I am interested in building quality control charts for time series data where every data point has different gradation within the range of 0 to 1. For example first data point X1 may be 0.1, 0.2,..,1 and second data point X2 may be 0, 1/3, 2/3, 1. Third data may have some another interval.
The data is not seasonal and there is no pattern in how the intervals look like (e.g., 0.1(X1), 1/3(X2) etc.). In other words I don't know what is the gradation of future data points but know that the range is between 0 and 1.
My questions are
1) Wether the limits that I will build based on some training data (UCL, LCL) will be effected as a result of having different gradation - the variance will be higher since the data is not continuous?
2) Is it a problem given the fact that this represents the nature of future data and that I have a training set of 30 samples?
3) The data points represent performance of student over different tests in consequent time, and were normalised to be between 0 and 1 (10 questions in test will lead to interval of 0.1, 3 questions will lead to interval of 1/3). Maybe there are some ways to normalise the data to avoid the problem of blowing up the variance?
Many thanks for your patience and help!