  A new vision in multidimensional statistics is proposed impacting
severalareas of application. In these applications, a set of noisy
measurementscharacterizing the repeatable response of a process is known as a
realizationand can be seen as a single point in $\mathbb{R}^N$. The projections
of thispoint on the N axes correspond to the N measurements. The contemporary
visionof a diffuse cloud of realizations distributed in $\mathbb{R}^N$ is
replaced bya cloud in the shape of a shell surrounding a topological manifold.
Thismanifold corresponds to the process's stabilized-response domain
observedwithout the measurement noise. The measurement noise, which accumulates
overseveral dimensions, distances each realization from the manifold.
Theprobability density function (PDF) of the realization-to-manifold
distancecreates the shell. Considering the central limit theorem as the number
ofdimensions increases, the PDF tends toward the normal distribution
N($\mu$,$\sigma$^2) where $\mu$ fixes the center shell location and
$\sigma$fixes the shell thickness. In vision, the likelihood of a realization
is afunction of the realization-to-shell distance rather than
therealization-to-manifold distance. The demonstration begins with the work
ofClaude Shannon followed by the introduction of the shell manifold and ends
withpractical applications to monitoring equipment.
