TECHNOLOGY OVERVIEW
# Confidence Intervals for the Cp and Cpk index sampled from a Normal distribution

The confidence interval for the CP index is calculated by evaluating the following expressions

LLCp = Cp * Sqrt(CHI_Square_Value(1 – alpha/2, N - 1) / (N - 1))

ULCp = Cp * sqrt(CHI_Square_Value(alpha, N - 1) / (N - 1))

Where Cp is the sample Cp obtained from the sample of n items.

The confidence interval for the Cpk index is calculated by evaluating the following expressions

LLCpk = Cpk * (1 - Z_Value(alpha) * Sqrt(1 / (9 * N * Cpk ^ 2) + 1 / (2 * (N - 1))))

ULCpk = Cpk * (1 + Z_Value(alpha) * Sqrt(1 / (9 * N * Cpk ^ 2) + 1 / (2 * (N - 1))))

Where Cpk is the sample Cpk obtained from the sample of n items.

Alpha is the specified level of significance. For a 95% confidence interval alpha =.05 as derived from (100-percent)/100

The above confidence interval for Cp provided in the free online version of BIS.Net Analyst does not provide the minimum width confidence interval for the chosen alpha.

Use the BIS.Net inferences APP to obtain minimum width confidence intervals through machine powered algorithms.

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