{"id":29,"date":"2026-05-09T08:04:29","date_gmt":"2026-05-09T08:04:29","guid":{"rendered":"https:\/\/sigmadesk.app\/blog2\/?p=29"},"modified":"2026-05-25T18:16:19","modified_gmt":"2026-05-25T18:16:19","slug":"what-is-a-control-chart","status":"publish","type":"post","link":"https:\/\/sigmadesk.app\/blog\/what-is-a-control-chart\/","title":{"rendered":"SPC Control Charts (I-MR, Xbar-R, Xbar-S) Explained &#8211; Complete Guide"},"content":{"rendered":"\n<p class=\"has-large-font-size wp-block-paragraph\">A practical guide to control charts \u2014 from common vs. special cause variation to I-MR, X\u0304-R and X\u0304-S charts, control limit formulas, and when to use each one.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\" style=\"margin-top:var(--wp--preset--spacing--20);margin-bottom:var(--wp--preset--spacing--20)\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"SPC Control Charts Explained (I-MR, Xbar-R, Xbar-S) Complete Guide | Practical Example\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/vGFVo24-nBc?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Control charts are one of the core tools used in&nbsp;<strong>Six Sigma<\/strong>, quality management, and process improvement methodologies. They are especially common in engineering and manufacturing, but their usefulness is not limited to these fields. In fact, control charts can be applied anywhere data is collected over time.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For example, you might use a control chart when you are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Measuring pressure values at regular intervals<\/li>\n\n\n\n<li>Tracking cycle time on a production line<\/li>\n\n\n\n<li>Monitoring patient recovery times in a clinic<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Although these examples come from different areas, they all have one important thing in common:&nbsp;<strong>they involve collecting data over time.<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Common Cause vs. Special Cause Variation<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A control chart helps answer a simple but very important question:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">Is the variation in this data normal, or is something going wrong?<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">In any process, some amount of variation is expected. No process produces exactly the same result every single time. However, not all variation is the same. Control charts help separate two types:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Common cause variation<\/strong>&nbsp;is the normal, expected statistical variation that naturally exists within a process.<\/li>\n\n\n\n<li><strong>Special cause variation<\/strong>&nbsp;is unusual variation that suggests something unexpected may be affecting the process.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">In other words, a control chart helps you understand whether the process is behaving normally, or whether there may be a problem that needs investigation.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">What Does a Control Chart Look Like?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">At its core, a control chart is simply a graph. Despite the statistical concepts behind it, the visual structure itself is quite straightforward. Instead of looking at isolated numbers in a spreadsheet, the control chart transforms the data into a visual story of how the process is behaving.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A standard control chart contains two main axes:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The&nbsp;<strong>Y-axis<\/strong>, which represents the scale for measured values<\/li>\n\n\n\n<li>The&nbsp;<strong>X-axis<\/strong>, which represents time, sequence order, or another logical progression of the data<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The most important rule is that the data points must be plotted in the order they occurred. The sequence matters because control charts are designed to show how a process behaves over time. If the data were randomly arranged, the chart would lose its meaning.<\/p>\n\n\n\n<figure class=\"wp-block-image has-custom-border\"><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"900\" src=\"https:\/\/sigmadesk.app\/blog2\/wp-content\/uploads\/2026\/05\/control-chart.jpg\" alt=\"A standard control chart with a center line, upper and lower control limits, and data points plotted over time\" class=\"wp-image-37\" style=\"border-top-left-radius:20px;border-top-right-radius:20px;border-bottom-left-radius:20px;border-bottom-right-radius:20px\" srcset=\"https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/control-chart.jpg 1600w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/control-chart-300x169.jpg 300w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/control-chart-1024x576.jpg 1024w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/control-chart-768x432.jpg 768w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/control-chart-1536x864.jpg 1536w\" sizes=\"auto, (max-width: 1600px) 100vw, 1600px\" \/><figcaption class=\"wp-element-caption\">The basic anatomy of a control chart.