ProblemSolving_Histogram

Histogram

  • Definition: A bar graph that shows the distribution of a group of observations. We can visualize the dispersion, the centering, and the shape of a group of observations. 
  • Advantages: 
    - Quick Overview of comparative analysis of a sequence of historical data;
    - Quick to prepare, either manually or using a software (eg, Excel, Minitab);
    - Facilitates the solution of problems, especially when it identifies a series history evolution and the tendency of a certain process.

Example 1) The table shows information of the diameters of 20 pins whose specification is 2.8895 +/- 0.0015”. Draw a histogram and interpret it.

Step 1: Obtain the specification limits and their range

  • Determine the range "R": R = higher value - lower value

Higher value = 2.8895+0.0015 = 2.9010

Lower value = 2.8895-0.0015 = 2.8880

$R = 2.901 - 2.888 = 0.00030$

  • Determine the "K" class. Choose the class number by using common sense. $ \sqrt{N}\approx K $ 
  • N = number of variations

N = 20

$ \sqrt{20}\approx 4 $

  • Determine the range of class "H". $ H = \frac {R} {k}  $

$ H = \frac {0.0030}{4} = 0.00075$

 

Step 2: Define the limits of the 6 classes. ( between the upper limit and the lower limit) 

  • L1 = 2.8880 - 0.00075 = 2.88725
  • L2 = 2.88725 + 0.00075 = 2.8880 = Lower Limit
  • L3 = 2.8880 + 0.00075 = 2.88875
  • L4 = 2.88875 + 0.00075 = 2.8895
  • L5 = 2.8895 + 0.00075 = 2.89025
  • L6 = 2.89025 + 0.00075 = 2.8910 = Upper Limit 
  • L7 = = 2.8910 + 0.00075 = 2.89175 

 

Step 3: Write on a sheet the  limits of the classes and indicate the specification limits (upper and lower).

 

Step:4: Assign each observation to its corresponding class and mark it with an “X”. ( If an observation has the same value than a class limit, such observation will be placed in the next class to the right of this limit.) 

 

Interpretation: