Sudden increase or decrease in time series There is a call center which records the number of complaints against a service on daily basis.
For example, the values below show the number of complaints for the last 6 months of a service:

Jan, Feb, Mar, Apr, May, Jun
  020, 030, 010, 030, 045, 065

Question: How one can find sudden increase/decrease in number of complaints for a service over a period of time OR sudden increase/decrease in number of accidents/births/tourists/students/etc in last 6 months? 
sudden increase/decrease should be adjustable for sudden and increase/decrease.
I need help and suggestions to figure out possible solutions.
Edit # 1
This approach has to be automated. A computer program will analyze a certain window of historic data and will identify sudden increase or decrease. So basically there are two problems:


*

*A modal to identify sudden change 

*Quantification of the modal


Time plot or Linear Graph can be used to plot the changes. But I don't know how to quantify this plot/graph. Any suggestion in this area will be helpful.
Edit # 2
I received following advice from someone. Hope it help

Take your deltas: 10, -20, 20, 15, 20 and find the mean and std dev of
  their absolute values.  The numbers outside of say two standard
  deviations that are big numbers show you sudden increase/decrease. 
  The small ones outside of two standard deviations show unusual
  stability. The rest are just your normal slow drift.  I only see slow
  drifting in these numbers.

Edit # 3
As shown in this picture, the red line is a normal condition for last 6 months while blue line indicates a sudden increase in last 4 months of 6 month window.

Edit # 4
Instead of rephrasing this whole question, i have posted a new question as How to quantify increasing nature of dataset. I will delete this question.
 A: A control chart is a helpful way to visualize the performance of the call center over time. It's good you applied edits to specify this is a problem of forecasting rather than inference, or prediction: forecasting relies on projecting forward in time, whereas prediction may borrow information from the future or the present to infer what trends may be.
Queuing theory often uses such models to forecast volumes to a call center. In queuing theory, you make some assumptions about the nature of the calls: namely that they arrive with independent interarrival times at a time-varying rate. Probabilistically, this leads to distributions over time intervals which are Poisson. Detecting changes in Poisson rates from one time interval to the next makes use of a Markov Chain. which utilizes several lagged states. As you allude to, 20 people calling within a one minute time frame may be a "peak", and may be a coincidence (or noise) in the signal, but if this rate is sustained for a number of "states" (intervals of time), you may eventually classify the state as a "peak time". 
In order to conduct this type of analysis a number of definitions must additionally be laid out: you must define what comprises a "peak time": if the control chart reveals that such times are visually compelling, then the choice of cut off may be arbitrary, since normal volume may be (say) 3 calls per minute and high volume would comprise 30 calls per minute, making cut-offs between 5 and 20 essentially the same. You must also decide upon what is the appropriate interval of time: if you choose too large a time frame (say one hour), the latency of your detection may be too delayed to be useful. If you choose too short a time frame, the Poisson estimates of caller rates may be unreliable. You must also determine how many lagged states you would like to consider before you conclude decisively that the process has landed in a "high volume" state. So with intervals of 1 minute, but a 3 minute evaluation period, you would use a Markov chain with 3 lagged states considering 3 consecutive periods of "high" volume evidence that you are now in a high call volume state.
Roughly, this process is a poor man's filtering. There are more sophisticated filtering processes that can be applied, such as Kalman's filter, Bayesian particle filter, and so on.
