Sigma Magic Help Version 15

Reliability Analysis

Overview

Reliability analysis can be used to analyze the failure or reliability data. The input for this analysis is information about how long a product or component lasts after performing life-cycle testing. The output of this analysis is the Weibull model fit, the model parameters estimated using regression, and estimated outputs such as reliability numbers for different times.

This tool can be added to your active workbook by clicking on Stats and then selecting Reliability Analysis.

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 type of failure data you are analyzing. There are two options available: Option Description Complete Complete data refers to the data for which we have exact failure times. Censored Censored data also includes data that has not failed (right censoring). Right censored data means that the test was stopped for whatever reason and the item/product had not failed by the time the test was stopped.
2	Method: Specify the analysis methodology. There are two options available: Option Description RRX Use the Rank Regression on the X variable. RRX uses Least Squares approach that minimizes the squared deviation along the X axis. RRY Use the Rank Regression on the Y variable. RRY uses Least Squares approach that minimizes the squared deviation along the Y axis.This is the default setting.
3	Num Rows: Specify the number of rows of input data you would like to consider for analysis. This data will be used to reformat the worksheet.
4	Create/Analyze: Select the checkbox for Create design if you would like to update the design onto the worksheet. Once you have entered the data on the worksheet, select the checkbox for Analyze design to analyze the data you have entered and generate analysis results.
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.

Worksheet

When a new worksheet is added to the workbook, you can directly enter the censor information and time to failure data in the worksheet input area. If you have specified complete data, then only enter the column for failure times. If you have selected the right censor as the data type, then enter two data columns. The time to failure can be entered either in time units (minutes, hours, days, months) or any other measure such as cycles, etc. The censor information if it is left blank indicates that the time refers to failure data or you can write the words "Failed" in the Censor column. If it is a suspended data, where the test was stopped before failure or the failure mode is of a different type/category, then you can indicate that the test was stopped by using the words "Suspended".

Data

If you click on the Data button, you will see the following dialog box. Here you can specify the data required for this analysis.

1	Search Data: The available data displays all the columns of data that are available for analysis. You can use the search bar to filter this list and to speed up finding the right data to use for analysis. Enter a few characters in the search field and the software will filter and display the filtered data in the Available Data box.
2	Available Data: The available data box contains the list of data available for analysis. If your workbook does not have any data in tabular format, this box will display "No Data Found". The information displayed in this box includes the row number, whether the data is Numeric (N) or Text (T), and the name of the column variable. Note that the software displays data from all the tables in the current workbook. Even though data within the same table have unique column names, columns across different tables can have similar names. Hence, it is important that you not only specify the column name but also the table name.
3	Add or View Data: Click on this button either to add more data into your workbook for analysis or to view more details about the data listed in the available data box. When you click on this button, it opens up the Data Editor dialog box where you can import more data into your workbook, or you can switch from the list view to a table view to see the individual data values for each column.
4	Required Data: The code for the required data specifies what data can be specified for that box. An example code is N: 2-4. If the code starts with an N, then you will need to select only numeric columns. If the code starts with a T, then you can select both numeric and text columns. The numbers to the right of the colon specify the min-max values. For example, if the min-max values are 2-4, then you need to select a minimum of 2 columns of data and a maximum of 4 columns of data in this box. If the minimum value is 0, then no data is required to be specified for this box.
5	Select Button: Click on this button to select the data for analysis. Any data you select for the analysis is moved to the right. To select a column, click on the columns in the Available Databox to highlight them and then click on the Select Button. A second method to select the data is to double click on the columns in the list of Available Data. Finally, you can also drag and drop the columns you are interested in by holding down the select columns using your left mouse key and dragging and dropping them in one of the boxes on the right.
6	Selected Data: If the right amount of data columns has been specified, the list box header will be displayed in the black color. If sufficient data has not been specified, then the list box header will be displayed in the red color. Note that you can double-click on any of the columns in this box to remove them from the box. The data you specify for this analysis depends on the options you have specified in the Setup tab. Option Description 1 If your data type is Complete, then you need to enter the column that contains failure data under Failure Time. The Failure Type variable is not required and hence disabled. All the failures are assumed to have occurred. 2 If your data type is Right Censor, then you need to enter the column that contains failure data under Failure Time and the column that contains the type of failure (Failed or Suspended status) under the Failure Type variable.
7	View Selection: Click on this button to view the data you have specified for this analysis. The data can be viewed either in a tablular format or in a graphical summary.

