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The process capability index is a tool for quality measurement and analysis widely used in the industry. It is also a good tool for the sales department to communicate with customers. Although the value of the process capability index can be affected by the accuracy and precision of the process, the index itself cannot be differentiated. Therefore, the process incapability index is directly divided into two items, accuracy and precision, based on the expected value of the Taguchi process loss function. In fact, accuracy and precision are two important reference items for improving the manufacturing process. Thus, the process incapability index is good for evaluating process quality. The process incapability index contains two unknown parameters, so it needs to be estimated with sample data. Since point estimates are subject to misjudgment incurred by the inaccuracy of sampling, and since modern businesses are in the era of rapid response, the size of sampling usually tends to be small. A number of studies have suggested that a fuzzy testing method built on the confidence interval be adopted at this time because it integrates experts and the experience accumulated in the past. In addition to a decrease in the possibility of misjudgment resulting from sampling error, this method can improve the test accuracy. Therefore, based on the confidence interval of the process incapability index, we proposed the fuzzy testing method to assess whether the process capability can attain a necessary level of quality. If the quality level fails to meet the requirement, then an improvement must be made. If the quality level exceeds the requirement, then it is equivalent to excess quality, and a resource transfer must be considered to reduce costs. [ABSTRACT FROM AUTHOR]

The usefulness of biodiversity indicators strongly increases if accompanied by measures of uncertainty. In the case of indicators that combine population indices of species, however, the inclusion of the uncertainty of the species indices has shown to be hard to realize, usually due to imperfections in monitoring programmes. Missing values and time series of different lengths preclude the use of analytical approaches, whereas bootstrapping across sites requires the raw abundance data on the site level, which may not always be available. Sometimes bootstrapping across species rather than sites is opted for, but this approach ignores the uncertainty attached to species indices. We developed a method to account for sampling error of species indices in the calculation of multi-species indicators based on Monte Carlo simulation of annual species indices. The construction of confidence intervals enables various trend assessments, like testing for linear or smooth trends, testing for changes between two time points, testing the significance of a suspected change-point and testing for differences between two multi-species indicators. Here, we compare our method with conventional methods and illustrate the benefits of our approach using Dutch breeding bird indicators. [ABSTRACT FROM AUTHOR]