## Inferences on Confidence Intervals #### Confidence Intervals for the ratio of two standard deviations of a Normal Variate The mainstream confidence interval limits are normally set at LL=sqrt(Sd1^2/(Sd2^2*F(n1-1,n2-1,alpha1))) and UL= sqrt((Sd1^2/(Sd2^2))*F(n2-1,n1-1,alpha2))), where: #### Confidence Intervals for the Cp and Cpk index sampled from a Normal distribution - mainstream 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)) and ULCp = Cp * sqrt(CHI_Square_Value(alpha, N - 1) / (N - 1)). #### Confidence Intervals for differences in proportions - mainstream In medical research differences in proportions are an important effect measure for randomized controlled trial (RCT) and cohort studies. In manufacturing the production manager may need to compare the proportion of defectives produced by two different processes. #### Confidence Intervals for proportions and parts per million - mainstream The following information is directed at proportions but also applicable to ppm as ppm is directly related to proportions. Proportions are based on underlying discreet (and hence are not on a continuous) scale as for the mean sampled from a Normal distribution. #### Confidence Intervals for proportions and parts per million Proportions are based on underlying discreet (and hence are not on a continuous) scale as for the mean sampled from a Normal distribution. Consider a sample size of 10 sampled from a Normal Population. #### Confidence Intervals for differences in proportions In medical research differences in proportions are an important effect measure for randomized controlled trial (RCT) and cohort studies. #### 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)) and ULCp = Cp * sqrt(CHI_Square_Value(alpha, N - 1) / (N - 1)). www.qtechinternational.com