Control Chart Rules and Interpretation


Quick Links

SPC for Excel Software

Visit our home page

SPC Training

SPC Consulting

Ordering Information

Thanks so much for reading our publication. We hope you find it informative and useful. Happy charting and may the data always support your position.

Sincerely,

Dr. Bill McNeese
BPI Consulting, LLC

View Bill McNeese

Connect with Us

Comments (64)

  • Jason S. KongOctober 12, 2016 Reply

    Hi!  Your page has been significantly helpful.  Can you tell me how these rules would apply for an individuals-moving range chart?  Can these zones still be created?  Thanks in advance!

    • billOctober 12, 2016 Reply

      The zones test can be applied to the individuals chart; not the moving range chart.  I probably need to do an article of what rules apply to which charts.  But all apply the individuals chart.  On the moving range, points beyond the limits, a run below or above the average (twice as long as individuals chart since each data point is reused in the moving range, overcontrol, an seven trending up or down.

  • SPC_MarkJanuary 4, 2017 Reply

    Hi Bill – useful stuff. However, I'm struggling to understand which Control Chart rules I should apply. For example, do I use Westgard, Nelson, WECO etc. – none of which seem to be the rules you've listed above. Are you able to shed any light on which rules to use on an individuals chart? Thanks.

    • billJanuary 4, 2017 Reply

      Of course, points beyond the control limits always apply.  With the X chart for individuals, you apply all the rules listed in the article.  However, with the moving range chart, you only use points beyond the control limts, and long runs above or below the average range or trending up or down.   This is because you are reusing the data.  I will do the next publication on which tests apply to which charts.  Software, like SPC for Excel, will automatically select the appropraite tests for the control chart although you can change those options.

  • SPC_MarkJanuary 4, 2017 Reply

    Sorry…I suppose what I was really trying to say is that there are slight variations to the available sets of rules. As I’m only just entering the world of SPC charts, my understanding is that WECO is the original set of rules (pretty much a cornerstone for all rule sets) and since then, newer iterations such as Nelson and Westgard have been developed. Therefore, I’m confused on which set of rules I should use. In Rule 5 above, you state the need to observe at least 7 consecutive points whereas Nelson rules (rule 3) state the requirement to observe at least 6. Is there a “correct” choice, or does it come down to how long you wish to observe a trend for before determining it to be out of control? Thanks.

    • billJanuary 4, 2017 Reply

      Yes, there are slight variations in the rules.   Some have 7, others 6, others 8.   There is not a correct choice as such.  You are correct – it is how "sure" you want to be that there is signal.  Suppose we were tossing a coin and you paid me a dollar each time it was heads and I paid you a dollar each times it was tails.  If I got six heads in a row, you would start wondering about the coin.  7 times in a row you would wonder even more.  By 8 times, I am sure you think the coin is not a true coin.
      For example, consider a run above the average.  What is the probablity of getting 6 points in a row above the average?  It is 1.56% (simply .5^6).  For 7 points, it is 0.78%.  For 8 points it is 0.39%.  It is really your choice.  The probability of getting a point beyond the control limits for a true normal distribution (doesn't exist) is 0.27%.  So, picking something around there for the other tests is a good way to approach this – so 7 or 8 points looks good to me.

  • John PindsJanuary 27, 2017 Reply

    Hi Bill,Thanks for your page. It is indeed very useful. Tell me, when is it possible for  a control chart which is in control to be actually out of control?Regards, John

    • billJanuary 27, 2017 Reply

      Thanks John.  Not sure I fully understand your question.  There is no way to assign a probability to a point being a special cause or not.  A point beyond the control limits could just be common cause of variation.  And just because a point is within the control limits does notmean there is a not a special cause of variation present.  The rules simply give a way of reacting to certain conditions that most likely are out of control points.

  • Kris MillerMay 22, 2017 Reply

    Your explanation in this article is really quite good, with one exception. Nowwhere in the article do you mention that the rules you are applying are intended only for use with averages; usually of n=2 to 5 individual points. This is vitally important. Grouped means (histograms) are always normal distributions, whereas grouped individuals are totally unpredictable. They can result in a wide variety of distributions, usually not normally distributed. The makes control charting of individuals very risky, because the distribution is not normal, most of the time. The Shewart control chart was derived soley for averages, because they are always normal distributions, therebye predictable.

