Exploratory Data Analysis: Stratification
The primary purpose Exploratory Data Analysis (EDA) is to identify the key variables that affect the quality measures. Two principles, mentioned by De Mast and Trip (2007), are helpful in identifying these variables. They are:
- Display the distribution of the data
- Display the distribution within individual stratum
Chang and Lu (1995) provide an example illustrating these principles. A steel sheet metal manufacturer had customers complaining about uneven thickness. The specification was 4.5 ± .5 mm. The production manager had data collected from 120 sheets giving the thickness measurements on the left, middle and right sides of the sheets. Employees selected five sheets at shift times of 0900, 1100, 1400 and 1700 over a period of five days. The histogram appearing below shows 13% of the sheet thickness measurements below the lower specification limit of 4.0 mm. Also, the mean is lower than 4.5 mm.
After discussions with shop-floor personnel, they stratified by position on the sheet and by time. Histograms for the two stratifications appear below. The stratification by position did not show distributions much different than the aggregate distribution. However, the stratification by time showed higher frequencies of thin measurements at 1100 and 1700. Twenty four of the 26 values in the histograms below 4 mm, 24 of them were at 1100 and 1700.
Discussions with shop-floor personnel identified mold wear out, build up of chips in a work holding device, and operator fatigue as possible causes. The corrective action was to take a 10 minute break at 1030 and 1630 each day and have maintenance performed during the breaks. The corrective action produced a substantial reduction in thin sheets.
- Chang, P.-L. and K.-H. Lu (1995). "The Construction of the Stratification Procedure for Quality Improvement." Qualilty Engineering 8(2): 237-247.Chang, P.-L. and K.-H. Lu (1995). "The Construction of the Stratification Procedure for Quality Improvement." (2): 237-247.
- De Mast, Jeroen and Albert Trip (2007). “Exploratory Data Analysis in Quality-Improvement Projects”, Journal of Quality Technology, 39(4): 301-311.