Type III Error

Pi in IMR Chart

The multiplier used to compute the Delta for Individual X Moving Range Chrts is 2.66. The Control Limits for the Individual X Values are given as X-Bar +/- 2.66 x MR-Bar. MR-bar is the Mean Pairwise Moving Range among the Individual X Values. Where does the multiplier 2.66 come from?

The value 2.66 is 3 / d2. The "3" is the traditional 3-Multiplier as in "3-sigma limits." The value of d2 for n=2 (pairwise case) is 2 / SquareRoot(Pi). Actually the value is about d2 = 1.128.

So, 3 / d2 = (3/2) x Squareroot(Pi) = 2.66

Pi is 3.14159...

The term d2 is used for the ratio of the Mean Range (of n Random Normal Variates) to the Standard Deviation of the Normal Distribution. In this case of Pairwise ranges, n=2.

posted by X-Bar @ 10:01 PM