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Stat > Reliability/Survival > Distribution Analysis > Parametric Distribution Analysis

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Select the data definition

Distribution ID Plot, Distribution Overview Plot, Parametric Distribution Analysis, and Nonparametric Distribution Analysis store reliability data definitions. Select an existing definition to quickly use the same sample and censoring columns.

To create a new definition, select Custom Definition.

By default, the definition name is the word "definition" followed by the date and time of creation in parentheses. To delete or rename a definition, select Manage Definitions.

Select the censoring scheme

Select the censoring scheme for the data. Censoring means that exact failure times are unknown for some data. In right-censored data, exact failure times are unknown for units that survive at the end of the data collection. In interval-censored data, exact failure times are unknown because the detection of failures occurs only at the end of an inspection interval. For more information on types of censoring, go to Data censoring.

Right censored data with censoring column
Select when the failure data are in one or more columns and have a column that identifies censored observations. Multiple columns of failure data can use the same censoring column if all the columns are the same length.
In this worksheet, Durability contains the failure times. Censoring indicates the censored observations.
C1 C2
Durability Censored
81 Censored
77 Censored
75 Failure
74 Failure
Right censored data by censoring time
Select when the failure data are in one or more columns and all observations that exceed an amount of time are censored. Enter a censoring time for each column.
Right censored data by number of failures
Select when the failure data are in one or more columns and you know the censoring number in each column. The censoring number is the number of exact failures. After that number of failures, the other observations in the column are right-censored. For each column, enter the censoring number.
The censoring number is per column. For example, if the censoring number is 20 for a column, then the 20 smallest values are failures. Any remaining observations after 20 are censored. If the number of failures for another column is 10, then the 10 smallest values are failures. Any remaining observations after 10 are censored.
Uncensored or complete data
Select when the failure data are in one or more columns. All observations represent exact failure times.
Interval censored data
Select when failures happen between a start time and an end time for an inspection interval. Usually, interval censored data have a frequency column that indicates the number of failures in the interval. Without a frequency column, each row represents one observation. To indicate right-censored observations, use * as the end time of the interval. To indicate an exact failure time, use the same value for the start time and the end time. To indicate left-censored observations, use * at the beginning of the interval.
In this worksheet, Start time has the beginning time of each inspection interval. End time has the end time of each inspection interval. Count has the number of failures in each interval. The first interval begins with * to indicate left-censored observations. The fourth interval begins and ends with 5 to indicate exact failure times. The final interval ends with * to indicate right-censored observations that survive at the end of the data collection.
C1 C2 C3
Start time End time Count
* 2 5
0 2 6
2 4 7
5 5 8
4 6 4
6 * 83
Warranty data
Select when the data format is a triangular matrix form that indicates shipment data and warranty return data. Enter the shipment quantities in a worksheet column or in the first row of the return columns.
Shipment quantities in a column
In this worksheet, the number of items shipped in each year is recorded in a single column. Each row represents shipments for a different year. The number of items returned each year is recorded in a separate column. For example, in Year 1, 15,000 items were shipped. Of those items, 78 were returned in Year 2, 130 were returned in Year 3, and 200 were returned in Year 4.
C1 C2 C3 C4 C5 C6
Year Shipped Quantity Shipped Returned in Year 2 Returned in Year 3 Returned in Year 4 Returned in Year 5
Year 1 10000 50 60 100 300
Year 2 15000   78 130 200
Year 3 23000     275 600
Year 4 32000       400
Shipment quantities in first row of return columns
In this worksheet, the first row contains the total number of items shipped in each year. Each column represents a different year. Each cell of a column indicates the number of items returned in each subsequent time period. For example, 23,000 items were shipped in Year 3. Of those items, 275 were returned in the following year. In the year after that, 600 were returned.
C1 C2 C3 C4
Shipped in Year 1 Shipped in Year 2 Shipped in Year 3 Shipped in Year 4
10000 15000 23000 32000
50 78 275 400
60 130 600  
100 200    
300      

Select the data structure

If the data have multiple samples, select whether the samples are in different columns or in the same column. The options depend on the censoring scheme of the data.

