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Data are plotted in time order. A control chart always has a central line for the average, an upper line for the upper control limit, and a lower line for the lower control limit. These lines are determined from historical data. By comparing current data to these lines, you can draw conclusions about whether the process variation is consistent (in control) or is unpredictable (out of control, affected by special causes of variation). This versatile data collection and analysis tool can be used by a variety of industries and is considered one of the seven basic quality tools. The top chart monitors the average, or the centering of the distribution of data from the process. The bottom chart monitors the range, or the width of the distribution. If your data were shots in target practice, the average is where the shots are clustering, and the range is how tightly they are clustered. Control charts for attribute data are used singly. When one is identified, mark it on the chart and investigate the cause. Document how you investigated, what you learned, the cause and how it was corrected. Out-of-control signals In Figure 1, point sixteen is above the UCL (upper control limit). In Figure 1, point 4 sends that signal. In Figure 1, point 11 sends that signal. Or 10 out of 11, 12 out of 14, or 16 out of 20. In Figure 1, point 21 is eighth in a row above the centerline. As each new data point is plotted, check for new out-of-control signals. If so, the control limits calculated from the first 20 points are conditional limits. When you have at least 20 sequential points from a period when the process is operating in control, recalculate control limits. Upon use of the case study in classrooms or organizations, readers should be able to create a control chart and interpret its results, and identify situations that would be appropriate for control chart analysis.
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The authors propose an intuitive algorithm that is robust against both types of disturbance and has better overall performance than existing estimators. Collectively, we are the voice of quality, and we increase the use and impact of quality in response to the diverse needs in the world. By using our site, you agree to our cookie policy.Learn why people trust wikiHow To create this article, 18 people, some anonymous, worked to edit and improve it over time.Control charts have many uses; they can be used in manufacturing to test if machinery are producing products within specifications. Also, they have many simple applications such as professors using them to evaluate tests scores. To create a control chart, it is helpful to have Excel; it will simplify your life.The amount in ounces over 16 oz.The data in the subgroups should be independent of the measurement number; each data point will have a subgroup and a measurement number. The graph is out-of-control if any of the following are true:In practice, however, they are reasonably robust to non-normal data. As explained by the Central Limit Theorem, Means tend to be normally distributed even if the underlying data are not. To create this article, 18 people, some anonymous, worked to edit and improve it over time. This article has been viewed 559,594 times.By continuing to use our site, you agree to our cookie policy. Please help us continue to provide you with our trusted how-to guides and videos for free by whitelisting wikiHow on your ad blocker. If you really can’t stand to see another ad again, then please consider supporting our work with a contribution to wikiHow. The Complete Guide to Understanding Control Charts By Carl Berardinelli 58 comments Control charts have two general uses in an improvement project. The most common application is as a tool to monitor process stability and control. A less common, although some might argue more powerful, use of control charts is as an analysis tool.
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The descriptions below provide an overview of the different types of control charts to help practitioners identify the best chart for any monitoring situation, followed by a description of the method for using control charts for analysis. Identifying Variation When a process is stable and in control, it displays common cause variation, variation that is inherent to the process. A process is in control when based on past experience it can be predicted how the process will vary (within limits) in the future. If the process is unstable, the process displays special cause variation, non-random variation from external factors. Control charts are simple, robust tools for understanding process variability. The Four Process States Processes fall into one of four states: 1) the ideal, 2) the threshold, 3) the brink of chaos and 4) the state of chaos (Figure 1). 3 When a process operates in the ideal state, that process is in statistical control and produces 100 percent conformance. This process has proven stability and target performance over time. This process is predictable and its output meets customer expectations. A process that is in the threshold state is characterized by being in statistical control but still producing the occasional nonconformance. This type of process will produce a constant level of nonconformances and exhibits low capability. Although predictable, this process does not consistently meet customer needs. The brink of chaos state reflects a process that is not in statistical control, but also is not producing defects. In other words, the process is unpredictable, but the outputs of the process still meet customer requirements. The lack of defects leads to a false sense of security, however, as such a process can produce nonconformances at any moment. It is only a matter of time. The fourth process state is the state of chaos. Here, the process is not in statistical control and produces unpredictable levels of nonconformance.
