Methods and formulas for overall Benchmark Zs in Nonnormal Capability Analysis

Z.Bench Z.LSL Z.USL

Benchmark Z statistics for overall capability are calculated by finding the Z value using the standard normal (0,1) distribution for the corresponding statistics.

Note

PPL and PPU are based on the method (ISO or Minitab) used in the analysis. For more information, go to Methods and formulas for overall capability measures in Nonnormal Capability Analysis. The formulas are based on the default tolerance of K = 6, which is 6 standard deviations wide (3 standard deviations on each side of the process mean).

Notation

TermDescription
P1Probability (Observations < LSL) based on the nonnormal distribution used in the analysis and the parameters that you specify (or the parameters that are estimated from the data)
P2Probability (Observations > USL) based on the nonnormal distribution used in the analysis and the parameters that you specify (or the parameters that are estimated from the data)
Φ (X) Cumulative distribution function (CDF) of a standard normal distribution
Φ–1 (X)Inverse CDF of a standard normal distribution
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