<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Plotting the Data<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Each measurement is plotted on the chart as an individual data point. Depending on the type of control chart being used, that data point may represent different things \u2014 for example, an individual measurement (such as a single pressure reading or cycle time) or a subgroup average (mean). We will explain these different chart types and calculations later in the article.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">After the points are plotted, they are connected with lines to make the behavior of the process easier to visualize: trends, sudden spikes or drops, repeating patterns, or stable behavior over time.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Control Limits vs. Specification Limits<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">One of the most important concepts to understand is that&nbsp;<strong>control limits are not the same thing as specification limits<\/strong>. These two are often confused, but they serve completely different purposes.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Specification Limits<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Specification limits are defined by:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Customer requirements<\/li>\n\n\n\n<li>Engineering drawings<\/li>\n\n\n\n<li>Product design standards<\/li>\n\n\n\n<li>Regulatory requirements<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">These limits define what is considered acceptable for the final product or process output. For example, a shaft diameter may be required to stay between 19.95 mm and 20.05 mm.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Specification limits are fixed targets. They usually do not change unless the product or customer requirements change. Most importantly:&nbsp;<em>specification limits do not tell you whether the process itself is stable.<\/em><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Control Limits<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Control limits are completely different because they are calculated directly from the actual process data. They reflect how the process is currently behaving over time. Unlike specification limits:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Control limits are statistically calculated<\/li>\n\n\n\n<li>They are based on variation within the process<\/li>\n\n\n\n<li>They can change as new data is collected<\/li>\n\n\n\n<li>They help evaluate process stability<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">In other words:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Specification limits<\/strong>&nbsp;tell you what the process&nbsp;<em>should<\/em>&nbsp;produce<\/li>\n\n\n\n<li><strong>Control limits<\/strong>&nbsp;tell you how the process is&nbsp;<em>actually behaving<\/em><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">A process can meet specifications while still being unstable and unpredictable \u2014 and conversely, a process can be stable while not meeting specification limits.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">The I-Chart (Individual Chart)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">One of the most common control charts is the&nbsp;<strong>I-Chart<\/strong>, which stands for&nbsp;<strong>Individual Chart<\/strong>. In an I-Chart:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Every single measurement is plotted individually<\/li>\n\n\n\n<li>Each data point represents one observation<\/li>\n\n\n\n<li>The chart is used when measurements are collected one at a time rather than in groups<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">This makes I-Charts especially useful when subgrouping data is not practical or when measurements occur individually over time. For example, an I-Chart could be used to monitor:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Daily production cycle times<\/li>\n\n\n\n<li>Individual pressure readings<\/li>\n\n\n\n<li>Customer waiting times<\/li>\n\n\n\n<li>Single temperature measurements<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Because every observation is shown separately, I-Charts provide a very detailed view of process behaviour over time.