  • Juliana ViannaJuly 26, 2017 Reply

    Hi! I work with pharmaceutical compressing process to create tablets, and I have some doubts about our chart crontol. From time to time we take some tablets samples and we analize some parameters like weight. The problem is: my samples have 30 tablets each, and I can't take the individual tablets in the exactly moment they leave the machine. So, how can I analize some events like shifts if I don't have the time precision of wich tablet? I'm from Brazil and we don't have here enought information about the topic. I really could use some help. =) Could you contact me?   Kind Regrats!  

  • hamza saadSeptember 10, 2017 Reply

    thanks for great explain, would u help to Calculate the probability that an in-control process will yield the “Simplified” Runs Rule violation of having 2 consecutive points at 1.5sigma or beyond

    • billSeptember 10, 2017 Reply

      If you have Excel, you can use the NORMSDIST(z) function (or NORM.S.DIST for Excel 2001 and later) to determine this.  For example, the probability of getting a point below 1.5 sigma is NORMSDIST(-1.5) = 0.0668 or about 6.68%.  The probability of geting two beyond 1.5 sigma on the same side of the average is 0.0668^2 or .0045.

  • CaseyMarch 24, 2018 Reply

    thanks for this article it’s really helpful. I wonder is there a standard to define when a process is back in control? How many points ‘under control’ would we need to observe after a special cause event to think it was back in control. I am trying to develop a simple “in control? Yes/No” indicator to sit along side our SPC charts. I don’t want to be continually alerting that there was a single blip 8 months ago for example. Any advice? Thanks

    • billMarch 24, 2018 Reply

      It is back in control, in my opinion, if the next point is back within the control limits – if it is a fleeting special cause of variation that comes and goes.  But suppose that out of control point stays around.  You have a point above the upper control limit.  The next point is back within the limits but it is above the upper control limit.  If it stays about the average for a run and you can't find out why, then you have re-calculate the control limits or adjust the process to bring it back into control.  This link has more details:

      <span style="font-size: 13.008px;">/knowledge/control-chart-basics/when-calculate-lock-and-recalculate-control-limits</span&gt;

  • NikitaJuly 6, 2018 Reply

    Dear Bill, thank you for the nice and clear explanation. I have one question, Shewhart control chart can still be created if the data are not normal, right? What about these interpretations, they can only be used if the data are normal? or can some of them be applied in case of non normality of the available whole data for the analysis? Thank you.

    • billJuly 6, 2018 Reply

      Thank you.  The data does not have to be normally distributed to use a control chart.  Most Xbar data is symmetrical assuming the subgroup size is large enough.  The zones tests require some symmetry about the average, but basically, you should not worry about normality.  You know  your process and will know if a control chart is signalling a special case most likely.

  • jagMarch 11, 2019 Reply

    the method of calculation and underlying statistical basis for establishing the UCL & LCL is not clear in your article.  what are the calculations, and on what are they based?? thanks.

  • Mike NguyenApril 12, 2019 Reply

    Hi Dr. Bill.Your info is really helpful. I just started to work on Control Chart that why have some basic question.We have a #4 trend for almost 2 years. I checked all the samples, Technician, collecting data process and machine are OK. I just keep an eye on it.  I have questions:1. If we have to make comment on this trend like  ” In control “ or “ Out of Control”.  Can we say “Our Control chart is IN CONTROL, we need to keep an eye on it and react whenever we got outliner“ ?2. If all condition is the same but the trend Is #4 for long time. Do we need to recalculate Control limit? What can I say to convince other ones to recalculate Control limit?Thx Dr. Mike Nguyen

    • billApril 12, 2019 Reply

      If you have a long run above the average (or below), it means that something has changed to cause the average to move up or down.  It is "out of contorl".  If you can't find what happened – and it doesn't bascially change the product, then you can recalculate the control limits starting with the shift changed.  And use those for the future.

