,

Byun

et al. 2023

Quality & Reliability Eng

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We consider the process capability index (PCI), a widely used quality‐related statistic used to assess the quality of products and performance of monitored processes in various industries. It is widely known that the conventional PCIs perform well when the quality process being monitored has a normal distribution. Unfortunately, using the indices to evaluate a non‐normally distributed process often leads to inaccurate results. In this article, we consider a new PCI, , that can be used in both normal and non‐normal scenarios. The objective of this article is threefold: (i) We provide a corrected form of the confidence interval for . (ii) We compare the performance of three nonparametric bootstrap confidence intervals (BCIs) for . Specifically, the standard bootstrap, percentile bootstrap, and bias‐corrected percentile bootstrap. Under various distributional assumptions such as the normal, chi‐square, Student t, Laplace, and two‐parameter exponential distributions, the estimated coverage probabilities and average width of the confidence intervals and BCIs for are compared. (iii) The power of the respective bootstrap approaches is evaluated by using the equivalence relation between confidence interval construction and two‐sided hypothesis testing. We also provide the receiver operating characteristic curves to evaluate their performance. Finally, as an illustrative example, an actual data set related to groove dimensions (in inches) measured from a manufacturing process of ignition keys is re‐analyzed to illustrate the utility of the proposed methods.

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Section: Discussionmentioning

confidence: 99%

“…Thus, a future study, which includes Taguchi's loss function, could also be considered. It should also be noted that the cost tolerance can be employed along with the loss function 53–55 . Thus, the development of a robust

C_{pc}

incorporating the Taguchi's loss function along with a cost tolerance parameter is warranted.…”

Section: Discussionmentioning

confidence: 99%

Confidence intervals of the process capability index Cpc$C_{pc}$ revisited via modified bootstrap technique and ROC curves

Ouyang

Dey²,

Byun

et al. 2023

Quality & Reliability Eng

View full text Add to dashboard Cite

show abstract

“…Abdolshah et al [21] discussed the index C pmk by assuming that the process mean and variance were both type-1 fuzzy based on fuzzy data and compared them with other indices. A review of fuzzy process capability indices was given by Abdolshah [22] in 2012. Yen [23] discussed the one-sided fuzzy test for the indices C pl and C pu in 2012.…”

Section: Literature Reviewmentioning

confidence: 99%

What can fuzziness do for capability analysis based on fuzzy data

Chen

Hung

2019

Scientia Iranica

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One advantage of process incapability index over the classical process capability index is that it provides uncontaminated separation between process accuracy and process precision. However, the value of the index is di cult to determine accurately when process parameters cannot be determined precisely. In such a case, fuzzy set theory can be applied to obtain more exible and sensitive information. In this paper, a fuzzy process incapability index is proposed when the speci cation limits are assumed to be type-2 fuzzy. When the process mean and variance are unknown and when the observations are measured imprecisely, three fuzzy estimators are considered. A simulation study is conducted based on the Thin-Film-Transistor Liquid-Crystal Display (TFT-LCD) fuzzy process. By applying the total integral value method to the membership function of a fuzzy index, it becomes easier to make a comparison of the quality of di erent processes.

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“…Owing to this, they often fail to meet customer's requirements. However, significance of loss functions in varied fields such as industrial engineering, quality engineering, capability analysis, and so forth has been established in statistical and quality control literature (see Abdolshah et al 11 …”

Section: Introductionmentioning

confidence: 99%

Modified estimation and confidence intervals of an asymmetric loss‐based process capability index Cpm′$\mathcal {C}^{\prime }_{pm}$

Dey¹,

Wang

Saha

2022

Quality & Reliability Eng

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In this article, we are interested to estimate a new capability index scriptCpm′$\mathcal {C}^{\prime }_{pm}$, which is based on asymmetric loss function (linear‐exponential) when the underlying process follows normal distribution. We estimate the parameters of the model using maximum likelihood method, bias‐corrected maximum likelihood method and bootstrap bias‐corrected maximum likelihood method and subsequently the process capability index (PCI) scriptCpm′$\mathcal {C}^{\prime }_{pm}$ using the cited methods. Through extensive simulation studies, we compare the performances of the aforementioned methods of estimation for the PCI scriptCpm′$\mathcal {C}^{\prime }_{pm}$ in terms of their absolute bias (AB) and MSEs. Besides, four bootstrap methods are employed for constructing the confidence intervals for the index scriptCpm′$\mathcal {C}^{\prime }_{pm}$ by using the considered methods of estimation. The performances of the bootstrap confidence intervals (BCIs) are also compared in terms of average widths (AWs) and coverage probabilities (CPs) using Monte Carlo simulation. Finally, for illustrating the effectiveness of the proposed methods of estimation and BCIs, two real data sets from electronic industries are analyzed. All these data sets show that width of bias‐corrected accelerated bootstrap interval is minimum among all other considered BCIs.

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Loss-based process capability indices: a review

Cited by 10 publications

References 44 publications

Confidence intervals of the process capability index Cpc$C_{pc}$ revisited via modified bootstrap technique and ROC curves

Confidence intervals of the process capability index Cpc$C_{pc}$ revisited via modified bootstrap technique and ROC curves

What can fuzziness do for capability analysis based on fuzzy data

Modified estimation and confidence intervals of an asymmetric loss‐based process capability index Cpm′$\mathcal {C}^{\prime }_{pm}$

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