# Methods and formulas for confidence intervals and bounds in Binomial Capability Analysis

## Average P confidence interval

The 95% confidence interval for average P is calculated as follows:

### Notation

TermDescription
v12 * Dtot
v22 * (Ntot - Dtot + 1)
v32 * (Dtot + 1)
v42 * (Ntot - Dtot)
DtotSum of all the defectives
NtotSum of all the sample sizes

## %Defective confidence interval

The 95% confidence interval (CI) for %defective is calculated as follows:

### Notation

TermDescription
Average PThe proportion of items in your process that are defective

## PPM Defective confidence interval

The 95% confidence interval for PPM defective is calculated as follows:

### Notation

TermDescription
Average PThe proportion of items in your process that are defective

## Process Z confidence interval

The 95% confidence interval for process Z is calculated as follows:

### Notation

TermDescription
Inverse cumulative distribution function (CDF) of a standard normal distribution
Average PThe proportion of items in your process that are defective