This chapter is a late entry, where we present final thoughts to help serve as a two page summary for the notions in this book. To do so we present the Theory of Organization for stability, reliability, and quality. Since we are often interested in the solution to the issues of degradation, the best general top-down approach that we can offer is to assert the following.

The Theory of Organization for stability, reliability, and quality: For a system, subsystem, component, material, or process, in general, the higher the organization, the more likely is the probability of success over time.

In fact, statistically, reliability is the probability of success over time (see Equations (A.2) and (A.10)). If P_i = 1/N for N different microstates (i = 1, 2, …, N) then, as we have stated in Equation (2.31), our measure of disorder for entropy is

(10.1)

This helps our notion of entropy, disorder, and, of course, order over time. The larger the number of N_i microstates that can be occupied, the greater is the potential for disorder. We therefore seek to simplify the number of possible states in a system and the capability of the system to fill the microstates. For example, we might model the capability of a system to fill the microstates in time and cause entropy damage as:

(10.2)

In this model, there are two variables to control disorder: N_max and the time constant τ. The variable N_max applies to our everyday notions in design and manufacturing. Reducing the potential for disorder through organization is equivalent to designing for a smaller N_max. Simplicity, reducing complexity, and structural order can be key for the probability of success for our systems, subsystems, components, materials, and processes. This does not necessarily mean we cannot have complexity. However, we would then need to focus on designing for small time constants τ. As we have seen, one should seek to maximize the free energy of a system and minimize variability in a system or a process. Processes often relate to the normal distribution (see Equation (2.35)); variations in our design and defects in our materials increase the potential for disorder, creating opportunities for entropy damage. Variability is therefore a strong measure of disorder. As we have noted in Chapter 2, variability can promote noise. We know that materials such as crystals and highly repetitive structures such as metals and diamonds (polynomial structures) are often the strongest and most reliable materials. Their redundant structure and designs can minimize the potential for entropy damage for materials and structures. Their free energy, that is, capacity to perform useful work, is higher than for amorphous materials or untidy structures. There are of course exceptions. We seek to dampen resonance in circuit boards to reduce issues of vibration failure. In many cases, common sense prevails: poor design creates loss of order and is strongly related to the probability of degradation occurring over time. Every chapter in this book supports the theory of organization in some way to increase our probability of success in preventing degradation, and is a validation of this theory to aid in our understanding of how to improve stability, quality, and reliability for our products.