MEASUREMENT PHASE FORMULAS AND SYMBOLS NOTE: Z-score and Sigma level are the same thing Z-score population = X - µ X = sample value µ = population mean σ = population standard deviation σ _ _ Z-score sample = X - X X = sample mean S = sample standard deviation S _ _ Z-score out of spec = USL – X or X – LSL USL = upper specification limit LSL = lower specification limit S S Z short term (sample) = Z long term + 1.5 Z long term = Z short term – 1.5 Z-score = Proportion in tail % Defects (1 – Yield) Yield = good units or estimate using log normal Yield = e-DPU Total (bad/good) total units Z0 =.5 Z.5=.3085 Z1=.1587 Z1.5= .0668 Z2=.0228 Z2.5=.00621 Z3=.00135 Z3.5=.03233 Z4=.04317 Z4.5=.05340 Z5=.06287 Z6=.09987 PPM = units failed * 1,000,000 PPM = % failed * 10,000 PPM = z-table value (proportion in tale) * 1,000,000 total units First Time Yield = units passed total units Rolled Throughput Yield = Yield1 * Yield2 * Yield3 * … Or estimated RTY using log normal RTY = e-DPU Total (bad/good) (Do not use if DPU > .1) Defects Per Unit = total defects DPU total = DPU1 + DPU2 + DPU3 + … DPMO = total defects * 1,000,000 total units produced * opportunities per unit (min) = use smaller value of USL - X or X - LSL _ _ Cp = USL - LSL Cpk = (min) USL - X or X - LSL Cpk = Z (min) Z = 3 * Cpk % Outside limits = Z score (min) * 100 6 * S 3 * S 3 * S 3