An individual control chart is not robust to non-normally distributed data. So you would need to transform theta or at the very least remove outliers.

See: Gest. Prod., São Carlos, v. 23, n. 1, p. 146–164, 2016 http://dx.doi.org/10.1590/0104–530X1445-14, Method for determining the control limits of nonparametric charts for monitoring location and scale.

Thank you for the upvote! I upvoted your question :-)

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the answer will indeed depend on your perspective : if your perspective is statistically-oriented, then, of course, non normal data should not be treated as if they were normal and there is a continuous flow of litterature on this topic ... but it is more relevant to the theory of statistical tests as opposed to the practice of control charts

shewhart should not be confused with neyman and if your perspective is that of a decision-maker using control charts to understand and improve his/her process, then the answer may be quite different

the following posts are very interesting (and provocative) if your perspective is that of a decision-maker :

http://www.qualitydigest.com/inside/quality-insider-article/myths-about-process-behavior-charts.html

http://www.qualitydigest.com/inside/twitter-ed/are-you-sure-we-don-t-need-normally-distributed-data.html

http://www.qualitydigest.com/inside/quality-insider-column/don-t-we-need-remove-outliers.html

http://www.qualitydigest.com/inside/quality-insider-column/process-behavior-charts-non-normal-data-part-1.html

http://www.qualitydigest.com/inside/quality-insider-column/process-behavior-charts-non-normal-data-part-2.html

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 Its not about the normality. Its all about the known mean and variance of your statistic (say theta). 

It depends on what theta actually is. If it is the mean, with a sufficiently large sample, the Central Limit Theorem may be invoked to allow for the application of the normal distribution which because of its symmetry lets the control limit to theta+/-SE(theta). If theta is the variance, the gamma distribution or chi-square is applicable and because it is not symmetric, the resultant control limit may not be of the theta+/- SE(theta) type.