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# Binomial Capability Help

The binomial capability analysis is used to determine if the percentage of defective items in a process meets customer specifications. There are only two possible outcomes when you examine one item: it is either defective or not defective. So, you use this analysis with yes/no type attributes data. This analysis has the following output:

### Data Entry

The data are entered into a worksheet as shown below (using the first part of the data into the example workbook). The data does not have to start in A1. It can be anywhere on the spreadsheet but must be in columns.

In this example, the percentage of calls that result in an order is being tracked. The data are collected daily. The first column is the number of calls made each day that result in order (np values). The second column is the subgroup size – the number of calls made that day (n). If there is a constant subgroup size, this range is not needed. You will enter the subgroup size below. The columns for np and n do not have to be together.

### Creating a Binomial Capability Analysis

If you uncheck the “Constant Subgroup Size” box in the form above, the subgroup range becomes visible as shown below:

A target of %5 was added to the form in this example. The output from the analysis is described below.

### Output for the Binomial Capability Analysis

The output from the analysis is placed a new worksheet. There are five parts to the output.

#### Statistical Metrics

This part of the output provides the statistical metrics from the analysis including average % defective and confidence interval associated with that average. The average % defective is the average percent defective in all the subgroups.

#### Histogram

The histogram shows the distribution of % defective items in the subgroups. If you entered a target values, it is plotted on the histogram to allow you to assess if most of the subgroups meet that target or not.

#### p Control Chart

The p control chart assesses the state of statistical control of the results. The center line is the average % defective. The two dotted lines are the upper and lower control points. The process is in statistical control if none of the selected control chart test above are violated. If the p control chart is in statistical control, the results are assumed to be valid. If there are too many out of control points, the process is not stable, and the results are not valid. Out of control points are in red.

#### Cumulative % Defectives Chart

This chart plots the cumulative % defective over time for each subgroup. It is used to determine if you have enough subgroups for a valid estimate of the average % defectives. The center line is the average % defective (same as the center line on the p control chart). The upper and lower confidence limits for the average % defectives are also plotted. You want the data to flatten out along the average % defective line. If this occurs, you have enough subgroups.

#### % Defectives vs Subgroup Size Chart

If the subgroup size varies, a % defectives vs subgroup size chart is included in the output. This chart plots the % defective against the subgroup size. It is used to help determine if the data comes from a binomial distribution. If it does, you would expect the points to be randomly distributed around the centerline, which is the average % defective.

#### P-P Plot

If the subgroup size is constant, a P-P Plot is included in the output. This P-P Plot is used to determine if the data comes from a binomial distribution. The P-P Plot plots the empirical cumulative distribution function (CDF) values (based on the data) against the theoretical CDF values (based on the binomial distribution). If the P-P plot is close to a straight line, then the binomial distribution fits the data.

### Options for the Binomial Capability Analysis

There are two options on the input form shown above: Out of Control Tests and Classes, Minimum. Both are described below.

#### Out of Control Tests

Selecting this option displays the input screen below. These options apply to the p control chart which is used in the Binomial Capability Analysis. This defines what out of control tests to apply to the control chart.

#### Classes, Minimum

If you select the “Classes, Minimum” option, the following input screen will appear:

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