Use DRT to reduce life test duration

[Arvind]

Hi ,

Currently we are testing 8 units to full life based on 80% reliability @80% CL. Testing products to life involves lots of resources & cost. I would like to get comments on using DRT so that we increase the sample size to may be 12 & demonstrate reliability @ a reduced life based on 80%rel @80% CL by assuming a beta value for the product. By doing this we would be reducing the cost to a great extent.

Please also let me what would be the best way to estimate the Beta value, is it better to use filed failures for this ??

Please pour in your valuable views & thanks in advance.

rgds
Arvind

[David]

Hi Arvind,

Do you have an estimate for Beta for a similar design? Any previous history? What type of failure rate do you expect the product to exhibit (infant mortality, constant failure rate, wear-out)? If you do not have any previous data from which to estimate the value of Beta, then you can assume a value based on failure rate characteristics. Another possible option is to conduct a life data test to provide you with more detailed information.

I hope this helps.

[Arvind]

Hi David,

Thanks for your inputs, i do have some field data from which i can make a reasonable estimate of Beta value & i expect it to be between 1.6 to 2.3. Is this method alright (i.e., using field data) to estimate beta value ?

However just was curious to know what did you mean by life data test ? you mean life data from a previous similar product ? can you elaborate please.

So once i have a reasonable estimate of beta value, can i proceed with DRT to execute the cost reduction objective?

Thanks
Arvind

[David]

Hi Arvind,

Using field data is fine. A life data test is a test where you test units to failure (some or all) and then analyze the data with a distribution (e.g. Weibull, lognormal, etc.). But since you have the field data to estimate Beta, that will work. You are correct that increasing the sample size will decrease the amount of time to test each unit.

Good luck with the test!

[Arvind]

Hi David,

Thanks. We have a wide range of products & by right each product/platform will have a unique Beta value. Also in my experience even products belonging to the same platform(technology) will have different failure rates, so is there any way of statistically determining an optimum beta value.

Lets say if the highest beta value i encounter with the field data is 2.3, is it ok to use this value for all products to be safe, Just wanted to know what is the risk involved in under or over estimating the beta value.

Thanks
Arvind.

[David]

Hi Arvind,

For the test design using the DRT, the required test time will increase as you increase Beta. So you can be conservative by assuming Beta = 2.3. It also comes down to hom much risk you are willing to accept. You can play with different values of Beta in the DRT to see how this affects the required test time.

I hope this helps.

[Arvind]

Hi David,

I was estimating the beta value for the field data to obtain an optimum value for DRT. Below are the values for 5 products. I have used a particular month with high failure (interms of no of units returned) & no of units suspended to estimate the parameters so that i get highest beta value.
Need your comments on the approach.

Beta Eta
2.13 60.19
1.77 68.3
1.98 52.48
1.84 59.56
1.32 91.64



I also tried using the entire data available for the products & did a warranty analysis, in this case i get a lower beta value.

Request your suggession on what value do i go for or is there a better way to estimate beta. Is there any way to get a confidence level for the estimated beta value?

Thanks
Arvind

[David]

Hi Arvind,

The required test time is higher for larger values of Beta, but you still want to use a value that is indicative of your product. I woud not recommend picking data within a certain month just to "force" a highter Beta. In this case you might as well just pick any Beta value. I would recommend using a value of Beta that is estimated from all of the data. The Beta value that you estimate is at a 50% confidence level. From this you could determine the confidence bounds on Beta. In Weibull++ 7 you can view the parameter confidence bounds, based on a given confidence level, on the Parameter Bounds tab of the Quick Calculation Pad. Given the range of the Beta values that you have mentioned, the effect on the required test time does not vary all that much. For Reliability = 0.80, Confidence Level = 0.8, Required Time = 100, Test Units = 12 and Beta = 1.6, the required test time = 72.7475. For Beta = 2.3, the required test time = 80.1444. In this case, you would have to test about 10% longer if you assume Beta = 2.3. Given the range of values for Beta that you mentioned, the required test time will not vary all that much.

[Arvind]

Hi David,

I understand your point. But my concern is that we may not be able to justify our selection of Beta value if we choose to just input some value ?? for beta.

Instead i would prefer to estimate a value for beta based on our data with 0.98 CL on parameter bounds, using the data of highest no of field failures for a particular build month so that we are conservative about Beta. The rationale is to estimate the highest Beta value that the product will exhibit. In this case its 2.4 with 0.98 CL.

Do you see any statistical violation in doing this.
Need your views Pl.

Thanks
Arvind.

[Pantelis]

Just to add something... have you thought of using a Bayesian Weibull model with a distribution for a beta prior.

For details please see link below...
http://www.weibull.com/LifeDataWeb/weibull-bayesian_analysis.htm

[David]

Hi Arvind,

I agree that you will be better off using existing data to estimate the value of Beta. Using the upper confidence bound on Beta as the input for the DRT is fine.

[Arvind]

Hi David,

If i were to use the test data to estimate the Beta value, since all are repairable systems i would want to take the first time to failure for all the units in the test & group them (add no of first time fails for all units @ a specific interval) & do a time to failure analysis. Is this approach right ?

Regards
Arvind

[David]

Hi Arvind,

That is fine as long as you are only concerned with modeling the first time-to-failure, and you are not concerned with the successive failures. Although you would not have to group the units based on a given interval. You can just use the individual times-to-failure for each unit (depending on how you are gathering the data) to conduct the life data analysis to estimate Beta (assuming a Weibull distribution).

I hope this helps.