Control chart, X-bar chart and R chart – ingredients for the success of any process

Control charts- introduction


Certainly, not once watching the process and collecting data, you are wondering whether it is stable, whether the parameters are at the right level or when you need to respond in case of deviations.

Fortunately, there are tools that support us in making decisions and provide knowledge about the process. We’re talking about control charts. Although there are at least several types of control charts, in this entry I will focus only on two – the card of average values and range.

Of course, the entry will be referred to not only in the context of production, but also to any parameterized process in the organization. It is equally possible to draw conclusions based on control charts in the case of HR processes, in accounting, purchases, as well as in maintenance or logistics.



Control chart – structure


As a preliminary remark, I mention that the control charts appeared in use in the 1920s, thanks to Shewhart. Due to the limited resources of qualitative measurement techniques in those times, they quickly became the basic statistical tool for process control.

It can be said that this trend continues to this day, despite significant technological progress.


How is the control chart built?


The basic elements of the control chart are marked in Scheme 1.

And these are:

Upper Control Limit (GGK) or UCL (Upper Control Limit)
Central line (LC) or from the English line (CL) (Center Line)
–  Lower Control Limit (DGK) or LCL (Lower Control Limit)
–  Measuring points (connected by a line)
Sample / measurement number



Diagram 1. Control chart – structure (own study)


On the horizontal axis, further samples are marked, which are taken from the tested process in a strictly defined way. On the vertical axis, the measurement values ​​are marked. Depending on the type of card, it may be different data. We will analyze the average values ​​and the range.

1. and 3.- GGK and DGK – upper and lower control limits; they are located on both sides of the central line and are usually separated from it by 3 sigma. It should be understood that within the limits of GGK and DGK should be 99.73% of all measurements.

2. – Central line – determines the average value of all measurements collected by us

Sometimes you can also find a graph with additional lines, namely Upper Warning Line (GLO) and Lower Warning Line (DLO) – Diagram 2. These are auxiliary lines characteristic for the requirements of a given process. They are usually applied in order to keep eg the internal requirements of a given organization at a certain level. Exceeding the GLO or DLO line in this case is associated with taking action on the part of process supervision, although the theoretical process is stable.


Diagram 2. Control card – GLO and DLO (own study)


Control cards for average value (X-bar) and range (R)


To see the correct image of the condition of the analyzed process, we need data that will allow us to understand where and which variation prevails in our process.

Simply put, it is not enough to discover that the results differ depending on, for example, a production change. We must also know whether there is variability between individual samples, measured parts.

That is why the basic analysis should be based on information from at least two control charts, i.e. the mean value and the range.


Medium value card (X-bar)


It helps to understand the variability between subgroups (ie, eg variation of measurements change to change).

The main question we should ask before analyzing this card is: Is there evidence of variation between subgroups?

NO – if no average value (X-bar) goes beyond the control limits. Then we can expect that the volatility dominates inside the subgroup (ie, for example, on a specific change during which data is collected).

YES – if at least the average value (X-bar) goes beyond the control limits (ie, for example, variability prevails in the measurements made on various changes).


Determining control lines on the average value card (X-bar)


We need to use the formulas:



(The values of the coefficients A2, D3 and D4 that are used in the formulas are constant and depend on the sample size, i.e. n. The table with the values of these coefficients is available in the network)





Is there evidence of variability between subgroups?

YES. We observe variability in the measurement results change to change.


Range card (R)


It helps to understand the variability within a subgroup (ie, for example, the variability between measured parts on a particular change, i.e. the variation of part to part).

The main question that we should ask before analyzing this card is: Is the variability within the subgroup SPC?

SPC = Stable, Predictable, Consistent (Stable, Consistent, Predictable)

NO – if at least one range goes beyond the control limits. Then the observed volatility is the so-called special variation.

YES – if none of the stretch marks goes beyond the control limits. The observed volatility is the so-called natural variability.



Determining control lines on the stretch marks card (R)


We need to use the formulas:






Is the variability within the subgroup SPC?

YES. The variability within the subgroup is natural.

Thus, having data from the average and range charts, we can conclude that it is necessary to work on the variability of measurements between individual changes. This is where the problem lies.


Natural variability and special variability



1. Natural, random variability – that is what we expect, we expect it, guarantees the normal distribution of the course of the process (Gauss curve) and may be caused by many different sources of variation.

2. Special variability is unexpected and usually caused by a specific cause that we can identify.

Finding out what triggered special volatility can be very easy if we start looking relatively quickly from the moment the non-conformities occur. It can also be very difficult and complicated if we minimize the problem and start analyzing it a long time after the occurrence.



What should you remember before using the X-bar and R control cards?



To use the X-bar and R cards, remember that the following conditions must be met:

– we can only control one parameter with one card

– data must have a normal distribution (Gauss curve)

– for the analysis to be reliable, we should measure min. 20 samples on the basis of which the central line and control limits will be crossed out

– each sample should be measured the same number of times



Why use control cards? Benefits


Each company strives to respond to negative changes in the process as quickly as possible. This is obviously logical from the financial point of view, because the sooner the cause of the problem is eliminated (i.e. uncontrolled change of parameters), the lower the costs for the organization.

The main advantage of the control cards is the possibility of using them to control the process during its course. Based on the results of the samples measurements, we will check whether the process is proceeding correctly.

Detection of some deviations is one thing, but the ability to interpret them is the second, and probably the most important. Thanks to the control cards, you can quickly determine the variability we are dealing with – natural or special, and it depends on what actions will be taken.



Leave a Reply

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