Many quality characteristics such as dimensions like length, width, temperature, tensile strength etc… of a product are measurable and are expressed in a specific unit of measurements. The variables are of continuous type and are regarded to follow normal probability law. For quality control of such data, there are two types of control charts used. They are as follows : (i) Charts for Mean ( X ) (ii) Charts for Range (R) .
. Construction of X and R charts Any production process is not perfect enough to produce all the products exactly the same. Some amount of variation is inherent in any production process. This variation is a total of number of characteristics of the production process such as raw materials, machine setting, operators, handling new operations and new machines, etc.
The X chart is used to show the quality averages of the samples taken from the given process. The R chart is used to show the XII Std - Business Maths & Stat EM Chapter - - Applied Statistics variability or dispersion of the samples taken from the given process. The control limits of the X and R charts shows the presence or absence of assignable causes in the production process. Both X and R charts are usually required for decision making to accept or reject the process.
The procedure for constructing X and R charts are outlined below. Procedure for X (i) Let X , X , X , etc. be the samples selected, each containing ‘ n ’ observations (usually n = , or ) (ii) Calculate mean for each samples .... by using i i i , , , ,....