  • John DominicJune 27, 2019 Reply

    Texts over the years have allowed  e.g. 1 in 25 or 2 in ~50 points outside Control Limits w/o stating "out of control."  In your experience with data or reference material texts have you encountered any rule re:  % of points beyond limits.  At times I will deal with >50 or 100 Control Chart points.  Thanks… 

  • billJune 28, 2019 Reply

    A rough rule i have used over the years is that a process is pretty stable if less than 5% of thepoints are out of control.  That is close to what you reference.

  • Scott A WagnerJuly 23, 2019 Reply

    Is there a hirearchy for these rules?  In other words, how would they be ranked in order of statictical significance?

    • billJuly 24, 2019 Reply

      You can theortically put a statistical probability to each rule assuming a normal distribution – they are all about the same probability.  In practical terms, start with the points beyond the control limits, then add the test for zone C later and then zone A and B after that.  This approach seems to work well.

  • Richard TellNovember 3, 2019 Reply

    Dr, McNeese: My background is in electromagnetic fields and measurements of such for safety purposes. The issue of how often instruments that are used for these measurements should be recalibrated is a common question. A presentation available on the web at http://aashtoresource.org/docs/default-source/newsletter/calibrationintervalspresentation.pdf suggests the use of control charts as one possible approach to assessing the need for recalibrating an instrument. Being totally unfamiliar with control charts, I am confused and hope you can shed some light on this matter. For instruments that are typicaly recalibrated once per year, how would control charts be used to suggest that either a longer, or shorter, recalibration interval might be acceptable? The primary objective is to determine an appropriate recalibration interval. If I follow the suggestion, it would seem that long term experience from repetititve calibrations would be required to accumulate sufficient data before one could deduce whether shorter or longer recal intervals were appropriate. Thank you for your insight. 

    • billNovember 4, 2019 Reply

      Hello Richard,
      You are correct that it takes experience to judge how often to check the calibration of an instrument.  If it is critical to production, you should check it more frequently.  For example, when I ran a QC lab years ago, we checked each crtiical test at the start of each shift.  There are probably istruments that don't move too much or don't move in such a way to impact production – you might check those for calibration monthly or longer – it all depends on the situation.  Your knowledge of the process is a key in deciding.

  • AnonymousFebruary 24, 2020 Reply

    if all the observations are within control limits, does that guarantee that the process variation contains only randomness? 

    • billFebruary 24, 2020 Reply

      No, it does not.  It is possible there are special causes of variation present even if the point is witin the control limits, just as it is possible that an out of control point could be due to common causes.  The control limits provide an economic way of being fairly sure there is a special cause of variation before you spend time and money looking for it.  

  • Hien DangApril 13, 2020 Reply

    Hi Bill, can you help me answer this question? Thank you so much.Control charts are used to monitor and control a process. They use control limits to define the range of natural variation in a process. If a sample is taken and the plot point falls outside of the control limits what does this​ signify? the process is in control. the process is out of control and should be checked for natural variation. the process should be monitored for future results. the process is out of control and should be checked for assignable variation.

    • billApril 13, 2020 Reply

      Am I taking a test for you? The process is out of control and should be checked for assignable cause variation. Please read this article

  • Thomson P. U.April 30, 2020 Reply

    Nicely presented

  • Tim E.June 12, 2020 Reply

    Hi Bill, I learned that we need to interpret control charts based on the 68-95-99 rule; and I would like to know, in your opinion, if there are no points outside the 3 Sigma limit (all points with 3Sigma each side), is a process still considered in control, if for example: only 1 of 3 consecutive points fall within 1 Sigma either side of the average.. meaning two of the three are either in the 2 or 3 sigma zones. If we have 100 points of data, we would expect 68 of them to be within 1Sigma from the average, if this is not true, but the process has no data point outside the 3Sigma, is the process considered "not in control"?Thank you.