Options

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

1	Sample Size: Specify the analysis methodology. There are two options available: Option Description None Do not perform any sample size analysis. Samples Estimate the number of samples required for a given time estimate. Time Estimate the time of testing for a given number of samples.
2	Parameter: Specify the parameter value for the sample size calculator. There are two options available: Option Description None No parameter value is required. Samples Specify the total testing time in this study. Time Specify the total number of samples in this study.
3	Scale: Specify the scale parameter for the distribution for sample size estimation. This parameter is not required if we are not using the sample size estimator. If you specify this value as "Auto" then the software will estimate this value from your failure data.
4	Shape: Specify the shape parameter for the distribution for sample size estimation. This parameter is not required if we are not using the sample size estimator. If you specify this value as "Auto" then the software will estimate this value from your failure data.
5	Max Failures: Specify the maximum number of failures that can be tolerated for the sample size study. This value can range from 0 to the number of samples.
6	Confidence Level: Specify the confidence level (1 - alpha) for this analysis. The default value is 95%.

Charts

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

0	Pick Charts: Select the charts you would like to display for this analysis.
1	Title: The system will automatically pick a title for your chart. However, if you would like to override that with your own title you can specify a title for your chart here. Note that this input is optional.
2	Sub Title: The system will automatically pick a subtitle for your chart. However, if you would like to override that with your own subtitle you can specify a subtitle for your chart here. Note that this input is optional.
3	X Label: The system will automatically pick a label for the x-axis. However, if you would like to override that with your own label for the x-axis you can specify a different label here. Note that this input is optional.
4	Y Label: The system will automatically pick a label for the y-axis. However, if you would like to override that with your own label for the y-axis you can specify a different label here. Note that this input is optional.
5	X Axis: The system will automatically pick a scale for the x-axis. However, if you would like to override that with your values for the x-axis, you can specify them here. The format for this input is to specify the minimum, increment, and maximum values separated by a semi-colon. For example, if you specify 10;20 then the minimum x-axis scale is set at 10 and the maximum x-axis scale is set at 20. If you specify 10;2;20, then, in addition to minimum and maximum values, the x-axis increment is set at 2. Note that this input is optional.
6	Y Axis: The system will automatically pick a scale for the y-axis. However, if you would like to override that with your values for the y-axis, you can specify them here. The format for this input is to specify the minimum, increment, and maximum values separated by a semi-colon. For example, if you specify 10;20 then the minimum y-axis scale is set at 10 and the maximum y-axis scale is set at 20. If you specify 10;2;20, then, in addition to minimum and maximum values, the y-axis increment is set at 2. Note that this input is optional.
7	Horizontal Lines: If you want to add a few extra horizontal reference lines on top of your chart you can specify the values here. The format for this input is numeric values separated by semi-colon. For example, if you specify 12;15 then two horizontal lines are plotted at Y = 12 and Y = 15 respectively. Note that this input is optional.
8	Vertical Lines: If you want to add a few extra vertical reference lines on top of your chart you can specify the values here. The format for this input is numeric values separated by semi-colon. For example, if you specify 2;5 then two vertical lines are plotted at X = 2 and X = 5 respectively. Note that this input is optional.

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 Compute Outputs to update the output calculations. A sample screenshot of the worksheet is shown below. The outputs area contains a summary of the inputs, specifically, the data type, the method for estimating parameters, the estimation of sample size or time, and the associated parameters. The assumptions check verifies if the sample size is sufficient for this analysis. The analysis results section contains the number of failures and censor data, the Weibull parameters (alpha or the characteristic life and beta or the slope). The characteristic life is the life of the product where 63.2% of them would have survived. The mean value of the data or the Mean Time to Failure (MTTF). The analysis results also list the failure times for different levels of reliability. Finally, the conclusion section lists the type of failure data - if it is infantile mortality (if beta < 1), random failures (beta ~ 1), and wear-out failures (beta > 1).

Two graphs are displayed for this analysis. The first one shows the Weibull fit line shown in blue along with the raw data points shown in red. If the red data points are close to the blue line, then we have a good fit for the Weibull model. The second graph shows the survival data where you can relate the survival probability for different failure times.

Notes

Here are a few pointers regarding this analysis:

• Note that the Weibull parameters are estimated using the Least Squares method.
• If you have fewer samples than the one mentioned by the analysis, then you will be making larger Type I and/or Type II errors when you perform hypothesis tests.

Examples

Following examples can be found in the Examples folder.

• For the failure data given in the reference file determine the Mean Time to Failure (MTTF) (Reliability 1.xlsm).