Appendix B 165
Miscellaneous
Learning Curve for Manufacturing Cost
C
n
= Cost of the nth unit, C
1
= Cost of the first unit.
n = number of units, r = learning factor.
k = ln r / ln 2,
k
n
nCC
1
=
unit.th th through theofcost average the jiC
ij
=
+
−
−
=
++
1
11
1
k
ij
ij
C
C
kk
ij
This formula is only approximate and may give appreciable error at small i.
Queuing and Waiting Theory
n = number of servers.
= arrival rate of customers (Poisson input).
=service rate for each server (exponential service).
< n for valid results).
0
P = Probability that all servers are idle.
b
P = Probability that all servers are busy.
q
L = Average number of customers in queue.
L = Average number of customers in the system (waiting and being served).
q
T = Average waiting time in queue.
T = Average total time through the system.
P(t) = Probability of waiting longer than time t.
1
1
0
0
1 !
−
−
=
−
+=
∑
n
n
k!
P
n
n
k
k
ρ
ρρ
−
=
n
n
P
P
n
b
ρ
ρ
1 !
0
ρ
ρ
−
=
n
P
L
b
q
,
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