Are they independent failure modes?

Of course they are independent. It just couldn´t be other way, as they take place in the same part. The failure mode that happens first place nulls the chance of the other ever shows up. It could be the case, for instance, of a part that normally wears out but, being subjected to shocks now and then, might brake too. The part is then replaced by a brand new one and the cycle repeats.

Allow me to call your attention for the fact that the case I described involves different failure modes and not different parts each one with a predominant failure mode (in which case, the problem would be very simple to solve). Only in this later case, it would be necessary to know whether the failure modes were independent or not and, if affirmative, the crossed probabilities of one part causing the failure of the other would be necessary too.

 

Independence and Dependence has little do with if one happens then the other doesn't- Its all about the underlying mechanism. Suppose you have two identical parts from a population of parts both with a very large crack- one suffers ductile fracture due to suffering a particular loading pattern and the other suffers ultimate tensile failure under different load conditions- do you think its a concidence that these two parts failed? Yet they suffered different failure modes. You have a lot of people some of which  ate a lot of saturated fat a subgroup- do you think its a coincidence that the subgroup all die of angina or a heart attack.  

I understand your point but it doesn't correspond to the case that I described. I mean one specific component of a machine that may experience two different failure modes (it could be the case of a ball bearing which might fail due to normal wear but might break too due improper use).   

When such a situation occurs, the computation of the reorder point for parts kept in stock becomes difficult. I normally solve this type of problem by recurring to Monte Carlo simulation in EXCEL, but it takes too long and cannot be automated. Things get still worse when a preventive routine is in place and the part is to be replaced every X hours of running time.  

Thanks,
 

Dear Assis,

Typical weibull analysis for mixed failure mode has no significance, beta do not tell what is happen. But if you use the Bi-Weibull model you can analyze them and get the combined failure frequency. RELCODE soft has the chance to analyze this problem with the Bi-Weibull distribution model. If you cant get acces to RELCOE you can send me your Time To Failure of each one and i will simulate for you.An alternative that is more conservative is to get the average of lambda. Lambda(average)=-ln(R(t))/t

Regards
Fernando  

Can't you superimpose the two curves and take the highest value at each point.

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