Metric to measure consistency (or randomness) of a group of time-series data I have hourly time series consumption data of four customers namely (F238, F262, F267, F264) for a complete month, plotted as 
Each line represents the consumption on a separate day. I want to find which among these customers is most stable/consistent in terms of repeating patterns across days and which among these is most random. Is there a specific metric which measures the randomness or shape consistency among different days of time-series data?
On visualisation, F238 seems most consistent as compared to others because of consistency in patterns followed across days of a month, while as F262 seems most random because every day seems to follow a different pattern. Is there any metric which can summarise this observation, such that the metric output may vary between fixed pair of values (like [0, 1])?
 A: A measure of randomness or predictability for a time series is the MSE or R-Sq from a reasonable model. Comparison of these measures across customer could facilitate groupings and exceptionally different customers. In order to build a good model for daily/hourly data which I am involved with all the time is to incorporate both memory (ARIMA) and deterministic structure (X's) (like days-of-the-week etc. ) for each hour. Please review Forecasting technique for daily data with monthly and day of week seasonality for some pointers on what factors (hidden layers) can be extracted that are statistically significant.
I have posted and you can search for "user:3382 daily data" to obtain other words and examples . If you wish to actually post daily data for two of your customers i will try to take the time to present you with examples of "useful models"
Another thought is to actually compute out-of-sample error measures (MAPE for example) and use that metric to summarize a customer.
A: You could compute the similiarity of all time-series within a cluster - the average intra cluster distance using either Euclidean Distance or Dynamic Time Warping Distance. 
In most cases for Time-Series Analysis, Dynamic Time Warping is recommended, since it is an elastic measure and yields low distance for two series which are out of phase yet very similiar. To evaluate the randomness for each class, you could compute the average distance of a single measurement to all others in the same class. If the distance is high, the class is more mixed/random, whereas if the distance is low, the variation in between samples of the class is low. 
YET, you might want to use euclidean distance if not the pattern but the time of the activity that you measured is of interest. Therefore you will chose a metric based on domain knowledge.
For more information I recommend the tutorials of Eamonn Keogh which can be found here. The following picture illustrates the difference betwen Euclidean Distance and Dynamic Time Warping and is taken from a tutorial of Eamonn Keogh. 
