# Control Charts

**Control Charts**

The concept of control charts is one of the most powerful techniques for on-line capability of a process and in making continuous improvements in the process. Recall the ref ill length problem mentioned above. We can use control chart technique to effectively solve this problem. But, firstly, let us see how a control chart is constructed. Typically, a control chart is a two-dimensional graph in which x-axis represents the sample numbers and y-axis represents a quality characteristic. It has a solid center line (CL) and two dotted lines called upper control limit (UCL) and lower control limit (LCL) (see Fig.).

Thus, the construction of control charts involves collecting samples periodically from the process, computing the quality characteristic for each sample and plotting it against the sample number. The consecutive points are joined by line segments.

As long as the plotted points are within the upper and lower control limits and do not exhibit any specific patterns, we have no evidence that the process is not under statistical control. When a point falls outside the control limits (below LCL or above UCL), it is a cause and indicates the presence of an assignable cause with a high probability.

However, control chart cannot tell us what went wrong with a process when something has gone wrong. It will only indicate that possibly something has gone wrong with the process. In fact, it is the responsibility of supervisor or QC manager to find out what has gone wrong.

In most situations, a quality characteristic follows a normal distribution or can be approximated by a normal distribution. Also, we know that the probability of a normally distributed random variable taking values below μ − 3σ or above μ 3σ, where μ is the mean and σ is the standard deviation, is very low (equal to .0027).

Therefore, if an observation falls outside 3σ limits, it is logical to suspect that possibly something might have gone wrong. For this reason, the control limits on a control chart are set up using 3σ limits. Consequently, when a point falls outside the control limits on a control chart, it is more likely that it is due to the presence of an assignable cause, rather than a mere chance cause.

Depending on the nature of quality characteristics, control charts are divided into two categories:

(i) control charts for variables; and

(ii) control charts for attributes.