Need Help Getting My Head Around Control Charts

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    Daniel Rempel

    Hi all,

    First post in joining this community. I’ve been into “Lean” for over 5 years now but am just now starting to appreciate the “Six Sigma” side of things. I’m trying to construct a useful control chart but am getting a little stumped trying to ensure I’m using the right approach.

    The first one I’m working on is tracking the number of new criminal cases entering the justice system by location (I work for a Justice ministry) each month. What’s throwing me off is that the book I’m working from is talking about measuring attributes of individual pieces, and sampling a certain number of pieces. Do I need to look at this as though I am measuring a population of “months” with “# new cases” being the attribute for each month?

    I have a complete data set (record of every new criminal case) so there’s no benefit in sampling, is there? Also, is a control chart even appropriate for charting the month-to-month variation in new cases?

    For the R chart, 2 and 3 standard deviations below average would both be less than zero, is there a special method for calculating control limits for the R chart?



    First the easy answer, if you have all the data then no need to sample. Typically sampling is used when you don’t have a complete set or in the data/measurement gathering phase.

    I am a believer in keeping it simple. If you are wanting to look at # of new cases by month then an ‘I chart’ (Individuals) would be the simplest way to go. By default your control limits will be 3 std deviations and you should be able to see a nice picture over time.

    Before you jump to this the first question to ask is, how am I going to use the information? That will tell you the tool/template best suited to get you that answer.

    My guess is your use is for a staffing or resource planning, so the control chart is a good tool for that.

    Best of luck


    Daniel Rempel

    Thanks John. I was just reviewing this page and getting confused by the references to d2 and D4 etc. – are those just shortcuts to calculating the standard deviation?

    The purpose of this information is to analyze the effectiveness of programs aimed at reducing the number of new cases each month.

    Other charts I will want to prepare, if I can get any thoughts on these:
    – Average number of cases concluded per month per location (as a counterpart to this first one to see if we are keeping ahead of things, and also an increase in this count should reflect increased capacity to deal with matters)
    – Average age of cases at conclusion – to measure how quickly cases are being resolved
    – Average number of court appearances required to get to conclusion – similar to above but here the focus is on resource utilization: can we get things through the system without having them appear in court for pointless appearances so many times?

    For each I am thinking of plotting an individual monthly (or weekly) average for each court location for different levels of severity of cases, since e.g. murder cases take much longer than petty crime cases so it makes sense to analyze them separately.

    Are there any special tricks to constructing or interpreting MR charts – calculate standard deviation the same way and use the same control tests?

    Also – I currently have 72 months historical data. What is the recommended practice for setting my Avg., UCL and LCL? Just use the whole period, the first 20 points, or some period that seems to be most “in control”, e.g. if the data seems stable for 40 months and then starts increasing, do I set my limits based on those first 40 months? Or do I want to set my limits based on what appears to be the current “control” state?

    I want to do two things – get a picture of historical performance to analyze impact of past initiatives, and then also monitor the impact of new initiatives being launched now.

    Thank you very much for your kind assistance!


    Chris Seider

    the constants you reference are for estimating standard deviations of the means for constructing the control limits around the xbar or xdouble bar



    Don’t get caught up in control charts as your only tool in the tool belt. It is critical to really think through and understand what you want to know, and more importantly how you can use each learning from the different tools to get to your success measures. Key questions to think through in dissecting your data; case types, different judges, different court rooms, different litigators, Case complexity, jury vs. judge etc.

    A histogram and Pareto charts can lead you into additional learning’s about your performance.

    For instance, I might suggest running a histogram for the ‘actual’ age of case at conclusion. The data isn’t really time sensitive and you should see some outliers that you can drill into further once identified. This assumes your goal to reduce the time it takes to complete. You could then dissect the reasons for the longer length cases in a Pareto chart and have some potential root causes to tackle. Taking it even a step further you could stratify the data by case type, I.E. murder vs. petty cases.

    The same logic applies for number of court appearances. This is also not really time sensitive data so a control chart is probably not your best tool.