<\/p>\n\n\n\n<figure class=\"wp-block-image has-custom-border\"><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"900\" src=\"https:\/\/sigmadesk.app\/blog2\/wp-content\/uploads\/2026\/05\/i-chart.jpg\" alt=\"An example I-Chart showing individual measurements plotted over time with UCL and LCL lines\" class=\"wp-image-33\" style=\"border-top-left-radius:20px;border-top-right-radius:20px;border-bottom-left-radius:20px;border-bottom-right-radius:20px\" srcset=\"https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/i-chart.jpg 1600w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/i-chart-300x169.jpg 300w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/i-chart-1024x576.jpg 1024w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/i-chart-768x432.jpg 768w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/i-chart-1536x864.jpg 1536w\" sizes=\"auto, (max-width: 1600px) 100vw, 1600px\" \/><figcaption class=\"wp-element-caption\">An example I-Chart with individual measurements plotted over time.<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Understanding Sigma and Control Limits<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">This is the point where a little statistics enters the picture, but the core idea is actually quite simple. Control charts are heavily based on the concept of the&nbsp;<strong>normal distribution<\/strong>, sometimes called the&nbsp;<strong>bell curve<\/strong>&nbsp;because of its shape. In a normal distribution:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>About&nbsp;<strong>68%<\/strong>&nbsp;of all values fall within \u00b11 standard deviation from the average<\/li>\n\n\n\n<li>About&nbsp;<strong>95%<\/strong>&nbsp;fall within \u00b12 standard deviations<\/li>\n\n\n\n<li>About&nbsp;<strong>99.7%<\/strong>&nbsp;fall within \u00b13 standard deviations<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image has-custom-border\"><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"900\" src=\"https:\/\/sigmadesk.app\/blog2\/wp-content\/uploads\/2026\/05\/sigma-leves.jpg\" alt=\"A normal distribution bell curve showing the 68-95-99.7 rule for \u00b11, \u00b12 and \u00b13 sigma ranges\" class=\"wp-image-36\" style=\"border-top-left-radius:20px;border-top-right-radius:20px;border-bottom-left-radius:20px;border-bottom-right-radius:20px\" srcset=\"https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/sigma-leves.jpg 1600w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/sigma-leves-300x169.jpg 300w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/sigma-leves-1024x576.jpg 1024w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/sigma-leves-768x432.jpg 768w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/sigma-leves-1536x864.jpg 1536w\" sizes=\"auto, (max-width: 1600px) 100vw, 1600px\" \/><figcaption class=\"wp-element-caption\">The 68-95-99.7 rule on a normal distribution.<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The term&nbsp;<strong>standard deviation<\/strong>&nbsp;is often represented by the Greek letter sigma (\u03c3). In I-Charts, the control limits are typically placed at the&nbsp;<strong>\u00b13\u03c3<\/strong>&nbsp;level around the process average.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">That means:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The&nbsp;<strong>Upper Control Limit (UCL)<\/strong>&nbsp;is usually located at:&nbsp;<code>UCL = \u03bc + 3\u03c3<\/code><\/li>\n\n\n\n<li>The&nbsp;<strong>Lower Control Limit (LCL)<\/strong>&nbsp;is usually located at:&nbsp;<code>LCL = \u03bc \u2212 3\u03c3<\/code><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>\u03bc<\/code>&nbsp;represents the process average (mean)<\/li>\n\n\n\n<li><code>\u03c3<\/code>&nbsp;represents the standard deviation of the process<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Since 99.7% of normally distributed data should naturally fall within the \u00b13\u03c3 range, any point outside those limits is statistically very unlikely to occur by random chance alone.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In practical terms:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">If a data point falls outside the control limits, something unusual may be happening in the process.<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">This is what control charts are designed to detect. The chart acts as an early warning system that tells you when the process behaviour may no longer be normal.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">The MR Chart (Moving Range Chart)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">So far, the I-Chart has focused on the actual measurement values themselves. But there is another important question we need to answer:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">How much are consecutive measurements changing from one point to the next?<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">This is where the&nbsp;<strong>MR Chart<\/strong>, or&nbsp;<strong>Moving Range Chart<\/strong>, comes in. Instead of plotting the original data values, the MR Chart focuses on the differences between consecutive measurements.