# Charts For Variable Such As (X,r Charts)

**Introduction:**

Control charts may be used partly to control variation and partly in the identification and control of the causes which give rise to these variations.

**Capability:**

- The capability of a production process which is in statistical control is equal to the acceptable spread of variation in the product specification divided by the variation due to system causes.
- Since the acceptable spread of variation in a production process can be expressed as the upper specification limit minus the lower specification limit, the capability can be calculated as:

Where:

USL=Upper Specification Limit, LSL=Lower Specification Limit, UCL=Upper Control Limit, LCL=Lower Control Limit, n=Sample size

δ=the standard deviation of the individual measurements.

**VARIABLES CONTROL CHART:**

- The grouping of observations is done in order to calculate and analyze the variation between the mean response times and the variation within the groups measured by the range.
- The suggestion system may be out of statistical control either because of non-random patterns in the means or non-random patterns in the range.

**Steps in constructing M-R Control charts:**

**Step 1:** Plot the calculated means *(M) *and ranges *(R) *in two different charts (diagrams) where the abscissa is equal to subgroup number and the ordinate measure are the means and ranges respectively.

**Step 2: **Calculate the average range and the process average (=the average of the subgroup means):

**Step 3: **Calculate the control limits UCL (Upper Control Limit) and LCL (Lower Control Limit):

Control limits for the means (=*M*):

Control Limits for the ranges (=*R*):

The following control limits can now be calculated: Control limits for the means (=*M*):

Control limits for the ranges (=*R*):