Cheatography

# ISE 362 EXAM 1 Cheat Sheet (DRAFT) by musikdr

This is a draft cheat sheet. It is a work in progress and is not finished yet.

### Reliab­ility

 Rseries = Rn Rparallel = 1-(1-R)n 2 Parallel Components in Series = (1-(1-R)2)2 2 Series Components in Parallel = 1-(1-R2)2 Legitimate Values of R 0<=­R<=1 Consider f(R) = R(2-R) where does f(R) achieve it's max and what' the max value? g(R) = R(2-R0 = 2R-R2 taking it's derivative and setting equal to 0 we get dg(R)/dR = 2-2R=0 Its max is achieved when R=1 Plugging this in for R in g(R) yields 2-1=1>0 k out of N Redundancy - system that operates if at least k out of N components function properly. R=Sum(I=k to n) of RI(1-R)n-i (ex Sum(I=2 to 3(for ito 3)(.0.9)i(0.1)^3-i)

### Economic Analysis

 How much would you need to invest on September 27th, 2019 to have \$10,000 on September 27th, 2027 given an interest rate of 5%? PV = FV(P/F­,i,­n)=­10k­(P/­F,5,7) How much would you need to deposit on January 1, 2020 in a fund that yields 5% annually in order to draw out \$250.00 at the end of each year starting December 31, 2020 for 7 years, leaving nothing in the fund at the end? PV=250­(P/­A,5%,7) Dominate - when one of the outcome paths is clearly the better choice for every case

### Review Session Material

 P34 = P[In State 4|Current State] - Take Pmatrix to the 4th power and look at position 34. EMV(i) = SUM(j=1 to N) Pj*rij How much does P have to change before another altern­ative is best. Add a z to one state and subtract z from another state, then set the equations = to each other and solve for z. If z is (-) then it's not better. EV of Perfect inform­ation means you take the largest value at each state and multiply it by it's probab­ility. Expected Loss of Sales cost (When D exceeds inventory) E[lost sales cost | Demand­=d,­Inv=I] MAX(d-i,0) To remove a condition E[lost sales] = SUM(d=0 to nd)SUM(I=0 to ni)max(d-i,0)Pd(d)*­Pi(i) Can also use PMF (PI)

### Markov Case

 Markov Case Stochastic process where we only take into account the present to predict the future. That is the probab­ility of going to state j(future) from state I(present) -If there is one (and only one) closed, aperiodic commun­icating class, the process is ergodic. Pi(n) = P[In state after transi­tions] Pi(1) = Pi1(0)p11 + Pi2(0)P21+...+ Pin(0)*Pn1

### Floyd's Barbershop

 Haircuts take exactly 15min, we have r.v. Y = # customers who arrive during a 15m interval Haircuts cost 10; each customer consumes \$1 of snacks every 15min Pi(n) = Pi(n-1)*P =Pi(0)*pn Q1 - We have 3 customers in the shop, what's the Probab­ility there will be 4 customers in the shop 4 periods from now? A - P434 What is the probab­ility in the long run, a customer comes to the shop but leaves because there is no seat available? P[A]=S­UM(I=0 to 4]P(A|­Sta­tei­)*P­(St­atei) What is the Long run expected number of customers that come to the shop but leaves? E[A] = SUM(I=1 to n) E[A|B}­*P[Bi] E[a|st­ate=0] = 0(.2) +0(.7) ......