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For example, imagine your individual measurements are:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\">Observation<\/th><th class=\"has-text-align-left\" data-align=\"left\">Value<\/th><\/tr><\/thead><tbody><tr><td>1<\/td><td>10<\/td><\/tr><tr><td>2<\/td><td>12<\/td><\/tr><tr><td>3<\/td><td>11<\/td><\/tr><tr><td>4<\/td><td>15<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The moving ranges would be calculated as the absolute differences between consecutive points:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>|12 \u2212 10| = 2<\/li>\n\n\n\n<li>|11 \u2212 12| = 1<\/li>\n\n\n\n<li>|15 \u2212 11| = 4<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">These moving range values are then plotted on a separate chart:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>MR\u1d62 = |X\u1d62 \u2212 X\u1d62\u208b\u2081|<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>MR\u1d62<\/code>&nbsp;= moving range for observation&nbsp;<code>i<\/code><\/li>\n\n\n\n<li><code>X\u1d62<\/code>&nbsp;= current observation<\/li>\n\n\n\n<li><code>X\u1d62\u208b\u2081<\/code>&nbsp;= previous observation<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The MR Chart therefore shows how much variation exists between consecutive measurements over time.<\/p>\n\n\n\n<figure class=\"wp-block-image has-custom-border\"><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"900\" src=\"https:\/\/sigmadesk.app\/blog2\/wp-content\/uploads\/2026\/05\/mr-chart.jpg\" alt=\"An example Moving Range chart showing the variation between consecutive measurements\" class=\"wp-image-32\" style=\"border-top-left-radius:20px;border-top-right-radius:20px;border-bottom-left-radius:20px;border-bottom-right-radius:20px\" srcset=\"https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/mr-chart.jpg 1600w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/mr-chart-300x169.jpg 300w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/mr-chart-1024x576.jpg 1024w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/mr-chart-768x432.jpg 768w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/mr-chart-1536x864.jpg 1536w\" sizes=\"auto, (max-width: 1600px) 100vw, 1600px\" \/><figcaption class=\"wp-element-caption\">An example MR Chart tracking variation between consecutive points.<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Why the MR Chart Matters<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The I-Chart shows whether the actual process values are stable. The MR Chart shows whether the&nbsp;<em>amount of variation itself<\/em>&nbsp;is stable. Together, these charts provide a much clearer picture of process behaviour. This is why you will almost always see the I-Chart and the MR-Chart displayed together side by side as a combined monitoring system \u2014 usually called an&nbsp;<strong>I-MR Chart<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Calculating Control Limits for the MR Chart<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The control limits for the MR Chart are calculated differently from the I-Chart. First, the average moving range is calculated:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>M\u0304R = \u03a3 MR\u1d62 \/ n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>M\u0304R<\/code>&nbsp;= average moving range<\/li>\n\n\n\n<li><code>MR\u1d62<\/code>&nbsp;= each moving range value<\/li>\n\n\n\n<li><code>n<\/code>&nbsp;= number of moving ranges<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The Upper Control Limit (UCL) is calculated using a statistical constant called&nbsp;<code>D\u2084<\/code>:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>UCL_MR = D\u2084 \u00d7 M\u0304R<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">The value of&nbsp;<code>D\u2084<\/code>&nbsp;depends on the subgroup size. For a standard moving range chart, the subgroup size is usually&nbsp;<strong>2<\/strong>, because each moving range compares two consecutive observations. The&nbsp;<code>D\u2084<\/code>&nbsp;constant is obtained from standard statistical control chart constant tables.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The Lower Control Limit (LCL) is calculated using another constant called&nbsp;<code>D\u2083<\/code>:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>LCL_MR = D\u2083 \u00d7 M\u0304R<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">For very small subgroup sizes \u2014 especially subgroup size 2, which is most common in MR Charts \u2014 the value of&nbsp;<code>D\u2083<\/code>&nbsp;is typically zero. That means:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>LCL_MR = 0<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">As a result, the MR Chart often has:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>An Upper Control Limit<\/li>\n\n\n\n<li>A center line representing the average moving range<\/li>\n\n\n\n<li>And a Lower Control Limit equal to zero<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">This makes sense because variation cannot be negative.