    • billJune 13, 2020 Reply

      I would not worry too much about probabilities – like 68 points out of 100 should be within one sigma of the average.  That is true for a perfect normal distribution but there are not no perfect normal distributions in real life processes.  If there are no points beyond the limits and none of teh zones tests have been violated, then the process is in statistical control.

  • Roberto SalazarJune 30, 2020 Reply

    Hi. Why aren't these rules applicable for the CUSUM and EWMA charts?

    • billJuly 1, 2020 Reply

      because the CUSUM and EWMA are only looking for a signal that goes beyond hte limits – the values are not symmetrical

  • ARGHYA MAITRASeptember 3, 2020 Reply

    HI SIR, , i HAVE GONE THROUGH THE EIGHT RULES OF CONTROL CHART . BUT IN THAT CONTEXT , WHAT IS THE IDEAL CONTOL CHART OR IS THERE ANY PICTURE OF THAT. 

    • billSeptember 3, 2020 Reply

      I am assuming you mean a control chart that is in control.   A control chart likes that will have most points near the  middle, a few near the control limits, no beyond the control limits and no patterns.

  • Caroline WalshSeptember 30, 2020 Reply

    Hi there,Thank you for this really great article, I have returned to it so many times since I became aware of run charts. Given that Covid had such an impact on data all over the world would you consider this to be a "fleeting" change and control for it  with process shifts or "the new normal" and leave the data as is? I work in the world of crime data so shops closing nd people staying at home impacted Theft from shop and Burglary. TIA

    • billSeptember 30, 2020 Reply

      Well, I wish the crystal ball to see into the future.  I think for now it is the new normal – at least until a vaccine is found and adminstered or better treatment is found and people get back to work like they were before the virus.  I think is good you are applying the control charts to crime data.

      • Caroline WalshAugust 6, 2021 Reply

        Thanks and here's hoping vaccines bring about normality again!

  • PrashantOctober 14, 2020 Reply

    If I am plotting c chart for customer complaints, and 0 being my lower control limit. If i have 4 consecutive points touching LCL, then should I assume my process is in control?

    • billOctober 14, 2020 Reply

      If the LCL is below zero, then there really is not a lower control limit. I don't set it to 0.  Yes 4 points in a row at zero is in statistical control.  You need 7 to 9 below the average to be an out of control situation.

  • [email protected]November 18, 2020 Reply

    if the trending days are 5 in the same direction then the 6th day comes in the the opposite direction slightly less or the same value of the 5th day what should I do:- Exclude this point and continuou counting from the 7 th day as number 6 in the trend OR -Restart counting from day 7 ?Thanks in advance 

    • billNovember 18, 2020 Reply

      Once a trend is broken, you start over with one point.

  • [email protected]November 18, 2020 Reply

    Also if the trending line is zigzag up then down then more up then down .How will I count the 7 trending points.?Thanks 

    • billNovember 18, 2020 Reply

      Not sure I understand but if it zig-zags, it is not a trend, each point must be above the last one for an upward trend.

  • Peter PanDecember 29, 2020 Reply

    Hi Bill, thanks for the great posting! I got several questions: Is it possible that a single point triggers several rules all at the same time? If it is possible, how can I tell which rule was triggered first? In other word, is there any hierarchy or ranking among these eight rules? 

    • billDecember 29, 2020 Reply

      Hello, 
      Thanks for the comment.  The only hierarchy I pay attention really is point beyond the control limits.  If that occurs, you work to find out what caused that.  A point beyond the limit can change the location of the average and sigma lines making the other tests not really valid.  After that, I would probably look at runs above the average if I have to pick another one (zone C).

  • maherJanuary 8, 2021 Reply

    U chart can be used in both when we have the same sample size or different sample sizes. Why do we still use c chart when we have the same sample size

    • billJanuary 8, 2021 Reply

      It is easier to explain and you don't have to select an inspection unit.  But there is no need to use it since the u chart works also.

  • GigiJune 8, 2021 Reply

    Hello Sirs and All…Can a high or increasing yield be a problem in SPC?Does it make sence to make a control chart for high yield?Example>>> LCL = 85% UCL = 95% CL=90% >>> Yield became higher than the UCL. Is this considered yield is out of control?

