Measure of variability of condition indicators at failure

`Y = prognosability(X)`

`Y = prognosability(X,lifetimeVar)`

`Y = prognosability(X,lifetimeVar,dataVar)`

`Y = prognosability(X,lifetimeVar,dataVar,memberVar)`

`Y = prognosability(___,Name,Value)`

`prognosability(___)`

returns the prognosability of the lifetime data `Y`

= prognosability(`X`

)`X`

. Use
`prognosability`

as a measure of the variability of a feature at
failure based on the trajectories of the feature measured in several run-to-failure
experiments. A more prognosable feature has less variation at failure relative to the
range between its initial and final values. The values of `Y`

range from
0 to 1, where `Y`

is 1 if `X`

is perfectly prognosable
and 0 if `X`

is non-prognosable.

returns the prognosability of the lifetime data `Y`

= prognosability(`X`

,`lifetimeVar`

)`X`

using the lifetime
variable `lifetimeVar`

.

returns the prognosability of the lifetime data `Y`

= prognosability(`X`

,`lifetimeVar`

,`dataVar`

)`X`

using the data
variables specified by `dataVar`

.

returns the prognosability of the lifetime data `Y`

= prognosability(`X`

,`lifetimeVar`

,`dataVar`

,`memberVar`

)`X`

using the lifetime
variable `lifetimeVar`

, the data variables specified by
`dataVar`

, and the member variable
`memberVar`

.

estimates the prognosability with additional options specified by one or more
`Y`

= prognosability(___,`Name,Value`

)`Name,Value`

pair arguments. You can use this syntax with any of the
previous input-argument combinations.

`prognosability(___)`

with no output arguments plots a
bar chart of ranked prognosability values.

When

`X`

is a tall table or tall timetable,`prognosability`

nevertheless loads the complete array into memory using`gather`

. If the memory available is inadequate, then`prognosability`

returns an error.

The computation of prognosability uses this formula:

$$\text{prognosability}=\text{exp}\left(-\frac{{\text{std}}_{j}\left({x}_{j}\left({N}_{j}\right)\right)}{{\text{mean}}_{j}\left|{x}_{j}\left(1\right)-{x}_{j}\left({N}_{j}\right)\right|}\right),\text{}j\text{=}1,\mathrm{...},M$$

where *x _{j}* represents the vector of measurements of a feature on the

[1] Coble, J., and J. W. Hines.
"Identifying Optimal Prognostic Parameters from Data: A Genetic Algorithms Approach." In
*Proceedings of the Annual Conference of the Prognostics and Health Management
Society*. 2009.

[2] Coble, J. "Merging Data Sources to Predict Remaining Useful Life - An Automated Method to Identify Prognostics Parameters." Ph.D. Thesis. University of Tennessee, Knoxville, TN, 2010.

[3] Lei, Y. *Intelligent Fault
Diagnosis and Remaining Useful Life Prediction of Rotating Machinery*. Xi'an,
China: Xi'an Jiaotong University Press, 2017.

[4] Lofti, S., J. B. Ali, E. Bechhoefer,
and M. Benbouzid. "Wind turbine high-speed shaft bearings health prognosis through a
spectral Kurtosis-derived indices and SVR." *Applied Acoustics* Vol. 120,
2017, pp. 1-8.