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Statistical Process Monitoring with Integrated Moving Ayerage Noise 267

Markovian, X, ₄_, is conditionally independent of X_ł+U, given X_k. Thus, /(*)/** (^Xk) = flk(^Xlk )fkn (^Xkn )    (³>

The corresponding equation, derived below, for h(-), the density of Y, implies that the elements of Y are Markovian.

Let

⁰<W =

where [•] denotes the greatest integer fiinction. As Ł ranges from 1 to 2"^+,*0/(^x)» generates all possible n-vectors with +x_t or -x_t in position /'. For

i<j let

v

For almost all y_y we have

(4)

^A*(y*)= Ź/«(^e<(y*))

t=i

Using (3) and (4) and the symmetry of/gives the following string of eąualities which finishes the proof.

= ²Z/(^e,(y))/«(^)

/=1

<=i

= ^(y.*K(yJ