    In answer to how far back to go with data…If you have it use it. The caveat here is that if there was any significant process change over time. If your process changed I would work backwards from most recent to that time frame. Any data older than that is most likely invalid anyway. If you aren’t aware of any process changes your control chart may actually show you that there was a shift. Look at the eight? rules for control charts to understand how to identify shifts over time.

    the biggest thing as you start out is to be a detective, think about what you want to solve, then use the data and correct tools to get you to root cause.



    I’m having trouble understanding why you want to use control charts. We use them in the control phase of DMAIC. They’re useful for monitoring stability of the process and for identifying variances that need corrective action. They won’t help much for your stated purpose.


    James Masefield

    Hi Dan @djnrempel,

    I notice your interested in tracking the number of new criminal cases by location. Do you have any data to share? That’s always useful.

    What you’re trying to get out of it I’m not sure but I’ll leave that to you and your team of experts in the field. I’ll talk about the principles and to start, I’d suggest an I-mR chart for each individual location.

    A problem you’d have I think is your sample frequency and that is months. This means you’ll have to wait an entire month just to enter 1 data point which could prove not useful. Control charts at times can already be slow to detect changes in process. Your monthly data entries will not help this. Could you enter data weekly? This will give you more data points to work with.

    I’d suggest gathering around 25 weeks of data and plotting it onto an I-mR. Once this is done, what can you see? Is the process stable and predictable? If yes, great, lock the limits and continue to plot points and look for assignable causes. If it’s not stable, you need to try and understand why.

    I’m a strong believer that control charts are applicable to everything we do in everyday life and even applicable to nature; time to make a drink, time to get to work, temperature of our gravy on Sunday dinners at serving point, how often the Sun gives off a solar flare as well as the engineering applications that I actually use them for in manufacturing. The list is endless. I’m not familiar with your field, but it sounds that if you do get an assignable cause by means of an increase or decrease in crimes, it may be difficult to correctly assign a cause to these signals?

    The control limits on the mR section of the chart is as follows.

    > LCL is always 0
    > UCL is +3 standard deviations Rbar (average range)

    Minitab will do this for you though. I’d recommend getting a copy if you feel you’d frequently use it.

    I hope this helps.




    @djnrempel – as @straydog mentions, a control chart is used to evaluate stability. While you might get some use out of a control chart to evaluate changes caused by various programs, it would not be my first choice. I would instead be looking at an hypothesis test such as a two-sample t test, or perhaps more appropriately if you are applying a program change to the entire group, the paired t test.

    Since you are new to the statistics, I would suggest finding a mentor – you might check out a community college that teaches six sigma – to pose these questions where you can have a longer and more meaningful discussion.

    Good luck.


    Roger Hill

    In place of a mentor is a great book ( and quick read ) on this kind of transactional-charting: Understanding Variation by Donal Wheeler. I wish I had read this books years ago.


    Mike Carnell

    @djnrempel I agree with @MBBinWI and @straydog. I do not see the logic in using a control chart. If it goes out of control or becomes unstable what are you going to do to bring it back into control or stabilize it? The way I understand this there really isn’t any adjustment to the process.

    Just my opinion.


    Daniel Rempel

    @RJHILL1, I have that book by Wheeler on my desk right now, it’s what got me into control charts when I read about it on Mark Graban’s blog a month or two ago. However, it is only about control charts and he advises using Rbar*2.66 as the control limit, not 3 Sigma. It seems like a good intro to quick and dirty control charting but the more I read the less sure I am about what tools to even start learning about.

    Re: the comments about entering data monthly – I actually only get data every three months currently. For charting purposes I could break it down by week or even by day but that doesn’t make it more timely, just more detailed. I’m working on getting access to data more frequently though.

    , @MBBinWI and @Mike-Carnell, basically I’m starting with control charts because I just learned about them and their main touted benefit was for detecting changes in a process. We are in a state right now where our department’s management essentially knows nothing about how the overall process is performing. They ask me to provide charts and until now I’ve been providing charts with no way of knowing whether they actually show a change or not.

    Finally, I’m not sure whether our process is stable or not, but I know a good percentage of cases exceed the maximum time that our Supreme Court has just imposed (18 months) – our process is not capable in other words. As a result of that Supreme Court decision there is a lot of activity now making changes to the system and I want to be able to report whether there is meaningful impact or not.

