100-Metodos-de-Qualidade-Total

228 100 METHODS FOR TOTAL QUALITY MANAGEMENT
Method 99
X moving range (X-MR) chart
Purpose
To identify when a value 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 value changes. X
moving range is used to monitor variables data, when the values can vary
over a continuous range, and when the sample size at each sampling point
is 1. This, for example is the case with monthly sales figures, when there is
only one figure, production figures or when the cost of taking the
measurement is very high.
How to use
There are six simple steps involved:
1 Collect the data. Draw up a table showing the readings for each of the
samples at each lot. The number of samples in each lot is 1. The total
number of lots is called rn.
2 For each lot calculate the moving range by subtracting the X value from
the previous X value. There is no moving range for the first X value.
3 Working down the table, add together all the X values and divide the
result by the number of lots rn. This value is the grand mean and is written
X (called X bar). Again, working down the table, add together all the
moving range values and divide by rn-l. This value is written MR.
4 Calculate the control limits for the X-MR chart using the formula:
Upper control limit (UCL) = X + 3 X MR/d2
Lower control limit (LCL) = X - 3 X MR/d2
d2 is a constant that when multiplied by 3MR gives 3 s.d. for the X-MR
chart.
S Plot the data from the table onto the X-MR control chart. The successive
lot numbers are shown on the horizontal axis; the X values are shown
on the vertical axis.
6 Interpret the results.
Benefits
It can be difficult to separate out random variation (often called common
cause or non-assignable variation) from real variation caused by changes to