100-Metodos-de-Qualidade-Total

DATA COLLECTION, ANALYSIS AND DISPLAY 231
Method 100
X-R chart
Purpose
To identify when the mean value or range in a sample of constant size is
changing over time.
When to use
When monitoring a process to detect changes, or when a change has been
made to process inputs to find out whether the mean or range changes. X-R
charts are used to monitor variables data, when the values can vary over a
continuous range, and when the sample size at each sampling point is
greater than l.
Examples of data drawn on an X-R chart include time to process insurance
claims, temperature of a chemical reaction and width of metal slabs.
How to use
There are seven simple steps involved:
1 Collect the data. Draw up a table showing the readings for each of the
samples at each sampling point. The number of samples at each sampling
point is called n. The total number of sampling points is called m.
2 For each sample, calculate the mean X by adding together the X values
and dividing by the sample size n. For each sample, calculate the range
by subtracting the smallest value in each sample from the largest. This
value i ' s called R.
3 Working down the table, add together all the X values and divide the
result by the number_of sampling points m. This value is the grand
mean and is written X (called X bar bar). Again, working down the
table, add together all the R values and divide by m. This value is
written R and called R bar.
4 Calculate the control limits for the X chart using the formula:
Upper control limit (UCL) = X + A2 X R
Lower control limit (LCL) = X - A2 X R
S
A2 is a constant, that when multiplied by R, gives 3 s.d. for the X chart.
Calculate the control limits for the R chart using the formula:
Upper control limit (UCL) = D4 X R