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

Kuen-Suan Chen,Tsun-Hung Huang

doi:10.3390/math9192513

Abstract

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.

Highlights

According to Yu et al [1], many key components of tool machines contain critical smaller-the-better-type (STB-type) quality characteristics
Since the proposed angle is based on the nominal-the-best-type quality characteristic, the measured value may be larger or smaller than the target value, while the measured value of the STB-type characteristic can only be larger than the target value in practice
The process quality index QIS can measure the process quality level but it has a one-to-one mathematical link with the process yield. This paper employs this index as well as proposes a confidence interval-based quality fuzzy evaluation model aimed at the STB-type quality characteristics, which will be used as a decision-making basis for improvement

Summary

Introduction

According to Yu et al [1], many key components of tool machines contain critical smaller-the-better-type (STB-type) quality characteristics. The process quality index QIS can measure the process quality level but it has a one-to-one mathematical link with the process yield This paper employs this index as well as proposes a confidence interval-based quality fuzzy evaluation model aimed at the STB-type quality characteristics, which will be used as a decision-making basis for improvement. The model developed by this study has the advantages of the traditional fuzzy evaluation but is capable of integrating the accumulated professional experience of the past production data [7,13], the accuracy of the evaluation can be maintained in the case of a small sample size As a result, it can meet the needs of enterprises to pursue rapid response as well as can help the industry move towards the goal of smart manufacturing. The upper confidence limit can be represented as: USL − (x − eL) σl q∗IS χ20.5+√1−α/2;n−1 + Z0.5−√√1−α/2

Developing a Fuzzy Evaluation Model

A Practical Application

Conclusions and Discussion

Limitations