﻿ VariableRandR_Xbar
 1. Data Entry & Initial Calculations Part Appraiser Trial # 1 2 3 4 5 6 7 8 9 10 Average A A 2 A 3 A Average $\bar{X_a}$ A Range $\bar{R_a}$ B 1 B 2 B 3 B Average $\bar{X_b}$ B Range $\bar{R_b}$ C 1 C 2 C 3 C Average $\bar{X_c}$ C Range $\bar{R_c}$ Part Average $\bar{\bar{X}}$ 2. Interim Calculations Formula Calculation Value Rp, Part Average Range = Max Part Average - Min Part Average - = ${R_p}$ $\frac{\bar{R_a} + \bar{R_b} + \bar{R_c} }{Number\; of\; Appraisers}$ / = $\bar{\bar{R}}$ $Maximum\; \bar{X} - Minimum\; \bar{X}$ - = $\bar{X}_{DIFF}$ $\bar{\bar{R}}\times {D_4}$ (where ${D_4}$ for 3 trials = 2.58) x = ${UCL_R}$ 3. Results Components of Variation Value % of Total Variation (TV) Repeatability, or Equipment Variation (EV) $\bar{\bar{R}} \times {K_1}$ (where ${K_1}$ for 3 trials = 0.5908) EV Reproducibility, or Appraiser Variation (AV) $\sqrt{(\bar{X}_{DIFF} \times {K_2})^2 - \frac{EV^2}{Num\; Parts \times Num\; trials}}$ (where ${K_2}$ for 3 appraisers = 0.5231) AV Repeatability and Reproducibility (GRR) $\sqrt{EV^2 + AV^2}$ GRR Part Variation (PV) ${R_p} \times {K_3}$ (where ${K_3}$ for 10 parts = 0.3146) PV Total Variation $\sqrt{GRR^2 + PV^2}$ Number of Distinct Categories $1.41 \times \sqrt{\frac{PV}{GRR}}$ ndc