In view of the advancement in the field of Statistical Process control, the development of the process capability indices for two correlated quality characteristics and characteristics following Weibull distribution have been made and their important sampling properties e.g. Mean/expectation and variance have been defined and explained. The tables for natural tolerance limits have been derived in case of the quality characteristics following normal distribution. The applications of various indices have been discussed. The reason for selecting 3¿ limits have been explained in respect of variability. These indices may prove to be important in the analysis, control and improvement of various processes in the production leading to the improvement of the quality of the production processes and systems, the satisfaction, delight of customers and interested parties in the global competitive market.