scholarly journals A Fuzzy Evaluation Model Aimed at Smaller-the-Better-Type Quality Characteristics

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2513
Author(s):  
Kuen-Suan Chen ◽  
Tsun-Hung Huang
Keyword(s):  
Confidence Interval ◽  
Quality Index ◽  
Evaluation Model ◽  
Quality Characteristics ◽  
Process Quality ◽  
Small Sample ◽  
Fuzzy Evaluation ◽  
Sample Sizes ◽  
Small Sample Sizes ◽  
Fuzzy Evaluation Model

Numerous key components of tool machines possess critical smaller-the-better-type quality characteristics. Under the assumption of normality, a one-to-one mathematical relationship exists between the process quality index and the process yield. Therefore, this paper utilized the index to produce a quality fuzzy evaluation model aimed at the small-the-better-type quality characteristics and adopted the model as a decision-making basis for improvement. First, we derived the 100(1 −α)% confidence region of the process mean and process standard deviation. Next, we obtained the 100(1 −α)% confidence interval of the quality index using the mathematical programming method. Furthermore, a one-tailed fuzzy testing method based on this confidence interval was proposed, aiming to assess the process quality. In addition, enterprises’ pursuit of rapid response often results in small sample sizes. Since the evaluation model is built on the basis of the confidence interval, not only can it diminish the risk of wrong judgment due to sampling errors, but it also can enhance the accuracy of evaluations for small sample sizes.

scholarly journals Fuzzy Quality Evaluation Model Constructed by Process Quality Index

2021 ◽  
Vol 11 (23) ◽  
pp. 11262
Author(s):  
Chun-Min Yu ◽  
Chih-Feng Wu ◽  
Kuen-Suan Chen ◽  
Chang-Hsien Hsu
Keyword(s):  
Quality Index ◽  
Quality Evaluation ◽  
Evaluation Model ◽  
Process Quality ◽  
Small Sample ◽  
Sample Sizes ◽  
Sampling Errors ◽  
Process Yield ◽  
Small Sample Sizes ◽  
Quality Evaluation Model

Many studies have pointed out that the-smaller-the-better quality characteristics (QC) can be found in many important components of machine tools, such as roundness, verticality, and surface roughness of axes, bearings, and gears. This paper applied a process quality index that is capable of measuring the level of process quality. Meanwhile, a model of fuzzy quality evaluation was developed by the process quality index as having a one-to-one mathematical relationship with the process yield. In addition to assessing the level of process quality, the model can also be employed as a basis for determining whether to improve the process quality at the same time. This model can cope with the problem of small sample sizes arising from the need for enterprises’ quick response, which means that the accuracy of the evaluation can still be maintained in the case of small sample sizes. Moreover, this fuzzy quality evaluation model is built on the confidence interval, enabling a decline in the probability of misjudgment incurred by sampling errors.

scholarly journals Developing a Novel Fuzzy Evaluation Model by One-Sided Specification Capability Indices

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1076
Author(s):  
Wei Lo ◽  
Chun-Ming Yang ◽  
Kuei-Kuei Lai ◽  
Shao-Yu Li ◽  
Chi-Han Chen
Keyword(s):  
Evaluation Model ◽  
Critical Value ◽  
Process Quality ◽  
Quality Characteristic ◽  
Fuzzy Membership Function ◽  
Environmental Damage ◽  
Quality Level ◽  
Fuzzy Evaluation ◽  
Radar Chart ◽  
Fuzzy Evaluation Model

