# monotonicity

## Syntax

## Description

returns the monotonicity of the lifetime data `Y`

= monotonicity(`X`

)`X`

. Use
`monotonicity`

to quantify the monotonic trend in condition indicators
as the system evolves toward failure. The values of `Y`

range from 0 to
1, where `Y`

is 1 if `X`

is perfectly monotonic and 0
if `X`

is non-monotonic.

As a system gets progressively closer to failure, a suitable condition indicator typically has a monotonic trend. Conversely, any feature with a non-monotonic trend is a less suitable condition indicator.

returns the monotonicity of the lifetime data `Y`

= monotonicity(`X`

,`lifetimeVar`

)`X`

using the lifetime
variable `lifetimeVar`

.

returns the monotonicity of the lifetime data `Y`

= monotonicity(`X`

,`lifetimeVar`

,`dataVar`

)`X`

using the data
variables specified by `dataVar`

.

returns the monotonicity of the lifetime data `Y`

= monotonicity(`X`

,`lifetimeVar`

,`dataVar`

,`memberVar`

)`X`

using the lifetime
variable `lifetimeVar`

, the data variables specified by
`dataVar`

, and the member variable
`memberVar`

.

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

= monotonicity(___,`Name,Value`

)`Name,Value`

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

`monotonicity(___)`

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

## Examples

## Input Arguments

## Output Arguments

## Limitations

When

`X`

is a tall table or tall timetable,`monotonicity`

nevertheless loads the complete array into memory using`gather`

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

returns an error.

## Algorithms

## References

[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.

## Version History

**Introduced in R2018b**