Tools › Reliability › Growth and Testing › Reliability Demonstration Test › Example
Demonstrating a reliability of 0.90 at 90 % confidence for a 1,000-hour mission: success run, MTBF test, sequential test and Weibull zero-failure plan
| Tool | Reliability Demonstration Test |
| Source | Illustrative requirement worked by the closed forms of U.S. Department of Defense (1996), Handbook for Reliability Test Methods, Plans, and Environments, MIL-HDBK-781A, Sections 5.9 and 5.10; the NIST/SEMATECH e-Handbook of Statistical Methods, Section 8.3.1.1; and Abernethy, R. B., et al. (1983), Weibull Analysis Handbook, AFWAL-TR-83-2079, Chapter 5. |
| Level | Professional |
Problem
A product must show a reliability of at least 0.90 at 1,000 hours with 90 % confidence. How many units must survive one mission without failure, how much total test time demonstrates the equivalent MTBF, what do a fixed-duration plan and a sequential test with 10 % risks and a discrimination ratio of 2 require, and how long must ten units run without failure if the failure mode is Weibull with shape 2? Unit cost 2,000 and 15 per unit-hour of test.
Inputs to Enter
- Plan: all plans compared; R = 0.90, confidence 90 %, mission 1,000 hours, 0 failures allowed
- Discrimination ratio 2.0, producer's risk 10 %, 10 units on test; design reliability 0.97 for the pass / fail sequential test
- Weibull shape 2.0, 10 units available; cost 2,000 per unit and 15 per unit-hour, 3 to 40 units in the search
Answers
- Success run: n = ln 0.1/ln 0.9 = 21.85, so 22 units without failure (38 with one failure allowed, 52 with two); 22 passes demonstrate R = 0.9006
- Exponential: MTBF 9,491 h, test-length factor 2.303, total test time 21,854 h with no failure; fixed-duration plan accepts 14 or fewer failures in 20.13 θ1 (true producer's risk 8.68 %)
- Sequential test (MIL-HDBK-781A constants): a = −3.170, c = 2.755, b = 0.7213 per θ1, truncated at 15 failures and 20.60 θ1; exact risks 12.79 % and 11.48 %
- Weibull β = 2: characteristic life 3,081 h; ten units each 1,478 h without failure; cheapest plan 3 units for 2,699 h each at a cost of 127,456.51
Notes
The default inputs are this case; press Submit. The requirement is illustrative; the formulas are checked in the tool's test script against the NIST test-length table, the twelve MIL-HDBK-781A fixed-duration plans, Test Plan III-D and Tables 5.1 and 5.2 of AFWAL-TR-83-2079.