7QC Tools: Why do we Require to Plot X-bar and R-charts Simultaneously

    Amrendra Roy

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    The main purpose of the control charts is to monitor the health of the process and this is done by monitoring both, accuracy and the precision of the process. The control charts is a tool that helps us in doing so by plotting following two control charts simultaneously for accuracy and precision.
    Control chart for mean (for accuracy of the process)
    Control chart of variability (for Precision of the process)
    E.g. X-bar  and R chart (also called averages and range chart) and X-bar  and s chart

    The Accuracy and the precision

    We all must be aware of the following diagram that explains the concept of precision and accuracy in that analytical development.


    If you are hitting the target all the time at the bull’s eye is called as  accuracy and if all your shots are concentrated at the same point then it is called as Precision.


    Figure-1: Accuracy and precision


    You are off the target (inaccurate) all the time but your shots are concentrated at the same point i.e. there is not much variation (Precision)


    It is an interesting case. Your shots are scattered around the bull’s eye but, on an average your shots are on the target (Accuracy), this is because of the average effect. But your shots are wide spread around the center (Imprecision).


    In this case all your shots are off target and precision is also lost.

    Before we could correlate the above concept with the manufacturing process, we must have a look at the following diagram that explains the characteristics of a given manufacturing process.

    Figure-2: Precision and Accuracy of a manufacturing process

    Figure-2: Precision and Accuracy of a manufacturing process

    The distance between the average of the process control limits and the target value (average of the specification limits) represents the accuracy of the process or how much the process mean is deviating from the target value.

    Whereas the spread of the process i.e. the difference between LCL and UCL of the process represents the precision of the process or how much variation is there in the process.

    Having understood the above two diagrams, it would be interesting to visualize the control chart patterns in all of the four cases discussed above. But, before that let’s have a look at the effect of time on a given process i.e. what happens to the process with respect to the time?

    As the process continue to run, there will be wear and tear of machines, change of operators etc. and because of that there will be shift and drift in the process as represented by four scenarios described in the following diagram.


    Figure-3: Process behavior in a long run

    A shift in the process mean from the target value is the loss of accuracy and change in the process control limits is the loss of precision. A process shift of ±1.5σ is acceptable in the long run.

    If we combine figure-1 and figure-3, we get the figure-4, which enable us to comprehend the control charts in a much better way. This gives picture of the manufacturing process in the form of control charts in four scenarios discussed above.


    Figure-4: Control chart pattern in case of precision and accuracy issue

    Above discussion is useful in understanding the reasons behind the importance of the control charts.

    1. Most processes don’t run under statistical control for long time. There are drifts and shift in the process with respect to the time, hence process needs adjustment at regular interval.
    2. Process deviation is caused by assignable and common factors/causes. Hence a monitoring tool is required to identify the assignable causes. This tool is called as control charts
    3. These control charts helps in determining whether the abnormality in the process is due to assignable causes or due to common causes
    4. It enables timely detection of abnormality prompt us to take timely corrective action
    5. It provides an online test of hypothesis that the process is under control
      1. Helps in taking decision whether to interfere with process or not.
        1. H0: Process is under control (common causes)
        2. Ha: Process is out of control (assignable causes)


    6.  Helps in continuous improvement:


    Figure-5: Control Charts provide an opportunity for continuous improvement



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    3 thoughts on “7QC Tools: Why do we Require to Plot X-bar and R-charts Simultaneously”

    1. Very nice article with examples and diagram; i have little daoubt. please it will be great if u can elaborate. My doubt is about Type I error-adjusting an in control process. if someone is doing improvement in controlled process then how it will be type I error?
      looking for your reply. please revert me on mail mentioned below.

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