Saturday, February 26, 2011

Run Chart

Run Chart is a basic line chart that may be use to monitor a process stability over time

Characteristic of Run Chart
1. Horizontal line plot across the data point are Median of the data set
2. It do not consist of UCL and LCL as shown in other Control Chart.

How to detect a Run
1. A "Run" could be a Single or Multiple data point above or below the Median
2. When a data point move from one side to another side of Median, a "Run" start and the "Run" ended when it cross the Median line again.

Type of Run could be observe from a Run Chart
1. Number of Run about Median
2. Number of Run Up or Down

Minitab software report Observed and Estimated Run in the Run Chart
Minitab test for two non-random behavior detect trends, oscillation, mixtures and clustering of the data. Such patterns suggest that the variation observed is due to "special cause"

Test for Randomness
Number of runs about the Median
More run observed than expected

Mixed data from two populations
Fewer run observed than expected

Clustering of data
Number of runs up or down
More runs observed than expected

Oscillation – data varies up and down rapidly
Fewer runs observed than expected

Trending of data

Minitab test the approximated p-value for Mixture, Clustering, Oscillation and Trend
Mixture Pattern - a mixture characteristic observed when there is absence of data point near to the Median line. Mixture often happen when combination of data from different population, or data set represent different process condition

Cluster pattern - Clusters may indicate variation due to special cause, such as, incident of broken tool, significant process parameter change.

Trend pattern - A trend is a sustained drift in data, either moving upward or downward. It may be an indication of process about toward out of control.

Oscillation pattern -  occurs when the data fluctuates continuously up and down rapidly, it indicate the process instability.

Data analysis ( based on above Run Chart )
Run across Median
- Fewer Run observed than expected
- approximated p-value for mixture = 0.96. ( no significant evident to proof the indication of data from different population )
- approximated p-value for clustering = 0.03 ( indicate strong evident of data clustering )

Run up or down
- Fewer run up or down than expected
- approximated p-value for trends = 0.13
- approximated p-value for oscillation = 0.86
- Data indicated significant of trends and oscillation, however, oscillation is more significant than trends in this case.

Reference - Minitab Release 14