As the rapid growth of Industrial society, many enterprises are inclined to ppm management from the traditional$3'{o}$ management method. Therefore it is need to extend process capability index for guarantee of quality assurance level to ppm unit. Thus, in this paper, using the probability of standard normal distribution from $ 3'{o}; to; 6'{o}$ which was developed by Song(1997), the capability index which is proposed considers the numbers of inspection facility and quality assurance level. Also, quality assurance level is determined by considering the precision of inspection when one and two sided specification limits are given for the probability which is out of the specification limit.