Check a requirement and plan a test

Requirements usually arrive as one line in a specification: B10 of at least 500 hours, at 90% confidence. That's two questions. Do the data you have already show it? And if they don't, how many units do you have to test, for how long, to show it?

Reliafy answers the first from a fitted life model and the second on the Test planning page, and one leads straight into the other. This guide uses the sample bearing model (a Weibull fit to 30 failure times) and the requirement B10 ≥ 500 hours at 90% confidence.

Check the requirement against the model

Open the model. At the foot of the Life card is a Requirement row: click Check. Enter the B-life as the percent failed (10 for B10) and the Required life (500 hours). The Confidence is the Life card's, 90% here. Press Check.

The requirement is judged on the lower bound, not the estimate, so a pass holds at that confidence:

✕ Does not meet: at 90% confidence B10 ≥ 467 hours, below the 500 required. Best estimate 582.

The best estimate meets it, but these data can't show it at 90% confidence yet: more data or a demonstration test could.

This is the common, frustrating case: the bearings probably are good enough (582 > 500), but 30 failures can't prove it at 90%. Try 450 hours instead and the verdict is Meets: 467 is at or above 450. The row on the Life card keeps the answer (B10 ≥ 500 · Does not meet) while you stay on the model.

A lower confidence would pass sooner, but the confidence is part of the requirement, so change it only if the specification allows. To see how the bounds move with confidence, read B-lives and confidence bounds.

Plan a test to demonstrate it

When the verdict is Does not meet, Plan a test to demonstrate this opens Test planning on its Demonstration tab with the requirement already filled in: a pass/fail test of B10 ≥ 500 hours at 90%, in hours, solving for the number of units to test. It also offers the model's Weibull shape: β from Bearing life — Weibull (sample): 2.5, 95% interval 1.88–3.32.

Press Compute with Failures allowed at 0 and a Test length per unit of 1 (× the life):

Test 22 units for 500 hours each; pass if none fail.

That's the classic success run: if 22 units all survive 500 hours, B10 ≥ 500 is shown at 90% confidence. It needs no assumption about the distribution, which is its strength and its cost.

Make it shorter or smaller with a known shape

If you're willing to assume the Weibull shape, each unit can be tested for longer than the requirement, and one long survivor counts for more than one short one (the extended success run, or Weibayes). Choose Lower bound 1.88 (conservative) for β, set the Test length per unit to 2 (× the life), and compute:

Test 6 units for 1,000 hours each; pass if none fail.

Six units instead of 22, at the price of 1,000 hours on test each. Use the lower bound of β rather than the estimate: if the true shape is lower than assumed, the test demonstrates less than it claims, and the plan's Assumptions say so.

Keep a good design from failing the test

A zero-failure test sized only for the consumer's risk has a catch: a design that is genuinely good can still fail it by bad luck. The result says how likely that is for a design exactly at the target (it passes 9.8% of the time), but not for a better one.

Fill in Design's true reliability (the reliability you expect the design really has at 500 hours, say 97%) and a Producer's risk (the chance you accept of failing that good design, say 20%). The plan now chooses the failures allowed as well:

Test 19 units for 1,000 hours each; pass if ≤ 3 fail.

A design at the target still passes 9.7% of the time; one with 97% reliability fails 13.4%.

More units, but a test a good design will pass 87% of the time instead of being a gamble.

Weigh the trade-off

The chart under the plan is the whole trade-off: the units to test against the test length per unit, one line for each number of failures allowed, with this plan marked. Details gives the same as a table, test lengths from 1× to 3× the life: at 1× and 0 failures it's 22 units; at 3× it's 3. The Operating characteristic chart below plots the chance of passing against the design's true reliability, with the target and the good design marked: the two risks of the test, in one picture.

Save analysis keeps the plan under Strategy, so the reasoning behind the test is on record when someone asks why it's 19 units.

Without a model

The planner works without a fitted model too: open Strategy → Test planning and type the requirement on the Demonstration tab. Choose Reliability over a mission for a requirement written as a reliability ("R ≥ 95% over 2,000 hours"), or the MTBF (constant rate) test type for an MTBF requirement. Solve for can also give the test time per unit for a number of units you already have.

Other kinds of test

A demonstration test answers one question: does it meet the target? The other tabs on Test planning answer the questions that come before and after it. Each opens with a worked example: press Compute to see it, then put in your own numbers. Every plan is free.

• Demonstration: show a design meets a reliability, B-life or MTBF target. Use it when a specification or a customer sets a pass mark.
• Sequential test: the same question, but you check after every failure and stop as soon as the answer is clear. Use it when test time is dear. The example (show an MTBF of 1,000 hours, where a good design has 2,000) decides a good design after about 10,800 hours of testing on average, against 20,100 for a fixed-length test with the same risks. The accept and reject lines tell you, failure by failure, whether to stop.
• Life test: how precisely a test will estimate a B-life or the mean life, rather than pass or fail it. Use it to size a test before you fit a model to its results. In the example, 30 units stopped at 500 hours give about 6.6 failures, enough to pin B10 down to within a factor of 1.5. Solve for turns it round: the units or the test length a precision needs.
• Accelerated test: which stresses to test at, and how many units at each, to estimate life at normal use. Use it before a high-stress test. See accelerated life testing for planning one from a fitted model.
• Comparison: did a change work? The operating time (one fleet, before and after) or the units (old and new side by side) it takes to tell a real drop in the failure rate from luck. Use it before you claim a design change or a new maintenance task made a difference.

The precision a life or accelerated plan quotes is an approximation that holds for large tests. Simulate this test (Pro) checks it: Reliafy runs your exact test hundreds of times, fits each result, and shows how far the estimates spread.

Old links to the demonstration test page still work: they open the Demonstration tab.