Figure 1: Four Process States Every process falls into one of these states at any given time, but will not remain in that state. All processes will migrate toward the state of chaos. Companies typically begin some type of improvement effort when a process reaches the state of chaos (although arguably they would be better served to initiate improvement plans at the brink of chaos or threshold state). Control charts are robust and effective tools to use as part of the strategy used to detect this natural process degradation (Figure 2). 3 Figure 2: Natural Process Degradation Elements of a Control Chart There are three main elements of a control chart as shown in Figure 3. A control chart begins with a time series graph. Upper and lower control limits (UCL and LCL) are computed from available data and placed equidistant from the central line. This is also referred to as process dispersion. Control limits are calculated by: Estimating the standard deviation, ?, of the sample data Multiplying that number by three Adding (3 x.Control rules take advantage of the normal curve in which 68.26 percent of all data is within plus or minus one standard deviation from the average, 95.44 percent of all data is within plus or minus two standard deviations from the average, and 99.73 percent of data will be within plus or minus three standard deviations from the average. As such, data should be normally distributed (or transformed) when using control charts, or the chart may signal an unexpectedly high rate of false alarms. Controlled Variation Controlled variation is characterized by a stable and consistent pattern of variation over time, and is associated with common causes. A process operating with controlled variation has an outcome that is predictable within the bounds of the control limits. Figure 4: Example of Controlled Variation Uncontrolled Variation Uncontrolled variation is characterized by variation that changes over time and is associated with special causes.
The outcomes of this process are unpredictable; a customer may be satisfied or unsatisfied given this unpredictability. Figure 5: Example of Uncontrolled Variation Please note: process control and process capability are two different things. A process should be stable and in control before process capability is assessed. Figure 6: Relationship of Control Chart to Normal Curve Control Charts for Continuous Data Individuals and Moving Range Chart The individuals and moving range (I-MR) chart is one of the most commonly used control charts for continuous data; it is applicable when one data point is collected at each point in time. The I-MR control chart is actually two charts used in tandem (Figure 7). Together they monitor the process average as well as process variation. With x-axes that are time based, the chart shows a history of the process. The I chart is used to detect trends and shifts in the data, and thus in the process. The individuals chart must have the data time-ordered; that is, the data must be entered in the sequence in which it was generated. If data is not correctly tracked, trends or shifts in the process may not be detected and may be incorrectly attributed to random (common cause) variation. There are advanced control chart analysis techniques that forego the detection of shifts and trends, but before applying these advanced methods, the data should be plotted and analyzed in time sequence. The moving range is the difference between consecutive observations. It is expected that the difference between consecutive points is predictable. Points outside the control limits indicate instability. If there are any out of control points, the special causes must be eliminated. Once the effect of any out-of-control points is removed from the MR chart, look at the I chart. Figure 7: Example of Individuals and Moving Range (I-MR) Chart The I-MR chart is best used when: The natural subgroup size is unknown.
The integrity of the data prevents a clear picture of a logical subgroup. The data is scarce (therefore subgrouping is not yet practical). The natural subgroup needing to be assessed is not yet defined. Xbar-Range Charts Another commonly used control chart for continuous data is the Xbar and range (Xbar-R) chart (Figure 8). Like the I-MR chart, it is comprised of two charts used in tandem. The Xbar-R chart is used when you can rationally collect measurements in subgroups of between two and 10 observations. Each subgroup is a snapshot of the process at a given point in time. The chart’s x-axes are time based, so that the chart shows a history of the process. For this reason, it is important that the data is in time-order. Handpicked Content: Control Chart Wizard - Average And Range - X-Bar and R The Xbar chart is used to evaluate consistency of process averages by plotting the average of each subgroup. It is efficient at detecting relatively large shifts (typically plus or minus 1.5 ? or larger) in the process average. The R chart, on the other hand, plot the ranges of each subgroup. The R chart is used to evaluate the consistency of process variation. Look at the R chart first; if the R chart is out of control, then the control limits on the Xbar chart are meaningless. Figure 8: Example of Xbar and Range (Xbar-R) Chart Table 1 shows the formulas for calculating control limits. Many software packages do these calculations without much user effort. (Note: For an I-MR chart, use a sample size, n, of 2.) Notice that the control limits are a function of the average range (Rbar). This is the technical reason why the R chart needs to be in control before further analysis. If the range is unstable, the control limits will be inflated, which could cause an errant analysis and subsequent work in the wrong area of the process. Yes, based on d 2, where d 2 is a control chart constant that depends on subgroup size.
