Control Charts

Z-MR (Short-Run Control Chart)

Standardised I-MR across multiple parts with different targets/spreads.

Statusvalidated

Version1.0.0

Minitab equivalentStat > Control Charts > Variables Charts for Individuals > Z-MR

Description

Computes mean x̄_j and σ̂_j (= MR̄_j/d₂) per part j. Values are transformed to z_ij = (x_ij − x̄_j)/σ̂_j; the z chart has fixed limits ±3. The MR chart uses UCL = D₄·MR̄_z, LCL = D₃·MR̄_z.

Formulas

Standardisation

z_{ij} = \frac{x _{ij} - x ˉ _{j}}{σ ^ _{j}}, \overset{σ}{^}_{j} = \overline{MR}_{j} / d_{2}

within each part

References

Wheeler, D. J. (1991), Short Run SPC, SPC Press
Montgomery, Introduction to Statistical Quality Control, 8th Ed.