# System Reliability Projections using the Series Probability Formula

#### SteveTIB

##### SteveTIB
I am trying to calculate our system "reliablity projection" using the series probability formula, Rs=(Ra)(Rb)(Rc).... I have received performance data from suppliers, e.g., 1,00,000 hrs or 1,000,000 cycles, and calculated a failure rate (lambda) based on Chi Square (X^2) where:

lambda=X^2(1-a)/2t
a=1-percent confidence desired (.05)
r= number of failures = (0)
dof=degrees of freedom= 2(r+1)
t= device hours= supplier data

I want to calculate Reliability from the reliability equation: R=e^(-lambda(T)), where "T" is a specified interval of time, but don't know:

1) Is there an industry standard definition for "T", e.g., machine life, shift duration, preventive maintenance interval, etc., or can I make and state an assumption?
2) Is this even a statistically valid way to calculate a "reliability projection"?

Z

#### Zanzi

Steve,

I have always worked on the premise that 'T' relates to a period of time that is defined as the shift period. The standard period I use is 8 hours (unless otherwise defined).

If you are not sure you could clarify the T value with your customer or define the rationale for yourselves always using 8 hours (or whatever period you chose). Basically as these figures are predictions simplify quantify you assumptions, e.g. shift period etc.

With regards the calculation, it is statistically valid in terms of calculating the reliability over time, however I would typically calculate lamda as the failure rate, using the formula -

Total number of equipment failures / operating time = 1/MTBF

I hope that this helps and good luck - I'm currently trying to fight my way though reliability predictions as we speak so it woudl be good to know how you get on - I have no end of trouble getting reliability information from suppliers, so any ideas you have would be appreciated.

Thanks

#### SteveTIB

##### SteveTIB
Reliability Projections - Supplier Data

Zanzi,

Thanks for your input. We did use a self defined mission/shift time "T" to make our calculations. I received a response on the SAE discussion site, the G-11 Reliability, Maintainability, Supportability and Logistics Division discussion forum confirming, as you did, this method.

Regarding your problem of getting supplier data, I wish I had an answer. Getting supplier data was excruciatingly painful and provided very little value and return on our "investment".

I am currently working on defining how we will make reliability projections so that we don't have to do this time consuming exercise that adds no value to our product, either for us or our customer.

Wish I had more to offer.

Steve

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