When all of the one-sided specification indices of each quality characteristic reach the requirements of the process quality level, they can ensure that the process capability of the product meets the requirements of the process quality level. This study constructs a fuzzy membership function based on the upper confidence limit of the index, derives the fuzzy critical value, and then labels the fuzzy critical value on the axis of the visualized radar chart as well as connects adjacent critical points to shape a regular polygonal critical region. Next, this study calculates the observed value of the index to estimate and mark it on the axis for forming a visualized fuzzy radar evaluation chart. Obviously, this fuzzy evaluation model not only reduces the testing cost but also makes the quality level quickly meet the requirements of the specifications. Further, the radar chart can reduce the risk of misjudgment attributable to sampling errors and help improve the accuracy of evaluation by a confidence-upper-limit-based fuzzy evaluation model. Therefore, this easy-to-use visualized fuzzy radar evaluation chart is used as an evaluation interface, which has good and convenient management performance to identify and improve critical-to-quality quickly. Improving the quality of the process before the product is completed will also have the advantage of reducing social losses and environmental damage costs.

scholarly journals Confidence Interval Based Fuzzy Evaluation Model for an Integrated-Circuit Packaging Molding Process

2019 ◽  
Vol 9 (13) ◽  
pp. 2623 ◽  
Author(s):  
Chun-Ming Yang ◽  
Kuo-Ping Lin ◽  
Kuen-Suan Chen
Keyword(s):  
Confidence Interval ◽  
Integrated Circuit ◽  
Evaluation Model ◽  
Measurement Data ◽  
Electronics Industry ◽  
Green Economy ◽  
Fuzzy Evaluation ◽  
Molding Process ◽  
Ic Packaging ◽  
Fuzzy Evaluation Model

The electronics industry in Taiwan has achieved a complete information and communication technology chain with a firm position in the global electronics industry. The integrated-circuit (IC) packaging industry chain adopts a professional division of labor model, and each process (including wafer dicing, die bonding, wire bonding, molding, and other subsequent processes) must have enhanced process capabilities to ensure the quality of the final product. Increasing quality can also lower the chances of waste and rework, lengthen product lifespan, and reduce maintenance, which means fewer resources invested, less pollution and damage to the environment, and smaller social losses. This contributes to the creation of a green process. This paper developed a complete quality evaluation model for the IC packaging molding process from the perspective of a green economy. The Six Sigma quality index (SSQI), which can fully reflect process yield and quality levels, is selected as a primary evaluation tool in this study. Since this index contains unknown parameters, a confidence interval based fuzzy evaluation model is proposed to increase estimation accuracy and overcome the issue of uncertainties in measurement data. Finally, a numerical example is given to illustrate the applicability and effectiveness of the proposed method.

A novel confidence interval for a single proportion in the presence of clustered binary outcome data

2019 ◽  
Vol 29 (1) ◽  
pp. 111-121
Author(s):  
Meghan I Short ◽  
Howard J Cabral ◽  
Janice M Weinberg ◽  
Michael P LaValley ◽  
Joseph M Massaro
Keyword(s):  
Confidence Interval ◽  
Clustered Data ◽  
Epidemiological Studies ◽  
Outcome Data ◽  
Small Sample ◽  
Interval Methods ◽  
Sample Sizes ◽  
Wide Range ◽  
Small Sample Sizes ◽  
Over Dispersion

Estimating the precision of a single proportion via a 100(1−α)% confidence interval in the presence of clustered data is an important statistical problem. It is necessary to account for possible over-dispersion, for instance, in animal-based teratology studies with within-litter correlation, epidemiological studies that involve clustered sampling, and clinical trial designs with multiple measurements per subject. Several asymptotic confidence interval methods have been developed, which have been found to have inadequate coverage of the true proportion for small-to-moderate sample sizes. In addition, many of the best-performing of these intervals have not been directly compared with regard to the operational characteristics of coverage probability and empirical length. This study uses Monte Carlo simulations to calculate coverage probabilities and empirical lengths of five existing confidence intervals for clustered data across various true correlations, true probabilities of interest, and sample sizes. In addition, we introduce a new score-based confidence interval method, which we find to have better coverage than existing intervals for small sample sizes under a wide range of scenarios.

