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475

An Algorithm and a Graphical Approach for Short Run Processes

in-control timc O = out-of-control timc

setup or end of run

1-1-1

setup    S    R

-1-h-

T

Figurę 1. Definition of Some Time Yariables Used in the Proposed Model.

hołd if the time between ąuality shifts is exponentially distributed with mean

\jX:

p{7?<r} = i+

E[min(R,T)\ =

1

X-fi 1

A.- fi.

(y.exp(-XT) - Xexp(-\if)} ^-(exp(-XT)-1)--(exp(-\iT) -1)

A.    fi

E[min(S, T)] = -(l - exp(-XT}) X

£[(7’-5)⁺-(7’-/?)⁺]

1

A, - fi

f

exp(-XT)

--exp(-\iT)

\

/

P{0<T} = \-exp(-\iT)

E[min(0,7¹)] = —(l - exp(-\x.T)} M’

where (X)⁺ = min(0,X),