Attribute Service Performance Index Based on Poisson Process

Kuen-Suan Chen, Chang-Hsien Hsu and Ting-Hsin Hsu
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Kuen-Suan Chen: Department of Industrial Engineering and Management, National Chin-Yi University of Technology, Taichung 411030, Taiwan
Chang-Hsien Hsu: Department of Business Administration, Asia University, Taichung 41354, Taiwan
Ting-Hsin Hsu: Department of Finance, National Taichung University of Science and Technology, Taichung 40401, Taiwan

Mathematics, 2021, vol. 9, issue 23, 1-10

Abstract: 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.

Keywords: confidence interval; fuzzy testing; membership function of fuzzy number; Poisson process; service performance index (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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