Right or uncensored data
One or more samples, each in a column
For multiple samples, each sample is in a different column.
In this worksheet, Days A contains the failure data for one sample. Days B contains the failure data from the second sample.
C1 C2
Days A Days B
81 77
75 74
77 70
78 71
Several samples, all in one column
The failure data are all in one column. A separate column identifies the sample for each row.
In this worksheet, Days contains the failure data for all samples. Sample ID indicates the sample for each row.
C1 C2
Days Sample ID
81 A
77 B
75 A
74 B
Interval censored data
One or more samples, each in separate start and end columns
Each sample has its own start column and end column. Usually, each sample has its own frequency column.
In this worksheet, Start time A, End time A, and Count A define the inspection intervals and the number of failures for one sample. Start time B, End time B, and Count B define the inspection intervals and the number of failures for another sample.
C1 C2 C3 C4 C5 C6
Start time A End time A Count A Start time B End time B Count B
0 2 6 0 8 16
2 4 7 8 16 27
4 6 4 16 * 157
6 * 83      
Several samples, all in one start column and one end column
The start times that define the inspection intervals are all in one column. The end times that define the inspection intervals are all in a second column. A column identifies the sample for each row. If the data have a frequency column, the sample identifiers also apply to the frequency column.
In this worksheet, Start time has the beginning time of each inspection interval. End time has the end time of each inspection interval. Sample ID identifies the sample for each row. Count has the number of failures in each interval.
C1 C2 C3 C4
Start time End time Sample ID Count
0 2 A 6
0 8 B 16
2 4 A 7
8 16 B 27
Warranty data
Shipment quantities in a column
Select this option if you recorded the total number of items shipped in a single column of the worksheet, and the number of items returned in each period in subsequent columns.
In this worksheet, the number of items shipped in each year is recorded in a single column. Each row represents shipments for a different year. The number of items returned each year is recorded in a separate column. For example, in Year 1, 15,000 items were shipped. Of those items, 78 were returned in Year 2, 130 were returned in Year 3, and 200 were returned in Year 4.
C1 C2 C3 C4 C5 C6
Year Shipped Quantity Shipped Returned in Year 2 Returned in Year 3 Returned in Year 4 Returned in Year 5
Year 1 10000 50 60 100 300
Year 2 15000   78 130 200
Year 3 23000     275 600
Year 4 32000       400
Shipment quantities in first row of return columns
Select this option if you recorded the total number of items shipped in the first row, and the number of items returned in each period in subsequent rows.
In this worksheet, the first row contains the total number of items shipped in each year. Each column represents a different year. Each cell of a column indicates the number of items returned in each subsequent time period. For example, 23,000 items were shipped in Year 3. Of those items, 275 were returned in the following year. In the year after that, 600 were returned.
C1 C2 C3 C5
Shipped in Year 1 Shipped in Year 2 Shipped in Year 3 Shipped in Year 4
10000 15000 23000 32000
50 78 275 400
60 130 600  
100 200    
300      

Select whether to analyze failure modes

If every sample in the data has a column that identifies a failure mode for each observation, the analysis can provide results by failure mode. Multiple samples can have the same failure mode column. To represent right-censored observations in the failure mode column, use an asterisk (*) for numeric columns or a space for text columns. For more information on failure modes, go to What is a failure mode?.

To analyze multiple failure modes, select In columns. The analysis adds a field for failure modes to the table for the reliability data definition. To show tables with results for individual failure modes, select Results, then select Display analysis results for individual failure modes.

To exclude failure modes, select Failure Mode Options. For Parametric Distribution Analysis, you can also select different distributions for different failure modes.

Complete the table for the reliability data definition

The values to enter depend on the censoring scheme for the data. Enter columns that are the same length. For more information on censored data, go to Data censoring.

Right censored data with censoring column

Enter the data columns and the censoring value.
Sample column
Enter a column of failure data for each sample.
Frequency column (optional)
Optionally, enter a column that identifies the number of failures for the failure time in the row. Without a frequency column, each row represents 1 failure.
Censoring column
Enter a column with 2 distinct values to identify which rows contain censored data. Enter a column for each sample.
Censoring value
Select the value from the censoring column that indicates that the row contains censored data.
Failure mode column
If the analysis includes failure modes, enter a column that identifies the failure mode for each row. To represent right-censored observations in the failure mode column, use an asterisk (*) for numeric columns or a space for text columns. Enter a column for each sample.
  • If the data have multiple samples in different columns, select Add Row for each additional sample.
  • If the data have multiple samples in the sample column, enter the column of sample identifiers in Sample ID column.

