# Formulating a multivariate time-series data in a survival analysis framework

I have a multivariate time series data originating from 200 sensors of a power plant. The task is to predict the next failure, i.e., after what time the failure is going to occur. There are different types and areas where failure can occur. Example Data: Maintenance

Start,Finish,Area,Plant
2013-01-01 11:54:00,2013-01-01 11:57:00,323,Plant_A
2013-01-06 05:30:00,2013-01-06 05:47:00,321,Plant_B
2013-01-11 17:07:00,2013-01-11 17:32:00,322,Plant_A
2013-01-16 00:08:00,2013-01-16 22:08:00,321,Plant_B
2013-01-22 04:40:00,2013-01-22 04:55:00,322,Plant_A


I have now sensor data for these power plants measured every minute: We can consider a matrix as: Example Data:

timestamps = seq(
from=as.POSIXct(min(maintenance$Start), tz="GMT"), to=as.POSIXct(max(maintenance$Finish), tz="GMT"),
by="mins"
)

set.seed(42)
sensors.data <- matrix(rnorm(length(timestamps)*200),length(timestamps),200)


I want to predict time until next failure. One way of doing that is survival analysis.

I have now question regarding how can I formulate this as a survival analysis problem. Normally, survival object require the format as:

Area_of_Failure, Time_to_failure,  Plant_type


I can prepare this from the maintenance data. However, I was wondering if there is any way of including the vast amount of sensor data I have to predict the next impending failure in a survival analysis framework?

Note:: I tried formulating this as a regression problem where time to next failure as the target variable without much success only with the sensor data.

• Please explain intuitively what is the relationship between 'sensor data' and time to failure Oct 2, 2016 at 15:48

## 1 Answer

I would recommend having a look at Cox-Proportional Hazards Regression, implemented in the survival package in R. You won't be able to predict in which plant, for example, the next failure is going to happen. But you will get an estimate of the instantaneous probability of failure for each plant type or area. You will also be able to answer if one plant type or area has a statistically higher or lower probability of failure.

Alternatively, you could consider fitting a generalized linear model (GLM) with a binomial distribution. Such a model would estimate the probability of survival based on the other variables you have sampled.