Product defect rate confidence bound with attribute and variable data

The upper confidence bound for a product defect rate is a very important index for evaluating the production process in industry. In this paper, we provide a bootstrap methodology to construct a (1-α)100% upper confidence bound for the overall defect rate of a product whose quality assessment involves multiple pass/fail binary data and multiple continuous data. When only the pass/fail data are included we propose using a bootstrap method which is consistent with the Clopper–Pearson one-sided confidence interval. When only the continuous data are included the BCa bootstrap method is recommended. These two methods are combined to provide an upper confidence bound for the overall defect rate of the product when multiple pass/fail binary data and multiple continuous data are present. All methods are clearly stated in algorithmic form, investigated through simulation and demonstrated using example data sets. In the simulation studies and examples the proposed algorithms show great advantages in both coverage probability and computational efficiency.