00349 ð7aa0405daf72b85273dc3cf6af42d1

353

A Monitoring Plan for Detecting Product Degradation

x-l _A-nQ_L

P{Xśx-l> = £

M> J

(nQ_L)^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>2nQ_L} = _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

nQ_lV

V x

f^nQt]	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]