1. 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 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= Z1= Z1.5= Z2= Z2.5= Z3= Z3.5= Z4= Z4.5= Z5= Z6=.09987
PPM = units failed * 1,000, PPM = % failed * 10, 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 * S * S