# How to determine the effect of different weather parameters (temp, wind speed etc) on component failure

I have a daily time series of the different weather parameters (temperature, wind speed, precipitation, Dew Point, ...) as well as a daily count of failure rates for an external component. I want to determine the effect of weather on the failure rate of the component.

I have done the following: correlation, lag correlation to determine max lag, lm, glm, analysis of variance, intervalizing the weather parameters and combining.

What is the best way to go about my general question How do I combine multiple weather time series into 1 or determine the most informative of the different time series. How do I address possible correlation within the weather parameters.

• You might want to add the survival tag. Do you know the age of the components? (or their deployment time, i.e. to estimate cumulative exposure) Sep 19, 2016 at 5:08
• @GeoMatt22 Thanks, I added the survival tag. I do have the age of the components and can estimate exposure. Sep 19, 2016 at 5:11
• Great. I would expect the failure rate to depend more on cumulative exposure, i.e. some time-integral of your factors, rather than their instantaneous values. So you might need to model $p[\mathrm{fail}\mid\mathrm{exposure}]$, which might be a fixed (conditional) PDF, and also $p[\mathrm{exposure}]$, which would vary in time (as exposure increases for live components, and as failed components drop out of the population). Sep 19, 2016 at 5:18
• Thanks for the suggestion. Is there a standard statistical method to do this (Cox proportional Hazards regression)? The problem is weather related parameters will not be the sole driver of component failure. I will take a look at the Cox method in the meantime. Sep 19, 2016 at 5:37

Here is one idea, although I cannot say how applicable it will be.

In an idealized scenario, let us assume that in addition to weather time series you also have, for each individual component, a number for the time it was created, the time it was deployed, and the time it failed. Therefore you can compute the age and cumulative exposure of the component at failure.

In this idealized scenario, say we the weather data is $\mathbb{x}_t$, for $x=[x_1,\ldots,x_n]$ and $t=1,\ldots,T$ (e.g. $x_1=$wind speed, $x_2=$temperature, etc.). Then a reasonable approach might be to compute a time-integrated exposure as $X_{t+1}=X_t+x_t\Delta t$ (or you could use a midpoint rule, i.e. $t+\frac{1}{2}$). Then for component $i$ you have exposure $E_t=X_t-X_{\mathrm{deploy}}$ and age $t-t_{\mathrm{create}}$, which for simplicity we can append to the end of $E$ as another exposure factor.

So for component $i$ the predictor will be $E_t^{(i)}$, while the dependent variable will be "failed". This can be defined as a binary variable $F_t^{(i)}=(t>t_\mathrm{fail}^{(i)})$, i.e. 0 prior to failure and 1 after failure. Then you could combine all the component's data into a pair of big $E$ and $F$ arrays. A simple approach then would be to essentially treat this as a classification problem ("failed" vs. "not failed"), and apply logistic regression.

Now I will have to think about how this could work in your case, where you know only bulk failure rates (and perhaps deployment rates?) per day. I will update the answer if I come up with a solution.

In terms of survival models, I am really not familiar with them (beyond their existence and a few buzzwords). You would want to essentially model some sort of conditional hazard function, I guess, in terms of some "exposure adjusted age".

So, all the environment parameters can be modeled as some ARMA process (in simple words, past values of temperature, for example, affect the current value of temperature). You must first ask the question: is the failure rate some sort of time-series process? If the failure count is only dependent on the current values of the environmental variables, and is not directly dependent on past failure count values, then the answer is no. If this is the case, then you may want to treat the data as unordered, where each day is a separate observation. Then, you'd want to fit some model (linear regression? (failure_counts ~ temperature + wind + ...) , I don't know much about environment data) and check out the weights.