## SUMMARY

In this chapter, we presented selected quantitative relationships that support systems engineering and project management. Most of these relationships were drawn from the field of probability theory. Other domain-specific relationships are too numerous to be considered here, but may have to be addressed, depending on the domain knowledge necessary with respect to a given project (e.g., guidance, control, or aerodynamics).

The essential purpose of mastering these and other relationships is to measure the performance of the system that is being designed and built. Other purposes include the effective management of the overall systems engineering effort and the support of the quantitative aspects of all of the thirty elements of systems engineering.

A brief summary of the most significant relationships covered in this chapter is provided in Exhibit 11.1.

Exhibit 11.1: Summary of Quantitative Relationships

General

P(A + B) = P(A) + P(B), if AB = 0 P(AB) = P(A | B)P(B) = P(B | A)P(A)

Variance = ct2 = /(x - m)2 p(x) dx Mean(X + Y) = mean(X + mean(Y)

ct 2(X + Y) = ct 2(X + ct 2(Y), when X and Y are independent E(xy) = //xyp(x, y) dx dy Cov (xy) = E(xy) - E(X)E(y)

Correlation coefficient = C°v fo?

Cumulative distribution function (CDF) = /p(x) dx Specific Distributions and Applications

2CT2

Reliability = R(t) = e-Xt = exp (-t/MTBF) Series reliability = R(A)R(B) = exp [-(Xa + Xb)t] Parallel reliability = 1 - [1 - exp (-Xat)][1 - exp (-Xbt)] MTBF

Availability =

MTBF + MDT