This new version of the MCR-ALS takes into account possible data uncertainties and it presents a more rigorous maximum likelihood least squares approach. Whereas in many chemical applications the assumption of independently identically distributed (iid) noise is reasonable and produces good estimates of the parameters, in other cases of having data with large non-homocedastic noise structures (heterocedastic or correlated noise), MCR-ALS may produce wrong estimates.The MCR-WALS method is based on a sounder maximum likelihood weighted alternating least squares approach initially proposed by Wentzell et al (BMC Bioinformatics 7 (2006), p. 343) and that it allows for different type of weighting schemes.