Statistical Estimation for Hazard Function and Process Capability Index under Bivariate Exponential Process

Higher sigma quality level is generally perceived by customers as improved performance by assigning a correspondingly higher satisfaction score. The process capability indices and the sigma level ave been widely used in six sigma industries to assess process performance. Most evaluations on process capability indices focus on statistical estimation under normal process which may result in unreliable assessments of process performance. In this paper, we consider statistical estimation for bivariate VPCI(Vector-valued Process Capability Index) under Marshall and Olkin (1967)'s bivariate exponential process. First, we derive some limiting distribution for statistical inference of bivariate VPCI . And we propose two asymptotic normal confidence regions for bivariate VPCI . The proposed method may be very useful under bivariate exponential process. A numerical result based on our proposed method shows to be more reliable.