For sample sizes less than 10, that estimate is more accurate than the sum of squares estimate. The constant, d 2, is dependent on sample size. For this reason most software packages automatically change from Xbar-R to Xbar-S charts around sample sizes of 10. The difference between these two charts is simply the estimate of standard deviation. Control Charts for Discrete Data c -Chart Used when identifying the total count of defects per unit ( c ) that occurred during the sampling period, the c -chart allows the practitioner to assign each sample more than one defect. This chart is used when the number of samples of each sampling period is essentially the same. Figure 9: Example of c -Chart u -Chart Similar to a c -chart, the u -chart is used to track the total count of defects per unit ( u ) that occur during the sampling period and can track a sample having more than one defect. However, unlike a c -chart, a u -chart is used when the number of samples of each sampling period may vary significantly. Figure 10: Example of u -Chart np -Chart Use an np -chart when identifying the total count of defective units (the unit may have one or more defects) with a constant sampling size. Figure 12: Example of p -Chart Notice that no discrete control charts have corresponding range charts as with the variable charts. The standard deviation is estimated from the parameter itself ( p, u or c ); therefore, a range is not required. How to Select a Control Chart Although this article describes a plethora of control charts, there are simple questions a practitioner can ask to find the appropriate chart for any given use. Figure 13 walks through these questions and directs the user to the appropriate chart.
Figure 13: How to Select a Control Chart A number of points may be taken into consideration when identifying the type of control chart to use, such as: Variables control charts (those that measure variation on a continuous scale) are more sensitive to change than attribute control charts (those that measure variation on a discrete scale). Variables charts are useful for processes such as measuring tool wear. Use an individuals chart when few measurements are available (e.g., when they are infrequent or are particularly costly). These charts should be used when the natural subgroup is not yet known. In a u -chart, the defects within the unit must be independent of one another, such as with component failures on a printed circuit board or the number of defects on a billing statement. Use a u -chart for continuous items, such as fabric (e.g., defects per square meter of cloth). A c -chart is a useful alternative to a u-chart when there are a lot of possible defects on a unit, but there is only a small chance of any one defect occurring (e.g., flaws in a roll of material). Handpicked Content: Steps in Constructing a u-Chart Subgrouping: Control Charts as a Tool for Analysis Subgrouping is the method for using control charts as an analysis tool. The concept of subgrouping is one of the most important components of the control chart method. The technique organizes data from the process to show the greatest similarity among the data in each subgroup and the greatest difference among the data in different subgroups. The aim of subgrouping is to include only common causes of variation within subgroups and to have all special causes of variation occur among subgroups. Within-subgroup Variation For each subgroup, the within variation is represented by the range. Figure 14: Within Subgroup Variation The R chart displays change in the within subgroup dispersion of the process and answers the question: Is the variation within subgroups consistent.
If the range chart is out of control, the system is not stable. It tells you that you need to look for the source of the instability, such as poor measurement repeatability. Analytically it is important because the control limits in the X chart are a function of R-bar. If the range chart is out of control then R-bar is inflated as are the control limit. This could increase the likelihood of calling between subgroup variation within subgroup variation and send you off working on the wrong area. The R chart must be in control to draw the Xbar chart. Figure 15: Example of R Chart Between Subgroup Variation Between-subgroup variation is represented by the difference in subgroup averages. Figure 16: Between Subgroup Variation Xbar Chart, Take Two The Xbar chart shows any changes in the average value of the process and answers the question: Is the variation between the averages of the subgroups more than the variation within the subgroup. If the Xbar chart is in control, the variation “between” is lower than the variation “within.” If the Xbar chart is not in control, the variation “between” is greater than the variation “within.” Figure 17: Xbar Chart Within Variation This is close to being a graphical analysis of variance (ANOVA). The between and within analyses provide a helpful graphical representation while also providing the ability to assess stability that ANOVA lacks. Using this analysis along with ANOVA is a powerful combination. Conclusion Knowing which control chart to use in a given situation will assure accurate monitoring of process stability. It will eliminate erroneous results and wasted effort, focusing attention on the true opportunities for meaningful improvement. References Quality Council of Indiana. The Certified Six Sigma Black Belt Prime r, Second Edition, Quality Council of Indiana, West Terre Haute, Ind., 2012. Tubiak, T.M. and Benbow, Donald W. T he Certified Six Sigma Black Belt Handbook, Second Edition, ASQ Quality Press, Milwaukee, Wisc.
