Download Fa12-3110-Formulas

Fall 2012 –MGT 3110: Exam 2 Formulas
Chapter 6 and 6S
Pareto diagram: Relative frequency=frequency/sum of frequencies
-Chart if  is known: X  z X , LCL = X  z X and UCL = X  z X
where,
X  mean of the sample means, or target value set for the process
 = Standard deviation of sample means =  / n
 = population (process) standard deviation
n = sample size
z = 2 for 95.45% confidence and 3 for 99.73% confidence
-Chart if  is unknown: X  A2 R , LCL = X  A2 R and UCL = X  A2 R
X  mean of the sample means, or target value set for the process
R  Average range of samples
A2 = Value found in Table S6.1
R-Chart
LCLR = D3 R , UCLR = D4 R ; Where, D3 and D4 are values from Table S6.1
where,
p-Chart: 𝑝̅ ± 𝑍𝑝̅
LCLp =
𝑝̅ − 𝑍𝑝̅ , and UCLp =
𝑝̅ + 𝑍𝑝̅
∑ 𝐷𝑒𝑓𝑒𝑐𝑡𝑠
where, p  mean fraction of defective = (𝑁𝑜.𝑜𝑓 𝑠𝑎𝑚𝑝𝑙𝑒𝑠)(𝑛) ,
p (1  p )
n
Z = 2 for 95.45% confidence and 3 for 99.73% confidence
p = defectives/n
 p  standard deviation of sampling distribution =
c-Chart: 𝑐̅ ± 𝑍√𝑐̅,
LCLc = 𝑐̅ − 𝑍√𝑐̅ and UCLc = 𝑐̅ + 𝑍√𝑐̅
where, c = number of defectives per unit output
Z = 2 for 95.45% confidence and 3 for 99.73% confidence
USL  X X  LSL 

,
Process Capability Index Cpk = Minimum of 

3 
 3

USL  LSL
6
Where LSL = Lower specification limit, USL = Upper specification limit
= Process average, and  = process standard deviation
>= 1⅓ for 4-Sigma capability and >= 2 for 6-Sigma capability
Process Capability Ratio Cp =
Acceptance Sampling
Pa = P(X<= c) = From Poisson table using nPd,
where,
Pa = Probability of accepting the sample
Pd = Probability of defectives in the lot
n = sample size
c = Critical number of defectives in the sample
X = number of defectives in the sample
Producer’s risk = 1 – Pa with Pd = AQL where, AQL = Acceptable Quality Limit
Consumer’s risk = Pa with Pd = LTPD, where, LTPD = Limit Tolerance Percent Defective
Average Outgoing Quality
AOQ =
where,
( Pd )( Pa )( N  n)
N
AOQ = Average Outgoing Quality
Pa = Probability of accepting the sample
Pd = Probability of defectives in the lot
n = sample size
N =Lot size
Chapter 12 Inventory Management
ABC Classification rule:
Class A: ~15% of items, 70-80% annual $ usage
Class B: ~30% of items, 15-25% annual $ usage
Class C: ~55% of items, 5% annual $ usage
Item
$ Usage
% of $ usage
Basic EOQ Model
Q* 
Cumulative % of $
Cumulative % of no. of items
where, D = Demand per year
S = Ordering cost for each order
H = Holding (carrying) cost per unit per year
2 DS
H
Expected number of orders (N) = D/Q
Expected time between orders (T) = (Q/D) No. of days per year = Q/d
Class
Annual ordering cost = NS = (D/Q)S
Annual carrying cost = (Q/2)H
Total annual cost (TC) = (D/Q)S + (Q/2)H
POQ Model
Q *p 
2 DS
H (1  d / p )
where, D = Demand per year
S = Ordering cost for each order
H = Holding (carrying) cost per unit per year
p = Daily production rate
d = Daily demand rate = D/No. of working days
Length of production run (t) = Q/p
Rate of increase of inventory during production = (p - d)
Maximum inventory = Imax = Q(1-d/p) = (Q/p)(p-d)
Average inventory = Imax/2
Expected number of batches (N) = D/Q
Expected time between orders (T) = (Q/D) or No. of days per year = Q/d
Annual setup cost = NS = (D/ Q)S
Annual carrying cost = (Imax/2)H
Total annual cost (TC) = (D/Q)S + (Imax /2)H
Quantity discount model
Q
2 DS
IP
where, D = Demand per year
S = Ordering cost for each order
IP = H = Holding (carrying) cost per unit per year
I = Holding cost as a % of item cost
P = Item cost per unit
Step 1: Determine Candidate Q
a. Compute Formula-Q for each price break price.
b. If Formula Q < Lower limit for price, then Candidate Q = Lower limit
If Formula Q is within the limits for the price, then Candidate Q = Formula Q
If Formula Q > Upper limit for price, then no candidate Q, ignore the Formula Q
Q-Range
Price
Holding cost/unit = % x P
Formula Q
Adjusted Q
Step 2: Compute total annual cost (TC) for each valid candidate Q and select the candidate Q with least
cost as EOQ.
Total annual cost (TC) = (D/Q)S + (Q/2)H + PD
Total annual cost = Annual holding cost + Annual ordering cost + Annual item cost
i.e. = (Q/2)H + (D/Q)S + PD, where P = cost of the item per unit
Q-Range
Price
Adjusted Q
Annual total cost = PD + (D/Q)S + (Q/2)H