1. Introduction to Probability & Statistics Data Analysis Industrial Engineering

2. Data Analysis Histograms Industrial Engineering

3. Experimental Data
Suppose we wish to make some estimates on time to fail for a new power supply. 40 units are randomly selected and tested to failure. Failure times are recorded follow:

4. Histogram
Perhaps the most useful method, histograms give the analyst a feel for the distribution from which the data was obtained.
Count observations within a set of ranges
Average 5 observations per interval class

5. Histogram
Perhaps the most useful method, histograms give the analyst a feel for the distribution from which the data was obtained.
Count observations with a set of ranges
Average 5 observations per interval class
Range for power supply data:
Intervals:

6. Histogram
Class Interval Count = 15

7. Histogram
Class Interval Count = 11

8. Histogram Class Intervals Frequency 0.0 - 10.0 15 10.1 - 20.0 11

9. Exponential Distributionf x e ( )   
Density
Cumulative
Mean /
Variance /2 F 1
, x > 0

10. Histogram; Change Interval
Class Intervals Frequency

11. Histogram; Change Interval
Class Intervals Frequency

12. Histogram; Change Class Mark
Class Intervals Frequency

13. Class Problem
The following data represents independent observations on deviations from the desired diameter of ball bearings produced on a new high speed machine.

14. Class Problem

15. Class Problem

16. Histogram Intervals & Class marks can alter the histogram
too many intervals leaves too many voids
too few intervals doesn’t give a good picture
Rule of Thumb
# Intervals = n/5
Sturges’ Rule
k = [1 + log2n] = [ log10n]

17. Class Problem
The following represents demand for a particular inventory during a 70 day period. Construct a histogram and hypothesize a distribution.

18. Relative Histogram Class Freq Rel. 0.0 - 10.0 15 0.375

19. Relative Histogram