What is censored data?

In reliability analysis, failure data frequently contain individual times to failure. For example, you might collect times to failure for units operating at a particular temperature. You might also collect samples of times to failure under different temperatures, or under different combinations of stress variables.

Sometimes you record exact times to failure. Other times, the exact times to failure of some test units are unknown. In this case, the data are called censored. Failure data are often censored in some way. Therefore, you may have any of the following types of observations:
  • Exact times to failure
  • Right-censored data
  • Interval-censored data
  • Left-censored data

Exact failure time data

The exact time that each item failed is known. For example, an engineer tests electric fans and records the exact time to failure of each fan.

Right-censored data

Failures are seen only if they occur before a particular time. A unit surviving longer than that time is considered a right-censored observation. Right-censored data are sometimes time-censored or failure-censored. Time censoring means that you perform the study for a specified period of time. All units still operating at the end of the study are time-censored. Time censoring is also known as Type I censoring on the right. Failure censoring means that you conduct the study until you observe a specified number of failures. Failure censoring is also known as Type II censoring on the right.

For example, suppose that an engineer tests five fan belts. Three fan belts fail in 67 hours, 76 hours, and 104 hours. The remaining two fan belts are still operating when the engineer stops the test at 110 hours. These last two fan belts are right-censored at 110 hours.

Right-censored data can be:
Singly-censored
All the test units operate for the same amount of time. Units surviving at the end of the study are considered censored data. Failed units are considered exact failures. Singly-censored data are more common in controlled studies.
Suppose you collect failure data until 12 units fail:
Item Unit Failure Time
1 Failed 18.5
2 Failed 20.5
3 Failed 22.0
4 Failed 23.5
5 Failed 24.3
6 Failed 25.0
7 Failed 25.6
8 Failed 26.3
9 Failed 27.0
10 Failed 29.0
11 Failed 32.0
12 Failed 33.0
13 Censored 33.0
14 Censored 33.0
15 Censored 33.0

Minitab interprets this data set as single censoring because the failure times of the censored items (units 13 - 15) are the same as the failure time of the 12th unit.

Multiply-censored
Test units are censored at different times. Failure times are intermixed with censoring times. Multiply-censored data are more common in the field, where units go into service at different times.
Suppose you collect failure data until 12 units fail:
Item Unit Failure Time
1 Failed 18.5
2 Failed 20.5
3 Failed 22.0
4 Failed 23.5
5 Failed 24.3
6 Failed 25.0
7 Failed 25.6
8 Failed 26.3
9 Failed 27.0
10 Failed 29.0
11 Failed 32.0
12 Failed 33.0
13 Censored 34.0
14 Censored 34.0
15 Censored 34.0

Minitab interprets this data set as multiple censoring because the failure times of units 13 - 15, are larger than the failure time of the 12th unit. If you stopped the study after the 12th failure, the subsequent times would not be greater than the time of that last failure. To have Minitab interpret the data as single censoring, you need to enter 33 in the 2nd column for rows 13-15.

Interval-censored data

Failures occur between two particular times. Interval-censored data contain uncertainty as to when units actually fail.

For example, suppose that instead of recording exactly when ten transistors fail, an engineer inspects them every 12 hours. Therefore, the engineer knows the status of each transistor (failed or still operating) only at the time of each inspection. Instead of exact failure times, the engineer records the data as failure time intervals. So, for example, a transistor may fail between 60 and 72 hours.

Left-censored data

Failures occur before a particular time. Left-censored data are a special case of interval-censored data in which failure times occur sometime between zero and an inspection time.

For example, glass capacitors are put on test at high voltage levels to accelerate their failure times. Engineers examine the capacitors every 12 hours to see which have failed. At the first inspections, 2 capacitors have failed. The failure times for these two units are left censored.

Should I use a right-censoring command or an arbitrary-censoring command?

Minitab's Reliability/Survival menu contains two sub-menus for distribution analysis. Choose the distribution submenu appropriate for your data:
  • Use the right-censoring commands when you have exact failures, right-censored observations, or both.
  • Use the arbitrary-censoring commands when your data include left-censored observations, interval-censored observations, or a varied censoring scheme, including right-censoring, left-censoring, and interval-censoring.

When should I use time censoring for test plans?

Testing all units to failure in a life test usually is not recommended, especially if you are only interested in the lower percentiles of the distribution. You should use time censoring for test plans when you have a specific period of time in mind for your test.

To minimize cost, you need to balance the test duration and sample size. For a particular precision, Minitab displays a list of sample sizes for each censoring time you provide. As time increases, the sample size decreases. Choose the time and sample size combination that minimizes costs.

For an accelerated life test plan, you only need to provide one set of censor times. Each time in the set corresponds to the censor time at a stress level. The first time corresponds to the lowest stress level, the second time corresponds to the second stress level, and so on.

When should I use failure censoring for test plans?

Use failure censoring when you are estimating lower percentiles or when you have limited test positions.

Testing lower percentiles
For any percentile, increasing the test duration improves the precision of your estimate. However, you will see little improvement in precision when you run a test far beyond the estimated percentile. For example, if you estimate the 10th percentile, you obtain important gains in precision by running the test until around 15% of the units fail, but small improvement by running the test longer. In fact, running the test beyond 15% of the units failing could bias your estimate of the 10th percentile.
Replacing test units
If you have a limited number of test positions, you can use failure censoring to determine when to replace unfailed units. For example, if you want to estimate the 10th percentile, but can only test 5 units at a time, you may want to replace all 5 units after the first failure in each group. In this case, you are failure-censoring when 20% of the units in each group have failed.
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