Miscellaneous; Learning Curve For Manufacturing Cost; Queuing And Waiting Theory - HP 12c Platinum Reference Manual

Miscellaneous

Learning Curve for Manufacturing Cost

C = Cost of the nth unit, C
n
n = number of units, r = learning factor.
k = ln r / ln 2,
=
C the
ij
C
1
=
C
ij
−
j
This formula is only approximate and may give appreciable error at small i.

Queuing and Waiting Theory

n = number of servers.
λ
= arrival rate of customers (Poisson input).
µ
=service rate for each server (exponential service).
ρ
= Intensity factor =
P = Probability that all servers are idle.
0
P = Probability that all servers are busy.
b
L = Average number of customers in queue.
q
L = Average number of customers in the system (waiting and being served).
T = Average waiting time in queue.
q
T = Average total time through the system.
P(t) = Probability of waiting longer than time t.


−
n 1

∑
=
P
0

=
k 0


ρ
=
P
b


n ! 1

ρ
P
=
L
q
−
n
( )
=
P t P e
b
1
k
=
C C n
n 1
average cost of the i
 + + 
k 1 k 1
−
j i
 
+
i k 1
 
 
λ µ
/
−
1


k n
ρ ρ

+
ρ 
 
k!
−
 
n ! 1

n
 

n
P
0
ρ

−

n

b
ρ
= +
, L L ,
q
ρ
( )
µ λ
− −
n t
= Cost of the first unit.
th through j th unit.
ρ
( < n for valid results).
L
q
λ
T = T =
/ L ,
q
λ
Appendix B 165