**X-bar Charts**

**02/12/18**

*“How can we use statistics to describe industrial quality?”*

Even with the most perfect manufacturing processes, flaws are expected to happen during production. As such, we need a way to quantify how stable a given industrial output is. So how can we use our engineering mindset to solve this? Well, we know that if an item’s measurements become three standard levels of deviations outside of the mean, then it is probably unusable. So what if we were to create a chart that would graph the average of all measurements for each part with along with the mean and the tolerance levels so we can visually see anything out of the ordinary? Well, this is called an **X-bar Chart **and the control limits can be calculated by the formula UCL/LCL = (mean of all measurements) +/- 3*(standard deviation of all measurements)/sqrt(number of measurements per sample).

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