Interval Estimation of Process Capability Indices Based on the Weibull Distributed Quality Data of Supplier Products

Abstract

Process capability indices (PCIs) play an important role in analyzing process quality capability. However, the occurrence of data fraud events indicates that suppliers may provide false information, which may result in inappropriate choices for customers. Thus, to estimate PCIs and further check authenticity of data provided by suppliers, it is necessary to carry out process capability analysis from supplier products. The quality data of supplier products are doubly truncated based on technical requirements. Considering many quality characteristics of products from practical processes follow Weibull distributions, we propose an interval estimation method of PCIs using the truncated Weibull data. First, Monte Carlo-EM algorithm is applied to estimate unknown parameters. Then, a quantile-filling algorithm is adopted to transform Weibull truncated data into pseudo-complete data. After pseudo-complete data are obtained, we apply generalized confidence interval to calculate interval estimation of PCIs. Finally, an example is provided to illustrate the implement of the proposed method.