Today we’re going to talk about something that might not be as exciting as the latest AI breakthroughs but is still crucial for ensuring our safety on the road: failure rates of autonomous vehicles (AVs). Specifically, we’ll compare two popular distributions used in reliability analysis Weibull and Gompertz.

Before anything else, let’s define what a failure rate is. In simple terms, it’s the probability that an AV will fail within a certain time frame. For example, if you have 100 AVs on the road for one year, and five of them break down during that period, then your failure rate would be 5%.

Now Weibull and Gompertz distributions. Both are commonly used in reliability analysis to model failure rates over time. The main difference between these two is how they handle the shape of the curve.

Weibull distribution has a flexible shape that can be either increasing or decreasing, depending on the value of its parameters. This makes it useful for modeling different types of failures some may have an initial high failure rate (e.g., teething problems) and then decrease over time as issues are resolved, while others may have a constant or even increasing failure rate due to wear and tear.

On the other hand, Gompertz distribution has a specific shape that is always concave downwards. This means it’s best suited for modeling failures caused by aging or degradation over time think of batteries in your phone or car tires wearing out after prolonged use.

So which one should you choose? Well, it depends on the type of failure you’re trying to model. If you have a good understanding of how the AV is likely to fail and what factors might affect its reliability over time, then you can make an informed decision based on your data. However, if you’re not sure which distribution to use or want to compare both options, there are some tools available that can help you visualize and analyze the results.

One such tool is R (a popular programming language for statistical computing), which has several packages specifically designed for reliability analysis. For example, the “survival” package provides functions for fitting Weibull and Gompertz models to your data, as well as tools for visualizing the results using survival curves or hazard plots.

Another tool that might be useful is MATLAB (a high-level programming language used in engineering and scientific computing), which also has several built-in functions for reliability analysis. For example, the “fitdist” function can fit Weibull and Gompertz models to your data using maximum likelihood estimation or least squares fitting.

Later!