By means of binomial distribution the optimum redundancy logic is calculated and the boundary factor of yield is introduced to determine whether the redundancy logic is worthy.

According to the low-yield status of power multi-chip module(MCM) assembly,the relation between the chip-scale cost and the total modules cost changing with the number of chips in the module and the module yield were analyzed and compared,critical yield concept was proposed.

This authors introduce the methods of a statistical and infinite calculus to determine the marginal grade of titanium placer in Panzhihua City,in order to make a complete analysis of reserves of titanium placers there.

Based on the grade distribution character of 320 Uranium Deposit and the technical economy indexes of mining and hydrometallurgy, the mine reasonable recovery marginal grade is determined with the assessment method of mathematical statistics by use of computer.

Marginal grade should go hand in hand with the price of mineral products.

The titanium border grade of Panzhihua is identified by means of statistical and infinitesimal calculus(referring to the data of Yunan’s titanium properly) to get optimum application.