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">The X\u0304 Chart (Xbar Chart)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">So far, we have discussed I-Charts and MR-Charts, which are typically used when measurements are collected one at a time. But in many real-world processes, measurements are often collected in small groups called&nbsp;<strong>subgroups<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Imagine we are measuring the weight of a plastic injection-moulded part. Instead of measuring only one part at a time, we decide to measure the&nbsp;<strong>first 5 parts produced each day<\/strong>. That means:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Each day becomes one subgroup<\/li>\n\n\n\n<li>Each subgroup contains 5 measurements<\/li>\n\n\n\n<li>The subgroup size is therefore&nbsp;<code>n = 5<\/code><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">For every subgroup of 5 parts, we calculate the average value. For example:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\">Day<\/th><th class=\"has-text-align-left\" data-align=\"left\">Measurements<\/th><th class=\"has-text-align-left\" data-align=\"left\">Subgroup Average<\/th><\/tr><\/thead><tbody><tr><td>1<\/td><td>10.1, 10.2, 10.0, 10.3, 10.1<\/td><td>10.14<\/td><\/tr><tr><td>2<\/td><td>10.0, 10.1, 10.2, 10.1, 10.0<\/td><td>10.08<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">When we plot all of these subgroup averages on a chart, the resulting chart is called an&nbsp;<strong>X\u0304 Chart<\/strong>&nbsp;(often written \u201cXbar Chart\u201d). The name comes from&nbsp;<code>X\u0304<\/code>, which represents the subgroup mean. The X\u0304 Chart monitors how the process average changes over time.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The center line of the X\u0304 Chart is calculated using the average of all subgroup averages. This point is important:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">The center line is NOT the average of all individual measurements directly. It is the average of the subgroup means.<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">If we have&nbsp;<code>k<\/code>&nbsp;subgroups:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>X\u033f = \u03a3 X\u0304\u1d62 \/ k<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>X\u033f<\/code>&nbsp;= overall average of subgroup means<\/li>\n\n\n\n<li><code>X\u0304\u1d62<\/code>&nbsp;= mean of subgroup&nbsp;<code>i<\/code><\/li>\n\n\n\n<li><code>k<\/code>&nbsp;= number of subgroups<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">This overall average becomes the center line of the X\u0304 Chart.<\/p>\n\n\n\n<figure class=\"wp-block-image has-custom-border\"><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"900\" src=\"https:\/\/sigmadesk.app\/blog2\/wp-content\/uploads\/2026\/05\/xbar-chart.jpg\" alt=\"An example X-bar Chart showing subgroup averages plotted over time with control limits\" class=\"wp-image-31\" style=\"border-top-left-radius:20px;border-top-right-radius:20px;border-bottom-left-radius:20px;border-bottom-right-radius:20px\" srcset=\"https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/xbar-chart.jpg 1600w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/xbar-chart-300x169.jpg 300w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/xbar-chart-1024x576.jpg 1024w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/xbar-chart-768x432.jpg 768w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/xbar-chart-1536x864.jpg 1536w\" sizes=\"auto, (max-width: 1600px) 100vw, 1600px\" \/><figcaption class=\"wp-element-caption\">An example X\u0304 Chart tracking subgroup averages over time.<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Control Limits for the X\u0304 Chart<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Now we need to determine the control limits. One common approach estimates the process standard deviation using the subgroup ranges.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 1: Calculate the range of each subgroup.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Within each subgroup of 5 measurements:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Identify the maximum value<\/li>\n\n\n\n<li>Identify the minimum value<\/li>\n\n\n\n<li>Subtract the minimum from the maximum<\/li>\n<\/ul>\n\n\n\n<pre class=\"wp-block-code\"><code>R = X_max \u2212 X_min<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">This gives the range for that subgroup.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 2: Calculate the average range.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">After calculating all subgroup ranges, we calculate their average:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>R\u0304 = \u03a3 R\u1d62 \/ k<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>R\u0304<\/code>&nbsp;= average range<\/li>\n\n\n\n<li><code>R\u1d62<\/code>&nbsp;= range of subgroup&nbsp;<code>i<\/code><\/li>\n\n\n\n<li><code>k<\/code>&nbsp;= number of subgroups<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 3: Estimate sigma from the average range.