Given individual observations instead of samples, the \(IM\!R\) control chart is a classical proposal in both SQC books and ISO standards (e,g., ISO 7870-2 whose revision is underway) for monitoring level and scale. The \(IM\!R\) chart consists of two well-established control charts, the individuals (I) Shewhart mean control chart and the moving range ( \(M\!R\) ) chart for monitoring the variance, respectively. Simple rules are given for setting the limits. However, it is known that the \(M\!R\) limits are misplaced. There are some early accurate numerical (zero-state) average run length (ARL) results by Crowder (J Qual Technol 19(2):98–102;1987a, https://doi.org/10.1080/00224065.1987.11979045 , J Qual Technol 19(2):103–106;1987b, https://doi.org/10.1080/00224065.1987.11979046 ) in 1987! However, they are not flawless. Another, accurate algorithm is proposed. Moreover, there was quite some discussion of \(IM\!R\) charts in the 1990s, cf. to Roes et al. (J Qual Technol 25(3):188–198;1993, https://doi.org/10.1080/00224065.1993.11979453 ), Rigdon et al. (J Qual Technol 26(4):274–287;1994, https://doi.org/10.1080/00224065.1994.11979539 ), Amin and Ethridge (J Qual Technol 30(1):70–74;1998, https://doi.org/10.1080/00224065.1998.11979820 ), which suggests that \(IM\!R\) charts are rather ineffectual tools. Later, Acosta-Mejía and Pignatiello (J Qual Technol 32(2):89–102;2000, https://doi.org/10.1080/00224065.2000.11979981 ) came up with a single \(M\!R\) chart for monitoring scale alone and made an erroneous assumption while calculating the ARL. We provide the whole numerical package for \(IM\!R\) and \(M\!R\) control charts including lower and two-sided limits designs (Crowder dealt with upper ones only). Eventually, we present some conclusions about whether and how \(IM\!R\) (and only \(M\!R\) ) control charts should be applied. Besides, the data form an independent series of normally distributed random variables.