How to use test data of subsystems

[Andrew]

I got test data for a system as a whole. This system contains two sub-systems (connected in series). I also got testing data for these two sub-systems separately. Now I want to estimate the MTTF of the System. How can I combine the individual sub-system test results with System test results to obtain a MTTF figure for the system?

Thank You.

[tarik]

Normally, people use subsystems’ data to understand the system’s reliability because of lack of data on the system level due to cost, logistic and difficulty issues related to testing the system as a whole.

In your case, you say you have data for the subsystem level and the system level. Since you can construct a reliability model using, either, the subsystem data or the system data, I recommend you use the two approaches to construct 2 reliability models and compare them as a way to perform a validation check.

1st Approach:
1- Use the data of each subsystem to construct a reliability distribution. For information about how to do life data analysis, visit: http://www.weibull.com/lifedatawebcontents.htm
2- Using the law that describes the reliability of series configuration, you can derive a reliability model that describes your system. For more info, visit: http://www.weibull.com/SystemRelWeb/series_system.htm

2nd Approach:
Simply use your system data to construct a system reliability distribution using life data analysis methods.

Once you have a system reliability model, you can then derive any metric of interest to you such as reliability at a certain time or MTTF.

Is your system (or subsystems) a repairable system?

[Andrew]

Thank You Tarik. They are non-repairable.

Can I combine 1st Sub-system test data along with whole system test data, considering all the failures happened during system testing associated to 2nd sub-system as censored, and then obtain the reliability distribution for 1st sub-system?
Similarly for second subsystem and then multiply the both to get the system reliability distribution?
I believe it will be theoretically possible. But am I going to lose any information from the data, if I do it this way?

Thank You.

[tarik]

Yes, theoretically it’s possible. It will even allow you to obtain results that are more accurate results as your data sets will be larger.

However, If you just use the system’s data, you would get an idea about how the subsystems perform when they are put together in the system as there might be some ‘interactions’ behaviors (ie. the simple series configuration may not be a completely valid assumption) and also the ‘environment’ the subsystems operate in might be different when they are part of the system.

How was your data collected for the subsystems and the system?

[Harry]

If you have the test data of the whole system, why not just use those data to estimate the reliability of the whole system.

The method your simply time the two sub-system together may not correct. It depends on the configuration of your system. If the two subsystems are independend, it is correct. Otherwise, not. The test of the whole system is telling the truth.

You can think of using Bayesian method which can incorperate your subsystem information into the calculation of the whole system. Since the systme is serie and looks sub-system 1 is more important, you can get the beta (assuming weibull distribution) of the sub-system1 and put this information into Bayesian calculation. The Weibull++7 has the nice function.