3. Elements of Time Series
Classical Decomposition of a Time Series – Trend, Seasonality, Cycles & Residuals
A ‘Time Series’ can be decomposed into four elements:
However, scope of this session is limited to identify & interpret variation in a ‘Time Series’, through
Run Chart & Control Chart
4. Run Chart
A ‘Run Chart’ is a graphical display of data plotted in ‘time’ order
‘Run Chart’ is used to study observed data for trends or patterns over a specified period of time
5. Run Chart contd….
What is a ‘Run’?
A ‘Run’ is defined as one or more consecutive data points on the same side of median. Some data points
might fall on the median line, those are ignored and not considered as runs
6. Run Chart contd….
Two ways to count the number of runs
• Draw a circle around each ‘Run’ & count the number of circles drawn
• Count the number of times the sequence of data points crosses the median line & add ‘1’
7. Run Chart contd….
‘Run Chart’ Rules:
At least 15 data points are needed in a ‘Run Chart’ to apply any of the ‘Run Chart’ rules
Shift Trend
Number of Runs Astronomical Point
A shift in the process is
indicated by 6 or more
consecutive points either all
above or below median.
Values on median do not
add or break a shift
A trend is indicated by 5 or
more consecutive data
points all going up or down.
Like values do not add or
break a trend
If values of 2 or more successive data points are
same include only one while counting.
An obviously, blatantly
different value
However a normal max
value of a data set is not an
astronomical point
To many or to few
number of runs basis
the number of
expected runs
8. Run Chart contd….
Number of Runs – Test of Randomness:
Expected number of ‘Run’ depends on total number of data points not on median
9. Control Chart
Control Chart is used to track process statistics over time & to detect the presence of special causes, if any
A process is considered to be in control if all the data points are within the bound of control limits & points
do not display any non-random patters
