# Moving Range (MR) Methodologies for Low Volume: MR Control Charts

The moving range methodology allows For a reasonable estimate ofσand process capability for both variable and attribute processes. It uses individual measurements or defect rates over a representative period of time. It is very useful when there is only one number to describe a particular condition or situation. It can be used to estimate production variables such as temperature, pressure，humidity，voltage, or conductivity. It can also be used for production support efforts such as costs, efficiencies, shipments, and purchasing activities. The moving range charts can also be used for attributes. Instead, of counting defects, the time between defects can be counted and entered as the variable in the chart.

The moving range stands for the difference between successive pairs of numbers in a series of numbers. The absolute value of the difference is used, creating a new set of range numbers, each with two successive elements. The number of differences or “ranges” is one less than the individual numbers in the series. The chart is built up from the following:

• The centerline of the chart is the average of all the individual measurements.

• The average of the ranges of the successive numbers is called the MR. The control limits are set by multiplying MR by the number 2.66. This is the result of using the factor d2 for n = 2 (1.128) estimation of the a in the following equation:

MR control limits =X ± 3 * MR/1.128 =X 土 MR • 2.66 (5.12)

Note that the conversion from the standard deviation of sample average to population 〇• that is performed on X，charts is not necessary here, since the moving range charts use the actual distribution of data, not those from sample distributions.

Example 5.11

Days between defects were counted as a measure of the quality of a manufacturing process. They occurred on the following production calendar days: 23, 45, 98, 123, 154, 167, 189, 232, 287, 311, and 340. Calculate the data for the moving range chart for days between defects.

Another method to plot this defect data would be defects/month, obtained by dividing the data by 30.

Example 5.12

Fuses are made in a production line，with specifications of 5 ± 2 ohms. A sample of six fuses measurement was taken at 3, 6, 6, 4, 5, and 5 ohms. If it is desired to have anX, R control chart, what is the quality data for the fuse line?

Moving range method data = 302 1 0

Average X = 4.83; MR = 1.2

σ = MR/d2 = 1.2/1.128 = 1.0638

UCLX = 4.83 + 2.66 • MR = 8.02

LCLX = 4.83 - 2.66 • MR = 1.64

UCLR = D4(n=2) • MR = 3.27 ■ 1.2 = 3.92

LCLR = 0

Cp = 2/3 • 1.0638 = 0.63; Cpk = (4.83 - 3)/3 • 1.0638 = 0.57

Z1 = (3 - 4.83)/1.0638 = -1.72; f(z1) = 0.0427

Z2 = (7 - 4.83)/1.0638 = 2.04; f(-z2) = 0.0207

Defect rate (RR) = 0.0427 + 0.0207 = 0.0634 or 6.34% or 63,400 PPM