, 2009. Wheeler, Donald J. and Chambers, David S. Understanding Statistical Process Control. Just wanted to share a couple of my thoughts that I end having to emphasize when introducing SPC. 1) The four points mentioned for the use of the I-mR chart (natural subgroup size is unknown, integrity of the data prevents a clear picture of a logical subgroup, data is scarce, natural subgroup needing to be assessed is not yet defined) do not limit its use to continuous data. Yes, when the conditions for discrete data are present, the discrete charts are preferred. When the conditions are not met, the I-mR will handle the load, so I am a fan of “or I-mR” at the end of each selection path for the discrete charts. 2) I agree the control limits for the Averages (might) be inflated if a Range is out of the control, but if there are still signals on the Average chart, then those signals will be even greater if the limits were not inflated. Thanks again. Great article. Pete February 18, 2013 at 3:50 am - Log in to Reply Pier Giorgio DELLA ROLE Hi Carl, compliments. A great contribution to clarify some basic concepts in Control Charts. February 18, 2013 at 4:47 am - Log in to Reply Dr. Steve Pollock, ASQ Fellow Good summary. February 18, 2013 at 11:15 am - Log in to Reply Kicab Four comments. A. Regarding your statements: “Control rules take advantage of the normal curve in which 68.26 percent of all data is within plus or minus one standard deviation from the average, 95.44 percent of all data is within plus or minus two standard deviations from the average, and 99.73 percent of data will be within plus or minus three standard deviations from the average. Thus, no attribute control chart depends on normality. Second, the range and standard deviations do not follow a normal distribution but the constants are based on the observations coming from a normal distribution. Your statement could apply to the MR-, R-, and S-charts.
There is evidence of the robustness (as you say) of these charts. Third, the Xbar chart easily relies on the central limit theorem without transformation to be approximately normal for many distributions of the observations. The reason is that the R-chart is less efficient (less powerful) than the S-chart. In addition, as you indicated, the limits are constructed by converting Rbar into an estimate of the standard deviation by dividing by d2.For the I- and Xbar-charts, the center line is the process location. For all other charts, it is not (or, I am misunderstanding what you mean by ?process location.?) A better way of understanding the center line on the chart is to recognize that each type of chart monitors a statistic of a subgroup: Xbar monitors averages, R monitors ranges, S monitors standard deviations, c monitors counts, etc. The center line is the average of this statistic across all subgroups. Now it should be clearer that, for example, the center line of the R-chart cannot be the process location?it is the average range. Similarly, for the S-, MR-, and all the attribute charts. D. ?1. Estimating the standard deviation, ?, of the sample data 2. Multiplying that number by three 3. Adding (3 x ? to the average) for the UCL and subtracting (3 x. It could be the average of means, the average of ranges, average of counts, etc. The ? that is used on the control limits is not an estimate of the population standard deviation. It is the standard error of the statistic that is plotted. That is, it is the standard deviation of averages in the Xbar-chart, the standard deviation of counts in the c-chart, the standard deviation of standard deviations in the S-chart, and so on. There is a specific way to get this ?. Because of the lack of clarity in the formula, manual construction of charts is often done incorrectly. This is why it is recommended that you use software. February 18, 2013 at 11:41 am - Log in to Reply Chris Seider Figure 1 was interesting.
Let’s also not forget to remind people to react to Out of Control indications immediately. And if they do, think about what the subgrouping assumptions really are.Then you limits can be off by 2 or 3 x. Where is the discussion of correlated subgroup samples and autocorreleated averages for X-bar charts. If you are ASQ member, check JQT article by Woodall around 2000, with comments from all the gurus, on Issues with SPC. Montgomery deals with many of the issues in his textbook on SPC. But don’t wait to plot the dots and trend the data, just do not assume that the simple textbook methods for setting limits (and rules) are valid for your data source. To successfully do that, we must, with high confidence, distinguish between Common Cause and Special Cause variation. SPC helps us make good decisions in our continual improvement efforts. February 19, 2013 at 6:04 am - Log in to Reply Chris Seider To Wayne G. Fischer. Isn’t an Out of Control indication by definition a special cause. How would you separate a special cause from the potential common cause variation indicated by the statistical uncertainty. I find your comment confusing and difficult to do practically. February 19, 2013 at 12:29 pm - Log in to Reply Robert Gerst I disagree with the assertion that; “Control rules take advantage of the normal curve in which 68.26 percent of all data is within plus or minus one standard deviation from the average, 95.44 percent of all data is within plus or minus two standard deviations from the average, and 99.73 percent of data will be within plus or minus three standard deviations from the average. As such, data should be normally distributed (or transformed) when using control charts, or the chart may signal an unexpectedly high rate of false alarms.
