9Process Stability and Capability

I asserted in Chapter 8 that common causes can increase to the point where they may destabilize the system, be it manufacturing or service. Causes that create unstable operations are the responsibility of management and in the event of systemic failure, misfeasance and process liability may follow. Hence, process stability is essential to the provision of products and services that conform to customer requirements. This assertion shall be proven in later chapters, but for now, we must understand what stability means.

9.1 Process Stability

In the Preface, I quoted Kalman’s definition of a dynamical system as an abstract mathematical concept defined by a set of vector spaces: admissible input functions, single‐valued output functions, system states, and a state transition function (Kalman et al., 1969). In principle the definition applies to stochastic as well as deterministic systems. In this context, we begin with the classical definition from Liapunov’s general theory on stability, taken from Siljak (1969):

An equilibrium state xe of a free dynamic system is stable if for every real ...

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