Nonparametric Test on Process Capability
The study of process capability is very important in designing a new product or service and in the definition of purchase agreements. In general we can define capability as the ability of the process to produce conforming products or deliver conforming se
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Abstract The study of process capability is very important in designing a new product or service and in the definition of purchase agreements. In general we can define capability as the ability of the process to produce conforming products or deliver conforming services. In the classical approach to the analysis of process capability, the assumption of normality is essential for the use of the indices and the interpretation of their values make sense but also to make inference on them. The present paper focuses on the two-sample testing problem where the capabilities of two processes are compared. The proposed solution is based on a nonparametric test. Hence the solution may be applied even if normality or other distributional assumptions are not true or not plausible and in the presence of ordered categorical variables. The good power behaviour and the main properties of the power function of the test are studied through Monte Carlo simulations. Keywords Process capability · Permutation test · Two-sample test
1 Introduction To ensure a high quality of product or service, the production process or service delivery process should be stable and a continuous quality improvement should be pursued. Control charts are the basic instruments for a statistical process control (SPC). One of the main goals of these and other statistical techniques consists in studying and controlling the capability of the process. A crucial aspect which should be studied and controlled is the process variability. Every process, even if well-designed, presents a natural variability due to unavoidable random factors. In the presence of specific factors that cause systematic variability, the process is out of control and its performances are unacceptable. In these situations the process variability is greater than the natural variability and high perS. Bonnini (B) Department of Economics and Management, University of Ferrara, Via Voltapaletto 11, Ferrara, Italy e-mail: [email protected] © Springer International Publishing Switzerland 2016 R. Cao et al. (eds.), Nonparametric Statistics, Springer Proceedings in Mathematics & Statistics 175, DOI 10.1007/978-3-319-41582-6_2
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centage of outputs (products, services, etc) could be nonconforming, that is the process would produce high percentages of waste. In other words, when the process is in control, most of the values of the response variable under monitoring falls between the specification limits. When the process is out of control, the probability that the response variable takes values outside the specification limits is high. Hence the main purpose of a SPC is to minimize the process variability. The study of process capability is very important in designing a new product or service and in the definition of purchase agreements. In general we can define capability as the ability of the process to produce conforming products/services. In other words the greater the probability of observing values of the response in the interval [LSL, USL], the greater the process capab
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