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The process standard deviation can then be estimated using the constant&nbsp;<code>d\u2082<\/code>:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u03c3\u0302 = R\u0304 \/ d\u2082<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">The value of&nbsp;<code>d\u2082<\/code>&nbsp;depends on the subgroup size. For subgroup size 5,&nbsp;<code>d\u2082 = 2.326<\/code>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 4: Calculate the X\u0304 control limits.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The Upper and Lower Control Limits are calculated as:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>UCL = X\u033f + 3 \u00b7 \u03c3\u0302 \/ \u221an\nLCL = X\u033f \u2212 3 \u00b7 \u03c3\u0302 \/ \u221an<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>X\u033f<\/code>&nbsp;= average of subgroup means<\/li>\n\n\n\n<li><code>\u03c3\u0302<\/code>&nbsp;= estimated process standard deviation<\/li>\n\n\n\n<li><code>n<\/code>&nbsp;= subgroup size<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The term&nbsp;<code>\u03c3\u0302 \/ \u221an<\/code>&nbsp;is called the&nbsp;<strong>standard error of the mean<\/strong>. These limits define the expected variation of subgroup averages over time. Once calculated, they are drawn directly onto the X\u0304 Chart.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">The R Chart (Range Chart)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Now let\u2019s go back to the subgroup ranges. Remember that for every subgroup we already calculated:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>R = X_max \u2212 X_min<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">When these range values are plotted over time, the resulting chart is called an&nbsp;<strong>R Chart<\/strong>, or&nbsp;<strong>Range Chart<\/strong>. The purpose of the R Chart is to monitor variation&nbsp;<em>within<\/em>&nbsp;the subgroups themselves.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">While the X\u0304 Chart monitors changes in the process average, the R Chart monitors changes in process spread or consistency.<\/p>\n\n\n\n<figure class=\"wp-block-image has-custom-border\"><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"900\" src=\"https:\/\/sigmadesk.app\/blog2\/wp-content\/uploads\/2026\/05\/r-chart.jpg\" alt=\"An example R Chart showing the range of each subgroup plotted over time\" class=\"wp-image-34\" style=\"border-top-left-radius:20px;border-top-right-radius:20px;border-bottom-left-radius:20px;border-bottom-right-radius:20px\" srcset=\"https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/r-chart.jpg 1600w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/r-chart-300x169.jpg 300w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/r-chart-1024x576.jpg 1024w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/r-chart-768x432.jpg 768w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/r-chart-1536x864.jpg 1536w\" sizes=\"auto, (max-width: 1600px) 100vw, 1600px\" \/><figcaption class=\"wp-element-caption\">An example R Chart monitoring within-subgroup variation.<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Control Limits for the R Chart<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The center line of the R Chart is the average range:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>CL = R\u0304<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">The Upper Control Limit is calculated using the constant&nbsp;<code>D\u2084<\/code>:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>UCL_R = D\u2084 \u00d7 R\u0304<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">The&nbsp;<code>D\u2084<\/code>&nbsp;constant comes from standard control chart tables and depends on the subgroup size. For subgroup size 5,&nbsp;<code>D\u2084 \u2248 2.114<\/code>; multiplying it by your&nbsp;<code>R\u0304<\/code>&nbsp;gives the chart\u2019s upper limit.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The Lower Control Limit uses another constant called&nbsp;<code>D\u2083<\/code>:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>LCL_R = D\u2083 \u00d7 R\u0304<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">For subgroup size 5,&nbsp;<code>D\u2083 = 0<\/code>, which means&nbsp;<code>LCL_R = 0<\/code>. In fact, for subgroup sizes up to 7, the value of&nbsp;<code>D\u2083<\/code>&nbsp;remains zero. This means the lower control limit on many R Charts is simply zero, because variation itself cannot be negative.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">The S Chart (Standard Deviation Chart)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">For every subgroup, we can also calculate its own standard deviation. If a subgroup contains&nbsp;<code>n<\/code>&nbsp;measurements:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>s = \u221a&#91; \u03a3 (x\u1d62 \u2212 x\u0304)\u00b2 \/ (n \u2212 1) ]<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>s<\/code>&nbsp;= subgroup standard deviation<\/li>\n\n\n\n<li><code>x\u1d62<\/code>&nbsp;= each measurement in the subgroup<\/li>\n\n\n\n<li><code>x\u0304<\/code>&nbsp;= subgroup mean<\/li>\n\n\n\n<li><code>n<\/code>&nbsp;= subgroup size<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">This value tells us how spread out the measurements are within that subgroup. After calculating the standard deviation for every subgroup, we plot those values on a chart. The resulting chart is called an&nbsp;<strong>S Chart<\/strong>, where \u201cS\u201d stands for standard deviation.