1-11] STATISTICAL CHARACTER OF MODELS 39 



This type of model is the most abstract. When such a model is formulated 

 and used without incurring prohibitive mathematical complexity, it is 

 the most useful model for obtaining quantitative answers to systems 

 problems. 



Many problems may be solved by either analogue or symbolic models. 

 Where a choice exists, it is preferable to employ the symbolic model, for it 

 allows one to examine the effect of changes by a few steps of mathematical 

 deduction. This process was implied in the example of the mid-air collision 

 analogy, just cited. Here the problem was transformed into an equivalent 

 gas dynamics analogue. However, for such a problem we should not con- 

 struct a complex instrument and make measurements — it is far simpler 

 to use the symbolic models already established for the kinetic behavior 

 of gases. Further, we would gain greater insight into the basic nature of 

 the problem in this way than would be obtained by empirical methods. 



The utility of symbolic models is particularly evident for problems in- 

 volving probability concepts. Often, answers may be obtained in closed 

 form for problems that would otherwise require many repeated tests of 

 an analogue model. 



The primary disadvantage of symbolic models arises from limitations in 

 available mathematical and computational techniques for obtaining 

 answers from the model. State-of-the-art improvements in applied 

 mathematics and large digital computers are relieving this problem. 

 Despite these advances, however, there will always be a great premium 

 on the ability to construct symbolic models that strike at the heart of a 

 problem and eliminate nonessentials that merely increase complexity. 



1-11 THE BASIC STATISTICAL CHARACTER OF WEAPONS 

 SYSTEM MODELS 



The model approach consists of abstracting from a complex system 

 certain persistent and discernible relations and using these relations to 

 construct a system model. Frequently, owing either to the inherent 

 nature of the process being examined or to the complex nature of the 

 process, the relations must be expressed in a statistical form. That is to 

 say, certain portions of the system — and as a result of this, the system 

 itself — will not possess a unique output for a given input. Rather, the 

 output must be expressed as a spectrum of possible events where each 

 event has a certain probability of occurrence. 



Two simple examples may serve to illustrate the nature of the phenomena 

 involved: 



Example 1 — Measurement Uncertainties. Measurements of time, 

 distance, temperature, etc., always possess a certain error tolerance. For 

 example, a large number of distance measurements made with the same 



