# Help Manual

### Contents

• Introduction
• Project
• Analytics Templates
• Change Templates
• Lean Templates
• Graph Templates
• Projects Templates
• Stats Templates
• Analysis
• Miscellaneous

Sigma Magic Help Version 15

# Probability Calculations

## Overview

The Probability calculations worksheet can be used to determine the probability and inverse probability values for a given distribution. For example, if you want to manually calculate the Sigma level or if you want to perform some calculations that are not available in Sigma Magic then you can use this worksheet

This tool can be added to your active workbook by clicking on Stats and then selecting Distribution > Probability Calculations.

## Inputs

Click on Analysis Setup to open the menu options for this tool.

### Setup

A sample screenshot of the setup menu is shown below.
1
Data Type: Specify the data type for this analysis. The available options are:
OptionDescription
DiscreteDiscrete data is like count data that has only finite set of values (like the number of defects in a product example 20, 30, 43).
ContinuousContinuous data can take any arbitrary value (like the temperature of the room example 34.53 deg centigrade).
2
Distribution Name: Specify the name of the distribution you want to use for this analysis. The available distributions shown in this dropdown box depends on the type of data you have selected in Step 3.
3
Distribution Parameters: Specify the values for the distribution parameters. Note that some distributions may have only 1 parameter, some may have 2, some may have 3 etc.
4
Calculate: Specify the type of analysis you want to perform. The available options are:
OptionDescription
Probability at XCalculate probability at x = X
Probability to the left of XCalculate probability at x <= X
Probability to the right of XCalculate probability at x > X
Probability between X1 and X2Calculate probability for X1 < x <= X2
Probability P on the leftCalculate X such that Prob (x <= X) = P
Probability P on the rightCalculate X such that Prob (x > X) = P
Probability P on the insideCalculate X1 and X2 such that Prob (X1 < x <= X2) = P
Probability P on the outsideCalculate X1 and X2 such that Prob (x <= X1) + Prob (x > X2) = P
5
Help Button: Click on this button to open the help file for this topic.
6
Cancel Button: Click on this button to cancel all changes to the settings and exit this dialog box.
7
OK Button: Click on this button to save all changes and compute the outputs for this analysis.
If you click on the Real-Time Viewer button, the software will open up a real-time viewer window. An example screenshot of the viewer is shown in the figure below.
 1 Distribution Details: Ensure that you are viewing the right distribution here. It contains the name of the distribution and the distribution parameters. 2 Help Button: Open the help file for this topic. 3 X Axis Values: Specify the X Left and/or X Right values. These values will be updated on the chart and all data points that fall to the left to the X Left value and to the right of the X Right value will be highlighted in red and the corresponding values willbe shown both on the chart and on the Probability Values textboxes. 4 Probability Values: Specify the P Left, P Middle, and/or P Right values. The software will determine the corresponding X Left and X Right values based on this data and all data points that fall to the left to the X Left value and to the right of the X Right value will be highlighted in red. 5 Fit Percent: Shows the value of the percentage of the graph that falls in each region. 6 Basic Statistics: Shows the basic descriptive statistics for the selected distribution. 7 PDF: Shows the probability density function for the given distribution. 8 OK Button: Click on the OK or Cancel Button to close this dialog box. No changes made in the dialog box are saved and no charts on the worksheet are updated from the real-time viewer.

### Charts

If you click on the Charts button, you will see the following dialog box.

### Verify

If you click on the Verify button, the software will perform some checks on the data you have entered. A sample screenshot of the dialog box is shown in the figure below. The objective of this analysis as well as any checks that are performed is listed in this dialog box. For example, the software may check if you have correctly specified the input options and entered the required data on the worksheet. The results of the analysis checks are listed on the right. If the checks are passed, then they are shown as a green-colored checkmark. If the verification checks fail, then they are shown as a red-colored cross. If the verification checks result in a warning, they are shown in the orange color exclamation mark and finally, any checks that are required to be performed by the user are shown as blue info icons.

## Outputs

Click on OK to perform the calculations. The probability or the X values are displayed in the output text box and the Conclusion box.

## Notes

Here are a few pointers regarding this analysis:
• Note that for a continuous distribution, the probability at X is the value of the probability density function and not the probability at a given value which is always 0 for continuous case.
• You can control the number of decimal places of the display result in the Options menu.

## Examples

Following examples can be found in the Examples folder.
• Determine the probability to the right of X = 30 for a normally distributed data with Mean = 25 and Stdev = 2.