Estimating total and specific process capability indices in three-stage processes with measurement errors

et al. 2020

Mathematics

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.

Section: Introductionmentioning

confidence: 99%

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

Luo

et al. 2020

Mathematics

“…According to many scholars' viewpoints, an index is a simple and unitless management tool, which is very convenient for management and communication [13][14][15]. Therefore, no matter whether it is the process quality index of the manufacturing industry or the service performance index of the service industry, it is a unitless and easy-to-use communication and management tool [16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Attribute Service Performance Index Based on Poisson Process

Chen

2021

Mathematics

The purpose of a shop enhancing customer satisfaction is to raise its total revenue as the rate of customer purchases in the shop increases. Some studies have pointed out that the amount of customer arrival at a shop is a Poisson process. A simple and easy-to-use evaluation index proposed for the Poisson process with the attribute characteristic will help various shops evaluate their business performance. In addition, developing an excellent and practical service performance evaluation method will be beneficial to the advancement of shop service quality as well as corporate image, thereby increasing the profitability and competitiveness of the shop. As the surroundings of the internet of things (IoT) are becoming gradually common and mature, various commercial data measurement and collection technologies are constantly being refined to form a huge amount of production data. Efficient data analysis and application can assist enterprises in making wise and efficient decisions within a short time. Thus, following the simple and easy-to-use principle, this paper proposes an attribute service performance index based on a Poisson process. Since the index had unknown parameters, this paper subsequently figured out the best estimator and used the central limit theorem to derive the confidence interval of the service efficiency index based on random samples. Then, we constructed the membership function based on the α-cuts of the triangular shaped fuzzy number. Finally, we came up with a fuzzy testing model based on the membership function to improve the accuracy of the test when the sample size is small in order to meet enterprises’ needs for quick responses as well as reducing the evaluation cost.

“…Many of the nominal-the-best quality characteristics (QCs) of important machine tool components, such as the inner or outer diameters of shafts, bearings, and gears, have asymmetric tolerances [6][7][8][9]. A process capability index (PCI) is not only a convenient tool for process capability assessment and analysis but also an effective tool for communication between sales departments and customers [10][11][12][13][14][15][16]. A process has a symmetric tolerance when the target value, T, equals the tolerance midpoint, M, where M = (USL + LSL)/2, and USL and LSL are the upper and lower specification limits, respectively.…”

Section: Introductionmentioning

confidence: 99%

Statistical Hypothesis Testing for Asymmetric Tolerance Index

Chen

et al. 2021

Applied Sciences

Many of the nominal-the-best quality characteristics of important machine tool components, such as inner or outer diameters, have asymmetric tolerances. An asymmetric tolerance index is a function for the average of the process and the standard deviation. Unfortunately, it is difficult to obtain the 100(1−α)% confidence interval of the index. Therefore, this study adopts Boole’s inequality and DeMorgan’s theorem to find the combined confidence region for the average of the process as well as the standard deviation. Next, using the asymmetric tolerance index for the target function and the combined confidence region for the feasible region, this study applies mathematical programming to find the confidence interval as well as employs this confidence interval for statistical hypothesis testing. Lastly, this study demonstrates the applicability of the proposed approach with an illustrative example.