7QC Tools — The Control Charts

    Amrendra Roy


    The Control Charts

    This is the most important topic to be covered in the 7QC tools. But in order to understand it, just remember following point for the moment as right now we can’t go into the details

    1. Two things that we must understand beyond doubt are
      1. There is a customer’s specifications, LSL & USL (upper and lower specification limits)
      2. Similarly there is a process capability, LCL & UCL (upper and lower control limits)
      3. The Process capability and customer’s specifications are two independent things however, it is desired that UCL-LCL < USL-LSL. The only way we can achieve this relationship is by decreasing the variation in the process as we can’t do anything about the customer’s specifications (they are sacrosanct).
      4. Picture13
    2. If a process is stable, will follow the bell shaped curve called as normal curve. It means that, if we plot all historical data obtained from a stable process – it will give a symmetrical curve as shown below. The σ represents the standard deviation (a measurement of variation)
      • picture88
    3. The main characteristic of the above curve is shown below. Example, the area under ±2σ would contain 95% of the total data
      • picture19
    4. Any process is affected by two types of input variables or factors. Input variables which can be controlled are called as assignable or special causes (e.g., person, material, unit operation, and machine), and factors which are uncontrollable are called noise factors or common causes (e.g., fluctuation in environmental factors such as temperature and humidity during the year).
    5. From the point number 2, we can conclude that, as long as the data is within ±3σ, the process is considered stable and whatever variation is there it is because of the common causes of variation. Any data point beyond ±3σ would represent an outlier indicating that the given process has deviated or there is an assignable or a special cause of variation which, needs immediate attention.
      • picture89
    6. Measurement of mean (μ) and σ used for calculating control limits, depends on the type and the distribution of the data used for preparing control chart.

    Having gone through the above points, let’s go back to the point number 2. In this graph, the entire data is plotted after all the data has been collected. But, these data were collected over a time! Now if we add a time-axis in this graph and try to plot all data with respect to time, then it would give a run-chart as shown below.


    The run-chart thus obtained is known as the control chart. It represents the data with respect to the time and ±3σ represents the upper and lower control limits of the process. We can also plot the customer’s specification limits (USL & LSL) if desired onto this graph. Now we can apply point number 3 and 4 in order to interpret the control chart or we can use Western Electric Rules if we want to interpret it in more detail.

    The Control Charts and the Continuous Improvement

    A given process can only be improved, if there are some tools available for timely detection of an abnormality due to any assignable causes. This timely and online signal of an abnormality (or an outlier) in the process could be achieved by plotting the process data points on an appropriate statistical control chart. But, these control charts can only tell that there is a problem in the process but cannot tell anything about its cause. Investigation and identification of the assignable causes associated with the abnormal signal allows timely corrective and preventive actions which, ultimately reduces the variability in the process and gradually takes the process to the next level of the improvement. This is an iterative process resulting in continuous improvement till abnormalities are no longer observed in the process and whatever variation is there, is because of the common causes only.

    It is not necessarily true that all the deviations on control charts are bad (e.g. the trend of an impurity drifting towards LCL, reduced waiting time of patients, which is good for the process). Regardless of the fact that the deviation is goodor badfor the process, the outlier points must be investigated. Reasons for good deviation then must be incorporated into the process, and reasons for bad deviation needs to be eliminated from the process. This is an iterative process till the process comes under statistical control. Gradually, it would be observed that the natural control limits become much tighter than the customer’s specification, which is the ultimate aim of any process improvement program like 6sigma.

    The significance of these control charts is evident by the fact that it was discovered in the 1920s by Walter A. Shewhart, since then it has been used extensively across the manufacturing industry and became an intrinsic part of the 6σ process.


    To conclude, the statistical control charts not only help in estimating these process control limits but also raises an alert when the process goes out of control. These alerts trigger the investigation through root cause analysis leading to the process improvements which in turn leads to the decreased variability in the process leading to a statistical controlled process.

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    4 thoughts on “7QC Tools — The Control Charts”

    1. The concept of turning the Gaussian distribution is very nice. This is a thing which was not explicitly given.

    2. After a long time It was interesting piece to read and refresh. Share more such type of articles.

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