Abstract
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.
Highlights
According to a number of studies, process capability indices (PCIs) are convenient tools for process quality assessment, such that they are widely employed in the manufacturing industry [1,2,3,4,5,6,7,8]
As to the rest of this paper, it will be arranged as follows: Section 2 indicates the confidence interval of a unilateral specification process quality index; Section 3 presents the two-tailed statistical hypothesis testing of a unilateral specification process quality index; Section 4 develops the two-tailed fuzzy testing model on the basis of the above rules with critical values; Section 5 employs an application to demonstrate the efficacy of the proposed approach
This study proposes a two-tailed fuzzy test method built on the basis of the process quality indices of the unilateral specification for performance evaluation conducted by the industry
Summary
According to a number of studies, process capability indices (PCIs) are convenient tools for process quality assessment, such that they are widely employed in the manufacturing industry [1,2,3,4,5,6,7,8]. Based on the above description, if the process quality level attains to k sigma, the unilateral specification process quality index value will be equal to k. We first derive the confidence interval for the unilateral specification process’ quality indices, and propose a confidence interval-based fuzzy membership function to establish the two-tailed fuzzy testing rules for a single index. As to the rest of this paper, it will be arranged as follows: Section 2 indicates the confidence interval of a unilateral specification process quality index; Section 3 presents the two-tailed statistical hypothesis testing of a unilateral specification process quality index; Section 4 develops the two-tailed fuzzy testing model on the basis of the above rules with critical values; Section 5 employs an application to demonstrate the efficacy of the proposed approach.
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