TECHNOLOGY OVERVIEW
Confidence Intervals for the Cp and Cpk index sampled from a Normal distribution
BIS.Net Team
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.