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):