Please refer the Section 9.3 of D C Montgomery (6th edition, page 428). He has given an example to construct an unweighted moving average control chart. Suppose that the target value and the Sigma value are unknown then how to construct the moving average control chart
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when you use control charts, you are supposed to have some prior knowledge of the nominal behaviour of the system ; this is why the mean and variance are usually supposed to be known or to have good estimates for the nominal behaviour
if your system is known to be nominal at the beginning of the observation, you can just waste your first observations too get an estimate of the mean and variance and plug those estimates in the formulas ; the more wasted samples, the better the estimate ... as long as the system stays nominal !.
if you cannot expect your system to be nominal at starting time, the above will not work (the mean and variance could be estimated from a non-nominal or mixed behaviour) and i fear that the best you can hope from a control chart is to help you find changes in behaviour
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