New process capability indices based on six sigma statistical approach for measuring the process performance in industries: a case study in Aden's oil refinery Yemen

The purpose of this study is to measure and evaluate the process performance of the industrial processes through the use of Process Capability Indices (PCIs) and Six Sigma (SS) concept. In light of this, this study proposed four different cases to estimate and measure the univariate process yield index SSS *pk* based on C *p*, C *pk*, S *pk*, SSC *pk*, SSQL *pk* indices. Moreover, this study extends the proposed univariate process yield index SSS *pk* to a multivariate generalized yield index called SMS *pk* and SSMS *pk PC* based on Tolerance Limits (TL) and Principal Component Analysis (PCA) respectively to measure the overall process yield of industrial processes. Overall, this study provided a statistical approach based on PCIs and SS concept to measure and improve process performance of the univariate and multivariate processes in industries. To demonstrate the applicability of the proposed approach, this study presents an industrial case study to assess the process performance of oil refinery in Aden, Yemen. Toward this end, the data for three essential quality characteristics of petroleum products namely density, octane number and vapor pressure were collected randomly from Aden refinery. The findings of this study indicated that the proposed indices SSMS *pk* and SSMS *pk.PC*outperformed the existing indices TS *pk,PC* , T *pk ..PC* and TS *pk, PC ,B*. The obtained results for SSMS *pk* by TL model for A, B, C and D cases are 0.7114, 1.19, 0.525 and 0.525 respectively. The obtained results for SSMS *pk.. PC* by PCA model is 0.367213. Meanwhile, the yield process results for TS *pk, PC*, S *T pk...PC* and TS *pk...PC ,B* indicators are 0.154, 0.25 and 0.28 respectively. This study has important implications for industrial practitioners, researchers and quality control experts interested in the evaluation of process performance. Finally, the proposed PCIs based on SS concept is a promising approach and thus can be extended and or utilized by other industries and practitioners to assess process performance in the aspect of precision and quality control.