00349 ð7aa0405daf72b85273dc3cf6af42d1

00349 ð7aa0405daf72b85273dc3cf6af42d1



353


A Monitoring Plan for Detecting Product Degradation

x-l A-nQL


P{Xśx-l> = £

M> J


(nQL)j


[4]


Because of the relationship of the cumulative Poisson with the chi-square distribution, [4] can be written (see Johnson and Kotz (1970))

[5]


P{XSx-l} = P{^x>2nQL} = r

where Zim is a chi-square variable with 2x degrees of freedom. Then, using the approximation (see Wilson and Hilferty (1931))

(V


Pizl < X} * O


VL


\y


9v


19y


[6]


where F is the standard normal cumulative distribution function, it is seen that P{Xśx-l}=l-P{^ <2ną>«l-(D


I

1

+

Is)

_1

(J_v 2x / 9-2x

2 J


= Y 17]


From [7] it follows that

nQlV


V x

fnQt]

f

l x J

V

1- —+ Z,

9x r(9x


-1 + —= (Z, l G-9x v '~rJ\9x

i \ or

n «


Ql


,    1 ^ { 1 N

1---ł"Z, „I —


9x


-r


9x


[8]


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