How do you use SPC to detect and correct skewness and kurtosis in your data?

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Statistical Process Control (SPC) is a method of monitoring and improving the quality and consistency of a process by using data and statistical tools. One of the aspects of data quality that SPC can help you with is the shape of the distribution of your measurements, which can be described by two parameters: skewness and kurtosis. Skewness measures how asymmetric your data is, while kurtosis measures how peaked or flat your data is. In this article, you will learn how to use SPC to detect and correct skewness and kurtosis in your data, and why it matters for your process performance.

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Nima Zafarpoor

QA & QC Expert* IRCA Certified Lead auditor*Project Management*Project Portfolio Management*QA Engineering*Quality…
Tom Bzik

ASTM E11 Quality and Statistics Leadership Roles

1 Why skewness and kurtosis matter

Skewness and kurtosis can affect the accuracy and reliability of your process indicators, such as the mean, standard deviation, control limits, and capability indices. If your data is skewed, it means that your process is not centered around the target value, and may have more variation in one direction than the other. This can lead to more defects, waste, or customer dissatisfaction. If your data is kurtotic, it means that your process has more or less extreme values than expected, which can indicate instability, outliers, or non-normality. This can affect the validity of your statistical tests and assumptions, and reduce your process capability.

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Nima Zafarpoor

QA & QC Expert* IRCA Certified Lead auditor*Project Management*Project Portfolio Management*QA Engineering*Quality Auditing*Administrative Management Expet*QA Manager at Yaks* Trainer*
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Using SPC to detect and correct skewness and kurtosis involves analyzing control charts for non-random patterns ??. Look for systematic shifts or trends indicating non-normality ??. Employ transformation techniques like logarithmic or square root transformations to mitigate skewness and kurtosis ??. Alternatively, utilize robust statistical methods or non-parametric tests for skewed data ??. Regular monitoring and adjustment ensure data conformity and accurate process control ??.

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2 How to detect skewness and kurtosis

One of the simplest ways to detect skewness and kurtosis in your data is to use a histogram, which is a graphical representation of the frequency of your measurements in different intervals. A histogram can show you the shape of your data distribution, and help you compare it to a normal distribution, which is symmetric and bell-shaped. A normal distribution has a skewness of zero and a kurtosis of three. If your histogram shows that your data is skewed to the right or left, or has a higher or lower peak than a normal distribution, then you have a problem with skewness or kurtosis. You can also use numerical measures of skewness and kurtosis, such as the sample skewness and kurtosis coefficients, which are calculated from your data values. These coefficients can be compared to standard thresholds or confidence intervals to determine if your data is significantly skewed or kurtotic.

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3 How to correct skewness and kurtosis

Once you have detected skewness and kurtosis in your data, you need to identify and eliminate the root causes of these problems. Skewness and kurtosis can be caused by various factors, such as measurement errors, process changes, special causes, non-normal distributions, or inappropriate data transformations. You can use SPC tools, such as Pareto charts, cause-and-effect diagrams, control charts, and process capability analysis, to investigate and address these factors. For example, you can use a Pareto chart to prioritize the most frequent sources of variation, a cause-and-effect diagram to brainstorm the potential causes of skewness or kurtosis, a control chart to monitor the stability and control of your process, and a process capability analysis to evaluate the fit of your data to a normal distribution. Depending on the results of your analysis, you may need to improve your measurement system, adjust your process parameters, remove special causes, change your data distribution, or apply a suitable data transformation.

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Tom Bzik

ASTM E11 Quality and Statistics Leadership Roles
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It is a misnomer to assume that skewness and kurtosis are generally indicative of problems solved by the methods listed under 3 How to correct skewness and kurtosis. For example, trace contamination data will typically exhibit right skew regardless of who sampled it and measured it by whatever talented means on well calibrated advanced instrumentation. Where skewness is pervasive a different (non-normal) model for defining control limits and their management is required. A typically reasonable approximate solution to the problem is provided by the process of skew correction. Adaptive use of the model provided in the paper "Control Charts for Skewed and Left-Censored Data that Approximately Control the Family Type I Error" is suggested.

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4 How to use data transformations

Data transformations are mathematical operations that can be used to correct skewness and kurtosis in your data, making the data more normal or symmetrical. This can improve the accuracy and validity of statistical calculations and tests, as well as increase process capability. However, data transformations can also change the meaning and interpretation of the data, introduce new sources of variation, or mask the true nature of the process. Therefore, it should only be used as a last resort after attempting to eliminate root causes. Common transformations for correcting skewness or kurtosis include square root, logarithmic, reciprocal, and Box-Cox transformations. The Box-Cox transformation is more general and flexible, involving raising each data value to a power determined by a parameter called lambda.

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5 How to check the effectiveness of your corrections

After you have corrected skewness and kurtosis in your data, you need to check the effectiveness of your corrections by using SPC tools again. You can use a histogram, numerical measures, control charts, and process capability analysis to compare your original and transformed data, and see if they have improved in terms of shape, symmetry, stability, normality, and capability. You should also check if your corrections have improved the quality and consistency of your process output, such as reducing defects, waste, or customer complaints. If your corrections have not achieved the desired results, you may need to revisit your root cause analysis, try a different data transformation, or consider other alternatives.

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6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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How do you use SPC to detect and correct skewness and kurtosis in your data?

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1 Why skewness and kurtosis matter

2 How to detect skewness and kurtosis

3 How to correct skewness and kurtosis

4 How to use data transformations

5 How to check the effectiveness of your corrections

6 Here’s what else to consider

Statistical Process Control (SPC)

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