Question

1)

i) A company wants to forecast its demand using the Simple Moving Average. If the company uses following FOUR prior yearly sales values, which of the following is the Simple Moving Average forecast for Year 5?

Year	Demand
1	100
2	120
3	140
4	210

a) 100.5

b) 142.5

c) 145.3

d) 155.0

e) None of the above

iI) We have taken four (4) samples of hundred (100) letters each from a typing pool and found the following proportions of defective letters: .04, .01, .01, and .02. A letter is considered defective if one or more errors are detected. Compute the lower and upper control limits for the p control chart. (Show the the work for this problem including formulas)
a) 0.05 and 0.95

b) 0.00 and 0.062

c) 0.00 and 0.0388

d) 0.00 and 0.140

e) None of the above

  

Answer 1

i) The correct answer is option b:142.5

Simple moving average forecast for year 5=Average of the demand for the four years=(100+120+140+210)/4

=142.5

ii)The correct answer is option b: 0.00 and 0.062

Given : n=100

we first calculate p-bar i.e the center line

p-bar =average of the proportions of defective letters=(0.04+0.01+0.01+0.02)/4=0.02

Next, we calculate Sp =sqrt(p-bar(1-p-bar)/n))

=sqrt(0.02*(1-0.02)/100))

=0.014

UCLp =p-bar+z *Sp=0.02+3*0.014=0.062

LCLp=p-bar-z*Sp=0.017-3*0.0108=-0.022=0.00