    • billJune 8, 2021 Reply

      Yes you can have a control chart on high yield.  If the result is above the UCL, it is out of control – but on the good side.  IF you can find out what happened and make it part of the process, then you have improved it.

  • NijaanAugust 27, 2021 Reply

    Are these rules meant to only be used for Xbar charts or can they be used for range and standard deviation control charts as well?

  • SandipSeptember 30, 2021 Reply

    Hi Bill,Nice article, I got clarifications of some finer points. I have a question that is how do you arrive at 2 out of 3 or 4 out of 5 points for different zones to come to conclusion that they could be likely assignable causes. How do you assign propability of occurances of these 2 cases. 

    • billSeptember 30, 2021 Reply

      You can estimate the probabilities using a normal distribution.  The tests for zone A and zone B give about the same probability as a point beyond the control limits.  The probability of getting a point beyond the upper control limit is 0.00135.  The probability of getting one point in zone A or beyond is 0.0228. The probability of getting two points in a row in zone A or beyond is then (0.0228)(0.0228) = 0.00052. Note that this probability is smaller than the probability of getting one point beyond one of the control limits. Thus, if two points in a row fall in zone A or beyond, it is a stronger indication of an out of control situation than a point beyond the control limits.
      <br />Since this probability is so small, the requirement can be loosen somewhat by saying two out of three consecutive points in zone A or beyond. The probability of getting a point somewhere else on the chart besides zone A or beyond is 1 – 0.0228 = 0.9772. The probability of getting two out of three consecutive points in zone A or beyond is then (0.0228)(0.0228)(0.9972)(3) = 0.00156 (or one out of 640). You multiply by 3 because the point not in zone A could be the first, second or third point. The probability of obtaining this pattern for a process that is in control is then 0.00156, a small number.
      A similar approach can be used for zone B.

    • billSeptember 30, 2021 Reply

      You can estimate the probabilities using a normal distribution.  The tests for zone A and zone B give about the same probability as a point beyond the control limits.  The probability of getting a point beyond the upper control limit is 0.00135.  The probability of getting one point in zone A or beyond is 0.0228. The probability of getting two points in a row in zone A or beyond is then (0.0228)(0.0228) = 0.00052. Note that this probability is smaller than the probability of getting one point beyond one of the control limits. Thus, if two points in a row fall in zone A or beyond, it is a stronger indication of an out of control situation than a point beyond the control limits.
      <br />Since this probability is so small, the requirement can be loosen somewhat by saying two out of three consecutive points in zone A or beyond. The probability of getting a point somewhere else on the chart besides zone A or beyond is 1 – 0.0228 = 0.9772. The probability of getting two out of three consecutive points in zone A or beyond is then (0.0228)(0.0228)(0.9972)(3) = 0.00156 (or one out of 640). You multiply by 3 because the point not in zone A could be the first, second or third point. The probability of obtaining this pattern for a process that is in control is then 0.00156, a small number.
      A similar approach can be used for zone B.

  • SnehaMarch 4, 2022 Reply

    If I plot control chart which has only upper limit, is my process in control? How will I summarize on the trend reporting?

  • RaveeshJune 24, 2022 Reply

    Many Thanks for the content!!!

  • LisaJuly 19, 2022 Reply

    Really useful.  Having difficulty as every chart I tend to create (usually to be used for assurance rather than improvement) the process limits are always hugely wide.  Its normally small numbers used and there is no baseline being applied.

  • Annabel MonterDecember 23, 2022 Reply

    Hello, Sir. Your data center line will always depend on your data mean? What if moving data? Does the mean or center line will also change? Thanks.

    • billDecember 23, 2022 Reply

      Your average only "changes" if the control chart shows that has been a significant change in the process.  Then you recalculate the average and limits and interpret that process again.

  • Randall ClagueOctober 30, 2023 Reply

    Taking a course on SPC, and they didn’t explain why stratification is undesirable. Having read this page, now I understand why. Thanks!

Leave a Reply

Your email address will not be published. Required fields are marked *