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The S Chart monitors variation within the process, similar to the R Chart:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The&nbsp;<strong>R Chart<\/strong>&nbsp;monitors variation using ranges<\/li>\n\n\n\n<li>The&nbsp;<strong>S Chart<\/strong>&nbsp;monitors variation using subgroup standard deviations<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">In many situations, especially with larger subgroup sizes, the S Chart provides a more reliable estimate of process variation.<\/p>\n\n\n\n<figure class=\"wp-block-image has-custom-border\"><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"900\" src=\"https:\/\/sigmadesk.app\/blog2\/wp-content\/uploads\/2026\/05\/s-chart.jpg\" alt=\"An example S Chart showing the standard deviation of each subgroup plotted over time\" class=\"wp-image-35\" style=\"border-top-left-radius:20px;border-top-right-radius:20px;border-bottom-left-radius:20px;border-bottom-right-radius:20px\" srcset=\"https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/s-chart.jpg 1600w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/s-chart-300x169.jpg 300w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/s-chart-1024x576.jpg 1024w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/s-chart-768x432.jpg 768w, https:\/\/sigmadesk.app\/blog\/wp-content\/uploads\/2026\/05\/s-chart-1536x864.jpg 1536w\" sizes=\"auto, (max-width: 1600px) 100vw, 1600px\" \/><figcaption class=\"wp-element-caption\">An example S Chart using subgroup standard deviations.<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Center Line of the S Chart<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The center line of the S Chart is simply the average of all subgroup standard deviations:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>S\u0304 = \u03a3 s\u1d62 \/ k<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>S\u0304<\/code>&nbsp;= average subgroup standard deviation<\/li>\n\n\n\n<li><code>s\u1d62<\/code>&nbsp;= standard deviation of subgroup&nbsp;<code>i<\/code><\/li>\n\n\n\n<li><code>k<\/code>&nbsp;= number of subgroups<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">For example, if the average subgroup standard deviation is&nbsp;<code>S\u0304 = 0.858<\/code>, that value becomes the center line of the S Chart.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Control Limits for the S Chart<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The control limits for the S Chart are calculated using statistical constants called&nbsp;<code>B\u2083<\/code>&nbsp;and&nbsp;<code>B\u2084<\/code>. These constants depend on the subgroup size.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The Upper Control Limit:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>UCL_S = B\u2084 \u00d7 S\u0304<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">For a typical small subgroup size,&nbsp;<code>B\u2084<\/code>&nbsp;might be around&nbsp;<code>2.089<\/code>. With&nbsp;<code>S\u0304 = 0.858<\/code>, the Upper Control Limit is obtained by multiplying these two values together.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The Lower Control Limit:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>LCL_S = B\u2083 \u00d7 S\u0304<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">For subgroup sizes up to 6,&nbsp;<code>B\u2083 = 0<\/code>, which means&nbsp;<code>LCL_S = 0<\/code>. As with the R Chart, this makes practical sense because variation cannot be negative.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">R Chart vs. S Chart: A Simple Rule of Thumb<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">When working with subgrouped data, the subgroup size plays a major role in choosing between an R Chart and an S Chart. A commonly used guideline is:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If the subgroup size is&nbsp;<strong>10 or less<\/strong>, an&nbsp;<strong>R Chart<\/strong>&nbsp;is usually sufficient<\/li>\n\n\n\n<li>If the subgroup size is&nbsp;<strong>greater than 10<\/strong>, an&nbsp;<strong>S Chart<\/strong>&nbsp;is generally preferred<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Why?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The R Chart estimates variation using only two values: the maximum and the minimum. This works well for smaller subgroup sizes because the range still represents the subgroup variation reasonably accurately. However, as subgroup sizes become larger, relying only on the maximum and minimum values can introduce more statistical noise and reduce accuracy.