Right censored data by censoring time

Enter the data columns and the censoring value.
Sample column
Enter a column of failure data for each sample.
Frequency column (optional)
Optionally, enter a column that identifies the number of failures for the failure time in the row. Without a frequency column, each row represents 1 failure.
Time censor at
Enter a numeric value for each sample. Any sample value that exceeds the censoring time is a censored row.
Failure mode column
If the analysis includes failure modes, enter a column that identifies the failure mode for each row. To represent right-censored observations in the failure mode column, use an asterisk (*) for numeric columns or a space for text columns. Enter a column for each sample.
  • If the data have multiple samples in different columns, select Add Row for each additional sample.
  • If the data have multiple samples in the sample column, enter the column of sample identifiers in Sample ID column.

Right censored data by number of failures

Enter the data columns and the censoring value.
Sample column
Enter a column of failure data for each sample.
Frequency column (optional)
Optionally, enter a column that identifies the number of failures for the failure time in the row. Without a frequency column, each row represents 1 failure.
Failure censor at
Enter a positive integer for the censoring number in the sample. The observations with the smallest values, up to that number, represent exact failures. The observations after that number of failures represent right-censored data.
Failure mode column
If the analysis includes failure modes, enter a column that identifies the failure mode for each row. To represent right-censored observations in the failure mode column, use an asterisk (*) for numeric columns or a space for text columns. Enter a column for each sample.
  • If the data have multiple samples in different columns, select Add Row for each additional sample.
  • If the data have multiple samples in the sample column, enter the column of sample identifiers in Sample ID column.

Uncensored or complete data

Enter the data columns and the censoring value.
Sample column
Enter a column of failure data for each sample.
Frequency column (optional)
Optionally, enter a column that identifies the number of failures for the failure time in the row. Without a frequency column, each row represents 1 failure.
Failure mode column
If the analysis includes failure modes, enter a column that identifies the failure mode for each row. To represent right-censored observations in the failure mode column, use an asterisk (*) for numeric columns or a space for text columns. Enter a column for each sample.
  • If the data have multiple samples in different columns, select Add Row for each additional sample.
  • If the data have multiple samples in the sample column, enter the column of sample identifiers in Sample ID column.

Interval censored data

Enter the data columns and the censoring value.
Start column
Enter a column that contains the start times for the inspection intervals.
End column
Enter a column that contains the end times for the inspection intervals.
Frequency column (optional)
Optionally, enter a column that identifies the number of failures for the failure time in the row. Without a frequency column, each row represents 1 failure.
Failure mode column
If the analysis includes failure modes, enter a column that identifies the failure mode for each row. To represent right-censored observations in the failure mode column, use an asterisk (*) for numeric columns or a space for text columns. Enter a column for each sample.
  • If the data have multiple samples in different columns, select Add Row for each additional sample.
  • If the data have multiple samples in the sample column, enter the column of sample identifiers in Sample ID column.

Warranty data

Select the arrangement of the number of units shipped. Then, enter the columns of data.
Shipment quantities in a column
Select this option if you recorded the total number of items shipped in a single column of the worksheet, and the number of items returned in each period in subsequent columns.
  1. In Shipment (sale) column, enter the column that contains the number of items shipped in specific time periods.
  2. In Return (failure) columns, enter the columns that contain the failures or returns for the production lots in subsequent time periods.
Shipment quantities in first row of return columns
Select this option if you recorded the total number of items shipped in the first row, and the number of items returned in each period in subsequent rows. In Return (failure) columns, enter the columns that contain the failures or returns for the production lots in subsequent time periods.

Select an Assumed distribution

Select a distribution to model your data. Base your decision on process knowledge or use probability plots to evaluate the model fit. For more information, go to Distribution fit for reliability analysis.

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