# 7Statistical Decisions

Statistics is the transdisciplinary science of data, employing mathematical relationships for probability and uncertainty to understand and generate a new knowledge. Statistics is a shared method which crosses disciplinary boundaries including engineering, medicine, government, education, agriculture, business, law and many others.

## 7.1 Random Variables

A function whose values cannot be predicted in a sample space is called a random variable. If a sample is selected in an arbitrary manner from a population, such a sample is said to be a random sample. It should be noted that the word randomness is used for the operation of selecting the sample. Rotary machines, such as turbines and compressors, are designed to operate in a vibration-free manner. However, bearing misalignment, material heterogeneity, and geometric variations, collectively or selectively, cause the rotor axial mass center to be non-coincident with the bearing axis. Such a deviation is termed rotor mass center eccentricity; it causes time-dependent bearing forces to occur in the rotor housing.1,2 The mass center eccentricity is not a design condition. Instead, the eccentricity is a randomly occurring event (random variable) and differs from rotor to rotor within each machine class.

A similar argument can be made for a radial clearance of the journal bearings of a high-speed integrally geared compressor as shown in Figure 7.1. Surface roughness, out-of-roundness and radial clearance are ...

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