    I would love a mentor. Not sure where to find one, this forum has been very helpful though.


    Mike Carnell

    @djnrempel Using them to help in your learning I can understand. You need to make it clear to your department management that regardless of the name of the chart you don’t have the ability to “control” anything which is the point of a control chart.

    Process stability is a figment of someone’s imagination. Because you are “stable” today means what about tomorrow? Nothing. That is people wanting to use terminology that doesn’t fit your process. Read Juran’s book “Managerial Breakthrough” so you understand what is meant by control.

    If you want to report how capable you are then you can do that with a capability study. As long as you know the amount of time cases have been in the system and you have an upper spec limit of 18 months then it is just a plug and chug calculation.

    I will be glad to help you if you need assistance. My email is [email protected]. People who are willing to do things like you are doing just to help you learn I always have time for.



    I may have a different opinion than some of the sentiments expressed. Control Charts (also known as Statistical Process Control (SPC) charts) aren’t limited to the Control phase of Six Sigma. They can be used as a diagnostic tool in Define as well as in Analyze and Improve control if you understand their purpose and limitations. One needs a hypothesis to perform a hypothesis test and control charts can help one constructively brainstorm those hypotheses.

    For example, on several quality improvement projects, a Control Chart in Define phase revealed patterns where the process seemed to have dramatically shifted. This started our “why” exploration and allowed us to identify in some cases quick wins, and in other cases critical Xs in the process.

    I’d also recommend graphing by week, not month. One needs more than 9 data points to really feel they have reliable LCL and UCL limits. Monthly only gives you 12 data points a year and it is therefore hard to detect patterns and trends. Also, the number of days (or working days) in a year varies. Going by weeks (assuming there is enough traffic by weeks) gives you 52 data points a year and makes it easier and faster to identify patterns and trends.

    Some would argue that processes need to be stable and in control to maximize the use of a control chart, and although that would be an ideal application, I wouldn’t feel discouraged from using one early on, SPC is a powerful tool for exploring your process. If you’d like to discuss more you can reach me at [email protected].


    Robert Butler

    As others have noted – I don’t think there is any point in a control chart. However, I do think you and your crew would benefit from a series of run charts. I would build an overall run chart with data from the lowest level and I would build additional run charts for the same period of time highlighting the trends of what are understood to be major crimes.

    Another option and, in light of your second post to this thread, one that might provide even more information than a run chart would be a series of time sequenced box plots focused on things like the number of cases concluded per month per location, age of cases at conclusion, and number of court appearances required to get to conclusion. If those plots were stratified by crime type you might find this visual apprehension of your system is all that you really need in order to understand what is going on.


    Chris Seider

    Control charts have their place and I’ve seen many ways to use them.

    However, control charts aren’t meant to be wallpaper. If something is out of control, the reason for plotting is to act on out of control points.

    If it’s used for investigating and solving a problem, then it’s used for something else but please don’t just create control charts without action plans on who is to do what to get things back in control.


    Michael Clayton

    Great discussion and important topic. But I agree with using MANY graphical tools for EXPLORATORY DATA ANALYSIS then show the graphs to domain knowlege folks for “ah-hah” reactions. Time series graphs are fine but its the CONTEXT data that is critical.
    Example: which TYPE of crime has most variance? Most far outliers? Does database have other FACTORS that can serve as HISTOGRAM CATEGORY or Component of Variance analysis. Get stat software or use online tools that allow many nominal factors as quick REPLOT by new selections for Histograms or Time Series Chart (like SPC which is subset for factory machine control and other issue Wheeler knows well) and also Multi-Vari or similar graph common in JMP or JMP or STATGRAPHICS or college online JAVA graphical tools.

    I would start with Histogram and list of all factors in database that could help you look at impact of one or many factors at same time.

    That means your dataset should have all data types in columns for factors and variables with each row simply a date or case number. Just my approach. Software often dictates a spreadsheet structure that works well for each major type of analysis.

    Excel is generic but can get messy if you mix NOMINAL and NUMERIC data in same column.

    Many court studies online or on city or state or gov web sites and many justice college home pages. Ask a student or professor.

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