Περίληψη :  The thesis is introduced and studied the initially capability indices and their youngest indices which appeared for the improvement of capability indices. The majority of the work refers to onedimensional characteristics of normal distribution, but there is an important reference in multidimensional of normal data. In the first chapter we will define the capability indices & the method sixsigma (6σ) and study the relationship between the indices. Also refer the advantages and disadvantages of each index& the advantages and disadvantages of the method sixsigma (6σ). In the second chapter we will present estimator of each capability indices, we will give the properties of these estimators and at the end we make a conclusion. In the third chapter we will construct confidence intervals for capability indices using various estimators and variance from the chapter above. In the fourth chapter we will define the multi process capability indices and we study each of them as the bibliography permit this. In the fifth chapter we will define a new class index Cp(u,v) ,this new index is a special case of the other indices. Also we will define “process yield” and finally we make a comparison between the indices for choosing the appropriate index. In the sixth chapter, we will make a mixture of chapter one and two but now we will have an important difference. This difference is that we will refer the capability indices and the estimator of each one with asymmetric tolerance.In the seven chapter, we will refer to several examples of such assessment and comparison of indices and the construct of confidence intervals. The examples that I will mention in this chapter is not only numerically but I will refer examples which based in applications in the industry and for this refer I collected various data from articles and web. Finally in this work I used ready routines in R programming language and mathematics for the construction of shapes and for the simulation of data in various examples.

