Sequential Reliability Testing

This tool provides the ability to plan a sequential reliability demonstration test for verification of equipment mean time between failure (MTBF), assuming an exponential failure distribution. Input parameters include the following:

• Lower test MTBF(θ₁). The test plan will reject an item whose true MTBF is θ₁ with a probability of 1 - β.
• Upper test MTBF(θ₀). The test plan will accept an item whose true MTBF is θ₀ with a probability of 1 - α.   θ₀ = d * θ₁.
• Discrimination ratio (d). The discrimination ratio is one of the standard test plan parameters which establishes the test plan envelope. d = θ₀/θ₁.
• Consumer’s risk (β). The consumer’s risk is the probability of accepting an equipment with a true MTBF equal to the lower test MTBF (θ₁).
• Producer’s risk (α). The producer’s risk is the probability of rejecting an equipment with a true MTBF equal to the upper test MTBF (θ₀).
• True MTBF. The MTBF that would be observed if an infinite number of units were tested for an infinite amount of time.

Calculation Inputs:

1. Lower test MTBF (θ₁, hours):

2. Nominal decision risks (α & β)5% 10% 20% 30%

3. Discrimination ratio (d)1.5 2.0 3.0

4. Chart overlay options: Use failure times entered in 4A Simulate testing using true MTBF entered in 4B

4A. Comma separated value failure times, measured in cumulative unit-hours (accounting for time accumulated on all test units from test start).
152, 287, 290, 598, 782, 1126, 1215, 1456, 1620, 1650, 1746, 1923, 1992, 2140, 2586

4B. True MTBF (hours): Number of tests:1 2 3 4 5 6 7 8 9 10

Featured Reference:

Reliability Theory and Practice

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Comments/Questions:


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References:

1. Bazovsky, Igor, Reliability Theory and Practice.
2. Wald, A., Sequential Analysis.
3. Wald, A. (1945). Sequential tests of statistical hypotheses. Annual Mathematica Statistics. 16, 117-186.
4. MIL-HDBK-781A, Reliability Test Methods, Plans, and Environments for Engineering Development, Qualification, and Production.
5. MIL-HDBK-781A (Full Document), Reliability Test Methods, Plans, and Environments for Engineering Development, Qualification, and Production.
6. Epstein, B., & Sobel, M. (1955). Sequential Life Tests in the Exponential Case. The Institute of Mathematical Statistics.

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