” As Understanding Statistical Process Control, by Wheeler and Chambers is used as a reference by the author, it is worth noting that this same text makes it clear that: “Myth One: it has been said that the data must be normally distributed before they can be placed on the control chart.” “Myth Two: It has been said the control charts works because of the central limit theorem.” The last thing anyone should do when using control charts is testing for normality or transforming the data. These are robust tools for describing real world behavior, not exercises in calculating probabilities. Why remove the very things you are looking for. To check special cause presence, Run chart would always be referred. Run chart will indicate special cause existence by way of Trend, osciallation, mixture and cluster (indicated by p value) in the data.Once run chart confirms process stability,control charts may be leveraged to spot random cause variations and take necessary control measures. March 5, 2013 at 7:34 am - Log in to Reply Mohamed Abdulhadi Can the I-MR chart be used to determine an Out-of-Trend of stability test result data during the course of a drug product shelf life. Kindly appreciate your help on this topic. December 5, 2013 at 7:52 pm - Log in to Reply Remarque No, Stability tracks change in a specific lot over time. Process control tracks how different lots adhere to a target. Statistics for stability center around multiple regression. January 30, 2020 at 10:17 am - Log in to Reply Daryn Hi, Thanks for a great post. Could you please provide advice on the following. Every week my team and I complete x number of tasks. Over time we would like to make improvements and increase the average number of completed tasks that we complete. In most uses, a control chart seems to help to keep a consistent average. Is that true? What kind of chart could we use to show a gradual increase in the average and also show the upper\lower control limits.
Thanks, Daryn February 15, 2014 at 5:55 am - Log in to Reply Bill I’m interested in tracking production data over time, with an 8 hour sample size. This is descrete data. Which control chart is correct. It has really helped me understand this concept better. June 13, 2015 at 2:58 am - Log in to Reply Jeanne Siegel I am working on P-chart. My LCL is showing as negative but no data falls below zero. How does that effect the mean. July 9, 2015 at 11:38 am - Log in to Reply Bryan Ostrowski Really nice summary. November 13, 2015 at 4:37 am - Log in to Reply D Limit I have a question about the control limits. The limits in the control chart must be set when the process is in statistical control. However, the amount of data used for this may still be too small in order to account for natural shifts in mean. Why not use 4,5 sigma instead. It’s expensive to stop production. November 29, 2015 at 9:47 am - Log in to Reply Keith Kornafel Hello D Limit, I would like to help provide an answer to parts of your question. If I read your question correctly, it illustrates a common point of confusion between Sigma, a measure of dispersion, and Sigma Level, a metric of process capability. But, Sigma Level and Sigma are NOT EQUIVALENT and many people struggle with this issue. Sigma Level refers to the number of Sigma, or process standard deviations, between the mean and the closest specification for a process output. Note that when we talk about Sigma Level, this is looking at the process capability to produce within the CUSTOMER SPECIFICATIONS. But the shift is used in the Sigma level to accommodate for process shifts that occur over time. Again, the Sigma level is the measurement of success in achieving a defect-free output which uses the standard deviation and the customers’ specification limit to determine process capability. Whereas, Sigma in the control charts is about the capability of your PROCESS. You start with the average (or median, mode, and etc.
,) which is a measure that represents the standard deviation. Regards, Keith Kornafel December 6, 2019 at 4:19 pm - Log in to Reply Sathish Rosario Dear Carl, It is a good effort. I learned more about control charts. I found small variation as follows: As per the np chart statement: the unit may have one or more defects As per flow chart “one defect per unit” is noted for np chart.Keep writing on such topics. March 30, 2016 at 12:14 pm - Log in to Reply Omkar Naik If all points in x and R chart lies within UCL and LCL limits,can all parts be accepted or is there any defetive part present can 6sigma method be used to decide whether or not defective parts are present May 10, 2016 at 9:49 am - Log in to Reply Prameswari Hi Carl. I wanna ask about np control chart for attribute data. There’s a point that lays below the LCL. Why the point is considered as “out of control”. Thanks for any answers. November 10, 2016 at 5:49 pm - Log in to Reply Pruthvi They have given just Number of errors and asked to calculate C chart. December 10, 2016 at 7:39 am - Log in to Reply Omar Abbaas Thank you for the good article. I have a question about when there is seasonality in the data, the trends are expected to happen and if fixed means and control limits for the entire time period are used, they will indicate false out of control alarms. What is the best approach to build a control chart for this kind of data, can you please recommend a reference. Thank you. January 31, 2017 at 6:47 am - Log in to Reply John Borneman Very good!! Excellent write up. February 10, 2017 at 5:53 am - Log in to Reply Kurnia I found difficulty in interpreting proportion of defect in this kind of data; I have 10 subgroup, each subgroup has different sampel size. The object that is being inspect is chair and there are 4 observed component per chair. This is what I’m confused about, what defect proportion is that. Is it the proportion of defective chair or proportion of defective component.