# Statistical software helps evaluates the reliability of products

Paul Boughton
In today's business environment, design engineers constantly need to evaluate the reliability of their products. The ability to define the probability that a product will perform its purpose for a specified period of time under precise environmental conditions is one type of reliability method which could be used.

Through a Demonstration Test Plan using Minitab Statistical Software, it is possible to prove, through testing, that a reliability specification or a redesigned system has been improved for reliability through sample size, test time and number of failures. This method verifies that only a certain number of failures occur in a set amount of time.

There are two different types of tests:

- Substantiation tests provide statistical evidence that a redesigned system has suppressed or significantly reduced a known cause of failure, eg proving that a redesigned jet engine turbo pump is better than the original.

- Reliability tests provide statistical evidence that a reliability specification has been achieved, eg if the reliability of the turbine engine combustor at 2000 cycles exceed 99 per cent.

Here is an example: To give a working example, a thermostat has been redesigned to increase its reliability. Six thermostats are available for testing. The design engineer will need to determine how much time they will need to test these units, with 0 failures, so that they can be 95 per cent confident that the time at the 5th percentile is at least 421 hours.

The failure times of the original thermostat fit a Weibull distribution with a shape of [g26] = 1.9.

Using the hypotheses:

- H0: 5th per centile = 421 hours.

- H1: 5th per centile > 421 hours.

Maximum number of failures Entering 0 results in the smallest sample size and test time. However, if just one failure occurs, the demonstration test fails and you cannot conclude that you have achieved the desired reliability.

Sample sizes or testing times The choice may be made as to whether to fix the sample size and determine the test time for each unit or the reverse option.

Interpreting the results the figure shows the Minitab Statistical Software results, while also displaying the sample size and testing time above the graph. This shows that six units each need to survive 1395 hours to demonstrate the desired reliability.

Ratio of improvement The x-axis in the graph is the ratio of improvement from the specified desired reliability. For example, a ratio of improvement of four means the true 5th per centile is 4*421 or 1684 hours.

The graph displays the likelihood of demonstrating the desired reliability for different ratios of improvement. The likelihood of passing the test appears as a percentage, this is the power of the test. In this particular example, the power is greater than 0.80 (a common reference point) for ratios of improvement greater than four. This means that the probability that you will pass the demonstration test when you have a real 5th per centile of more than 4*421 or 1,684 hours is greater than 80 per cent.

Enter 80 or XX at www.engineerlive.com/ede

Minitab Ltd is based Binley, Coventry, UK. www.minitab.co.uk