Economic Control Chart Models with Cycle Duration Constraints
18S
t
+ l(l-p)e-XhlN(° J elx
hN(t)
Nowleta2 = (l-p)e ^ and let
g(x;t) = J eXx
and we have
i_,-e(t-x)y PMf i=0 i!
r-1
2
i=0
dx
N(t)—1
pTnntW = al ^ 2 4 [g(*»0+l);t)-g(hj;t)] + a^(t) [g(t;t)
j=0
- g(hN(t);t)]
= ai
r N(t>-i |
N(t)-1 | |
.2 4 |
g(h(j+l);t) - |
2 Ą g(hj;t) + |
l J=o |
j=0 | |
g(hN(t);t)] |
\ | |
rN(,) •, |
N(t)—1 | |
[ 5 * |
g(hj;t) - 2 j=0 |
4 g(hj;t) + a^(t) |
N(t) 1 2
g(hN(t);t)]