Censoring and MTBF and MCBF Calculations

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At times, several items are tested simultaneously, and the results are combined to estimate the mean time before failure/mean cycles before failure (MTBF/MCBF). When performing tests of this type, two common test results occur:
type I censoring(also called time-truncated censoring) and type II censoring (also called failure-truncated censoring).

Note that the MTBF/MCBF (θ) is the reciprocal of the failure rate (λ).

 

Type I Censoring

This is when a total of n items are placed on test. Each test stand operates each test item a given number of hours or cycles. As test items fail, they are replaced. The test time is defined in advance, so the test is said to be truncated after the specified number of hours or cycles.

A time- or cycle-truncated test is called type I censoring.

The formula for type I censoring is:

type I

 

Type II Censoring

Type II censoring is where n items are placed on test one at a time, and the test is truncated after a total of r failures occurs. As items fail, they are not replaced or repaired.

type II

Example: A total of 20 items are placed on test. The test is to be truncated when the fourth failure occurs. The failures occur at the following number of hours into the test.

example

The remaining 16 items were in good operating order when the test was truncated at the fourth failure. What is the estimate of the MTBF?

sol01

What is the failure rate?

sol02

 

Source:

Practical engineering, process, and reliability statistics / Mark Allen Durivage

ISBN: 978-0-87389-889-8

Picture © B. Poncelet https://bennyponcelet.wordpress.com

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