How can you use control charts to monitor non-normal data?

In control charts some of control limits are calculated based on assuming data are normally distributed. But when it is actually not normally distribution calculations would be no more reliable.

Non-normal data matters simply because the distribution often does not align with the data. In my experience, the assumption of normality is wrong but is often overlooked. The reason - it makes life simple to churn out nonsense. There are many solutions to using control charts with non-normal data. You could try transforming the data or using a non-parametric solution. First rule - understand your data before applying techniques to interpret outcomes.

I try to switch my technique depending on the data but in the case of non normal data I think bootstrapping would get best estimate of the the variability and confidence intervals.

There are misconceptions in science that most of the data can be statistically analysed to test the stastical hypothesis with t-test (2 groups) or Anova. These are parametric test that are based of the Assumptions of normal distributed data. If such Assumptions are not met using these test is statistically speaking wrong.

To monitor non-normal data using control charts, you can use non-parametric or distribution-free methods that don't assume data follows a normal distribution. Techniques such as the Individual and Moving Range (I-MR) chart, which uses individual observations and their variability, or the Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) charts, which are sensitive to small shifts in the process mean, are effective. Alternatively, transforming the data to approximate normality or using charts designed for specific distributions (e.g., Poisson for count data) can also be viable strategies. These approaches enable accurate monitoring and quality control for processes with non-normal data distributions.

Try this experiment: Generate a bunch of random normal numbers and put it through these tests. Determine the probability of having defective data. I used to do simulations before settling on a strategy. The truth is engineering is a bunch of compromises driven economic factors. Perfect is the enemy of good is the mantra. I usually found a good subgroup and determined the average and standard deviation. Let the Central Limit Theorem do the work of making averages normal enough.

I have found using a Q-Q plot to check for normality visually is a robust tool. It is easy to construct and deviations are glaringly obvious.

There are many ways to check the distribution of data. Using histogram, dotplot, box plot can get an idea about the shape of distribution either it symmetric or asymmetric one. Then we can move further steps. To test the normality assumption Anderson Darling test, Shapiro Wilk normality test also can be used.

To check the distribution of your data, start with a visual inspection using plots such as histograms, box plots, or Q-Q (quantile-quantile) plots, which can reveal the data's shape, central tendency, and spread. For a more quantitative assessment, perform statistical tests like the Shapiro-Wilk or Kolmogorov-Smirnov tests for normality, or use skewness and kurtosis measures to evaluate asymmetry and tail heaviness. Additionally, comparing summary statistics, such as mean and median, can provide insights into the distribution's characteristics. These methods combined give a holistic view of your data’s distribution, helping to inform appropriate analysis techniques.

To transform non-normal data for use with control charts, apply mathematical transformations to make the data distribution more normal. Common transformations include the logarithmic, square root, or Box-Cox transformation. These adjustments can stabilize variance and make the data symmetric, fitting better to the assumptions of traditional control charts. After transformation, use the transformed data to calculate control limits and plot the control chart. Regularly assess the effectiveness of the transformation by checking the transformed data's distribution. This approach allows for the application of standard control charts, like X-bar and R charts, to effectively monitor processes with initially non-normal data distributions.

Using non-parametric control charts to monitor non-normal data involves leveraging charts that do not assume a specific data distribution. The Individual and Moving Range (I-MR) chart is widely used for its simplicity and effectiveness in handling non-normal data by tracking each individual measurement and the range between successive measurements. The Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) charts are also suitable for detecting small shifts in the process mean or variation, regardless of the data distribution. These charts focus on the median or other robust measures instead of the mean, making them more resilient to non-normal data characteristics.

To use distribution-specific control charts for monitoring non-normal data, first identify the data's underlying distribution (e.g., Poisson, Weibull, Binomial). Then select a control chart designed for that specific distribution. For count data following a Poisson distribution, use a c-chart for monitoring the number of defects per unit. For data with a fixed number of trials and success probability, such as Binomial distribution, employ a p-chart to track the proportion of defective items. Implementing these distribution-specific charts ensures that the control limits accurately reflect the process variability, enabling effective monitoring and quality control of processes with non-normal data distributions.

We know that if we have a normal distribution we calculate the ctrl limits byb6 std. Deviatio . So Alternativaly is it possible annother approach example the 75% Delta appeoach? The formula is: UCL= average of data set + 0,75 (USL - average of data set). LCL= average data set - 0,75 (average - LSL). Please can you give me your feedback? Thank you very much. Angelo