Supply Chain Management

Q1: Distribution estimation

1. (10 points) Estimate the probability density function using histograms (bins) of width

20. Plot it.

Using Matlab:

>> x = [PRODUCTIONHRS];

>> NBINS=128

>>NBINS =

128

>>h=histogram(x,NBINS)

Histogram with properties:

Data: [1498x1 double]

Values: [1x128 double]

NumBins: 128

BinEdges: [1x129 double]

BinWidth: 20.1000

BinLimits: [0 2.5728e+03]

Normalization: 'count'

FaceColor: 'auto'

EdgeColor: [0 0 0]

Figure 1. Histogram of the dataset

And the Pdf:

Figure 2. PDF of the dataset

2. (10 points) Using the density, estimate the cumulative distribution function. Plot it.

Figure 3. CDF of the dataset

3. (10 points) Suppose that X1;X2; : : : are i.i.d., what kind of guarantee does the DKW

Inequality give us about the estimated distribution and the true unknown distribution?

The DKW inequality predicts how close our distribution estimation with true

unknown distribution, from which the samples are drawn. Thus if we apply

DKW we are going to be able to know how accurate our estimation is.

4. (10 points) pick a value of in the interval (0, 1). Using the above estimated

distribution, find a value z() such that you can give a guarantee of the form

ℙ !"## ≤

≥ 1 −

Q2: Control charts

1. (10 points) Draw the control chart diagram on the production time data using chunks

of n = 10 data points. First estimate the mean via the sample mean u and standard

deviation via the sample variance 2 using the first chunk of data points.

The Production data were grouped into chucks of 10 data points and so, the mean

and standard deviation were estimated from the first chuck of data.

Mean = 250.4

Standard deviation = 115.14

UCL = 359.63

LCL = 141.16

1600.00

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