scholarly journals A Note on Inferences About the Probability of Success

2020 ◽  
Vol 18 (1) ◽  
Author(s):  
Rand Wilcox
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
Small Sample ◽  
Extensive Literature ◽  
Sample Sizes ◽  
Probability Of Success ◽  
Small Sample Sizes ◽  
A Minor ◽  
Sample Case

There is an extensive literature dealing with inferences about the probability of success. A minor goal in this note is to point out when certain recommended methods can be unsatisfactory when the sample size is small. The main goal is to report results on the two-sample case. Extant results suggest using one of four methods. The results indicate when computing a 0.95 confidence interval, two of these methods can be more satisfactory when dealing with small sample sizes.

scholarly journals Two-Tailed Fuzzy Hypothesis Testing for Unilateral Specification Process Quality Index

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2129
Author(s):  
Chun-Min Yu ◽  
Win-Jet Luo ◽  
Ting-Hsin Hsu ◽  
Kuei-Kuei Lai
Keyword(s):  
Confidence Interval ◽  
Quality Index ◽  
Quality Characteristics ◽  
Process Quality ◽  
Estimation Accuracy ◽  
Fuzzy Membership Function ◽  
Quality Indices ◽  
Sampling Errors ◽  
Unknown Parameters ◽  
Target Values

The quality characteristics with unilateral specifications include the smaller-the-better (STB) and larger-the-better (LTB) quality characteristics. Roundness, verticality, and concentricity are categorized into the STB quality characteristics, while the wire pull and the ball shear of gold wire bonding are categorized into the LTB quality characteristics. In terms of the tolerance, zero and infinity (∞) can be viewed as the target values in line with the STB and LTB quality characteristics, respectively. However, cost and timeliness considerations, or the restrictions of practical technical capabilities in the industry, mean that the process mean is generally far more than 1.5 standard deviations away from the target value. Researchers have accordingly proposed a process quality index conforming to the STB quality characteristics. In this study, we come up with a process quality index conforming to the LTB quality characteristics. We refer to these two types of indices as the unilateral specification process quality indices. These indices and the process yield have a one-to-one mathematical relationship. Besides, the process quality levels can be completely reflected as well. These indices possess unknown parameters. Therefore, sample data are required for calculation. Nevertheless, interval estimates can lower the misjudgment risk resulting from sampling errors more than point estimates can. In addition, considering cost and timeliness in the industry, samples are generally small, which lowers estimation accuracy. In an attempt to increase the accuracy of estimation as well as overcome the uncertainty of measured data, we first derive the confidence interval for unilateral specification process quality indices, and then propose a fuzzy membership function on the basis of the confidence interval to establish the two-tailed fuzzy testing rules for a single indicator. Lastly, we determine whether the process quality has improved.

No Evidence that Experiencing Physical Warmth Promotes Interpersonal Warmth: Two Failures to Replicate Williams and Bargh (2008)

2018 ◽  
Author(s):  
Christopher Chabris ◽  
Patrick Ryan Heck ◽  
Jaclyn Mandart ◽  
Daniel Jacob Benjamin ◽  
Daniel J. Simons
Keyword(s):  
Null Hypothesis ◽  
Small Sample ◽  
Sample Sizes ◽  
Double Blind ◽  
Bayesian Analyses ◽  
Physical Warmth ◽  
Small Sample Sizes ◽  
Interpersonal Warmth

Williams and Bargh (2008) reported that holding a hot cup of coffee caused participants to judge a person’s personality as warmer, and that holding a therapeutic heat pad caused participants to choose rewards for other people rather than for themselves. These experiments featured large effects (r = .28 and .31), small sample sizes (41 and 53 participants), and barely statistically significant results. We attempted to replicate both experiments in field settings with more than triple the sample sizes (128 and 177) and double-blind procedures, but found near-zero effects (r = –.03 and .02). In both cases, Bayesian analyses suggest there is substantially more evidence for the null hypothesis of no effect than for the original physical warmth priming hypothesis.

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