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The S Chart becomes more reliable in larger subgroups because it uses&nbsp;<em>all observations<\/em>&nbsp;when calculating variation through standard deviation.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Estimating Sigma from Subgroup Standard Deviations<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Earlier, the process sigma&nbsp;<code>\u03c3<\/code>&nbsp;was estimated using the average range:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u03c3\u0302 = R\u0304 \/ d\u2082<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">But there is another method. Instead of using the average range, we can estimate sigma using the average subgroup standard deviation. To do this, we use a correction factor called&nbsp;<code>c\u2084<\/code>. The formula becomes:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u03c3\u0302 = S\u0304 \/ c\u2084<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>S\u0304<\/code>&nbsp;= average subgroup standard deviation<\/li>\n\n\n\n<li><code>c\u2084<\/code>&nbsp;= statistical correction factor based on subgroup size<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Applying this formula to the example above gives&nbsp;<code>\u03c3\u0302 \u2248 0.9127<\/code>. This result is slightly different from the sigma value obtained using the average range method.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Why Do the Control Limits Sometimes Differ Slightly?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Once sigma is estimated, the remaining control limit calculations stay essentially the same. However, because the estimated sigma value changes slightly depending on the method used, the final control limits may also shift slightly. This explains why an X\u0304\u2013R Chart and an X\u0304\u2013S Chart may appear to tell the exact same process story while still showing slightly different control limits.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The difference comes entirely from&nbsp;<em>how the process standard deviation is estimated<\/em>. In practice, the difference is usually small enough that most people barely notice it.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Summary<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Control charts turn raw measurements into a clear picture of how a process behaves over time. By separating common cause from special cause variation, they let you react to real signals instead of normal noise. Choose your chart based on how data is collected:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>I\u2013MR Chart<\/strong>&nbsp;\u2014 when measurements come one at a time<\/li>\n\n\n\n<li><strong>X\u0304\u2013R Chart<\/strong>&nbsp;\u2014 when data is grouped in small subgroups (\u2264 10)<\/li>\n\n\n\n<li><strong>X\u0304\u2013S Chart<\/strong>&nbsp;\u2014 when subgroup sizes are larger (&gt; 10)<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">With SIGMADESK, you don\u2019t have to calculate&nbsp;<code>d\u2082<\/code>,&nbsp;<code>D\u2083<\/code>,&nbsp;<code>D\u2084<\/code>,&nbsp;<code>B\u2083<\/code>,&nbsp;<code>B\u2084<\/code>&nbsp;or&nbsp;<code>c\u2084<\/code>&nbsp;by hand \u2014 just feed your data in and the platform handles the rest, with built-in rule checking and capability analysis on top.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A practical guide to control charts \u2014 from common vs. special cause variation to I-MR, X\u0304-R and X\u0304-S charts, control limit formulas, and when to use each one. Control charts are one of the core tools used in&nbsp;Six Sigma, quality management, and process improvement methodologies. They are especially common in engineering and manufacturing, but their [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-29","post","type-post","status-publish","format-standard","hentry","category-educational"],"_links":{"self":[{"href":"https:\/\/sigmadesk.app\/blog\/wp-json\/wp\/v2\/posts\/29","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sigmadesk.app\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sigmadesk.app\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sigmadesk.app\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sigmadesk.app\/blog\/wp-json\/wp\/v2\/comments?post=29"}],"version-history":[{"count":4,"href":"https:\/\/sigmadesk.app\/blog\/wp-json\/wp\/v2\/posts\/29\/revisions"}],"predecessor-version":[{"id":108,"href":"https:\/\/sigmadesk.app\/blog\/wp-json\/wp\/v2\/posts\/29\/revisions\/108"}],"wp:attachment":[{"href":"https:\/\/sigmadesk.app\/blog\/wp-json\/wp\/v2\/media?parent=29"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sigmadesk.app\/blog\/wp-json\/wp\/v2\/categories?post=29"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sigmadesk.app\/blog\/wp-json\/wp\/v2\/tags?post=29"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}