Robust testing procedures of process locations

Abstract

In many manufacturing and service industries, the quality department of the organization works continuously to ensure that the mean or location of the process is close to the target value. In order to understand the process, it is necessary to provide numerical statements of the processes that are being investigated. That is why the researcher needs to check the validity of the hypotheses that are concerned with some physical phenomena. It is usually assumed that the collected data behave well. However, sometimes the data may contain outliers. The presence of one or more outliers might seriously distort the statistical inference. Since the sample mean is very sensitive to outliers, this research will use the smooth adaptive (SA) estimator to estimate the population mean. The SA estimator will be used to construct testing procedures, called smooth adaptive test (SA test), for testing various null hypotheses. A Monte Carlo study is used to simulate the values of the probability of a Type I error and the power of the SA test. This is accomplished by constructing confidence intervals of the process mean by using the SA estimator and bootstrap methods. The SA test will be compared with other tests such as the normal test, t test and a nonparametric statistical method, namely, the Wilcoxon signed-rank test. Also, the cases with and without outliers will be considered. For the right-skewed distributions, the SA test is the best choice. When the population is a right-skewed distribution with one outlier, the SA test controls the probability of a Type I error better than other tests and is recommended.