How do you apply SPC to non-normal data in service and healthcare industries?

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Statistical Process Control (SPC) is a method of monitoring and improving the quality and performance of processes by using statistical tools and techniques. SPC can help you identify and reduce variation, detect and prevent defects, and optimize your outcomes. However, not all data follow a normal distribution, which is the assumption of many SPC charts and methods. In service and healthcare industries, where data are often skewed, discrete, or categorical, you need to apply SPC to non-normal data in a different way. In this article, you will learn how to do that in four steps.

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Nima Zafarpoor

QA & QC Expert* IRCA Certified Lead auditor*Project Management*Project Portfolio Management*QA Engineering*Quality…
Christopher Joyce

Principal Analyst { CMath FIMA | 25+ years of experience of using data analysis and modelling to generate intelligence…

1 Step 1: Identify the type of data

The first step is to identify the type of data you are dealing with. Depending on the nature and source of your data, you may have continuous or discrete data, and either symmetrical or asymmetrical data. Continuous data are measured on a scale, such as weight, time, or temperature. Discrete data are counted or classified, such as defects, errors, or categories. Symmetrical data have a bell-shaped curve, with most values clustered around the mean. Asymmetrical data have a skewed curve, with more values on one side of the mean than the other.

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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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Applying SPC to non-normal data in service and healthcare industries involves using robust statistical methods suitable for skewed or non-parametric distributions ??. Utilize techniques like transformation or non-parametric tests to analyze data effectively ??. Emphasize control chart rules based on data behavior rather than strict adherence to normality ??. Incorporate tools like run charts and cumulative sum (CUSUM) charts to detect shifts or trends in process performance ??. Flexibility and adaptation ensure accurate monitoring and improvement in non-normal environments ??.

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2 Step 2: Choose the appropriate SPC chart

The second step is to choose the appropriate SPC chart for your data type. SPC charts are graphical tools that display the variation and trends of a process over time. They consist of a center line, which represents the average or target value, and upper and lower control limits, which represent the acceptable range of variation. There are different types of SPC charts for different types of data. For continuous symmetrical data, you can use X-bar and R charts, which plot the mean and range of subgroups of samples. For continuous asymmetrical data, you can use Box-Cox or Johnson transformations, which convert the data to a normal distribution, or nonparametric methods, such as median and range charts, which do not rely on the normality assumption. For discrete symmetrical data, you can use p, np, c, or u charts, which plot the proportion, number, count, or rate of defects or nonconformities. For discrete asymmetrical data, you can use attribute charts with modified control limits, such as Laney p' and u' charts, which account for the overdispersion of the data.

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3 Step 3: Analyze the SPC chart

The third step is to analyze the SPC chart and look for any signals of special causes of variation. Special causes are unusual or unpredictable events that affect the process and cause it to deviate from its normal state. They are indicated by points that fall outside the control limits, or by patterns or trends that suggest a change in the process behavior. For example, you may see a run of seven or more points on one side of the center line, a shift of six or more points above or below the center line, or a cycle of alternating high and low points. If you detect any special causes, you should investigate and eliminate them as soon as possible.

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4 Step 4: Improve the process

The fourth step is to improve the process by reducing the common causes of variation. Common causes are inherent and random sources of variation that affect the process and cause it to fluctuate within the control limits. They are part of the normal variation of the process and cannot be eliminated completely, but they can be reduced by improving the process design, standardization, and management. For example, you may use tools such as Pareto charts, fishbone diagrams, or 5 whys to identify and prioritize the factors that contribute to the common causes. Then, you may implement solutions such as process redesign, training, or preventive maintenance to minimize their impact.

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Christopher Joyce

Principal Analyst { CMath FIMA | 25+ years of experience of using data analysis and modelling to generate intelligence and insight that helps organisations ask/answer questions and formulate/solve problems }
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Data plotted over time can exhibit two types of variation. Common cause variation: inherent random regular variation that impacts upon all outcomes (often referred to as "noise"), and results in a stable ("in control") process with predictable variation. Special cause variation: acquired non-random irregular variation that does not impact upon all outcomes (often referred to as "signals"), and results in an unstable ("out of control") process with unpredictable variation. When encountering a process with common and/or special cause variation, the appropriate order of improvement strategy is to, (1) Remove special cause variation. (2) Reduce common cause variation. (3) Realign the process centre to specification.

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5 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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Christopher Joyce

Principal Analyst { CMath FIMA | 25+ years of experience of using data analysis and modelling to generate intelligence and insight that helps organisations ask/answer questions and formulate/solve problems }
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One of the most common misconceptions I've heard re SPC charts is that the sigma (σ) used is not the standard deviation (σ). While this is false, the misconception comes from the practice of estimating σ via: a constant multiplied by the average moving range; and not the usual square root of the average squared deviation from the mean (n.b. for a normal distribution the average moving range multiplied by √π is equal to x2 the square root of the average squared deviation from the mean). The first method above (constant = (√π)/2 ≈ 0.886) is used because it provides a more robust estimate of σ when: the data isn't normally distributed; consecutive data points aren't independent; and/or there are changes in the process mean and/or variation.

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How do you apply SPC to non-normal data in service and healthcare industries?

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1 Step 1: Identify the type of data

2 Step 2: Choose the appropriate SPC chart

3 Step 3: Analyze the SPC chart

4 Step 4: Improve the process

5 Here’s what else to consider

Statistical Process Control (SPC)

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