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 BISNET Analyst) does not provide the minimum width confidence interval for the chosen alpha.

The minimum width occurs at different tail end values used by the mainstream approach. A machine powered algorithm is required to find the best tail end probabilities, subject to the total tail end probabilities being equal to alpha.

This is technology is used in the BIS.Net Inferences APP.

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