Weibull analysis of life time test of 8 electric motors until failure

tahirawan11

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Hi

I have performed a life time test of 8 electric motors until failure under normal stress. The time to failure is attached. I have performed a Weibull analysis to assess the reliability of motor @ 400 hours (life time of motor). Based on the results can I say that I would expect 0.4% of motors to fail by 400 hours or I have demonstrated a reliability of 99.6% @ 400 hours?

thanks
 

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Steve Prevette

Deming Disciple
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Re: Weibull analysis

Since this is only based upon 8 data values, I'd be wary of making that assertion, especially with the central 6 data values very tightly grouped and on a ramp.

Better at this point would be to use the upper dashed blue line (or the equivalent upper boundary of the green region) as the estimate, declaring whatever setting was used for the confidence interval (I assume 95%?).
 

Miner

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I have performed a life time test of 8 electric motors until failure under normal stress. The time to failure is attached. I have performed a Weibull analysis to assess the reliability of motor @ 400 hours (life time of motor). Based on the results can I say that I would expect 0.4% of motors to fail by 400 hours or I have demonstrated a reliability of 99.6% @ 400 hours?

Based on the data that you provided, I would state it as R(400hrs) = .996. However, as Steve stated, this is a small sample size, so you might want to use the 95% confidence lower bound and state R.95 Lower Bound(400hrs) = .954.

You could also use an Lq life such as L1 = 453, or L1 (.95 lower bound) = 343.

Did you have a consistent wear out failure mode, or were there different failure modes? Do you have a historical estimate of the shape parameter, Beta?
 

tahirawan11

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Thanks for the replies. When you say R.95 Lowe bound (400 hours) then shouldnt it be 0.907 (1-0.092693). How did you get 0.954? I have also attached the weibull parameteres and the estimated Beta is 7.27 so a rapid wear out mechanism, Is it common for electric motors? Unfortunately I do not have any historical estimates of the Beta as this is a new suppliers' motor we are testing. The failure mode is same in all the machines and it is 'Carbon brushes worn out'.

I do see the 6 central data values being very tightly grouped together but is it correct to say that only one point @ 590 hours can give low confidence in our results as i would always expect some variation. What else i can learn from these results which can tell me about the reliability of the motors.
 

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Steve Prevette

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Do you understand the colored areas around the curve fits and where they come from (Confidence Intervals)?
 

tahirawan11

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Ok, so i guess the Lwr. conf. was calculated from curved areas. But i thought the 95% conf. interval @ 400 hours was given in the right hand graph. See red box in the attachement
 

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Steve Prevette

Deming Disciple
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Ok, so i guess the Lwr. conf. was calculated from curved areas. But i thought the 95% conf. interval @ 400 hours was given in the right hand graph. See red box in the attachement

Don't know - I don't use that software. The charts don't label what it is, or what confidence level was used. So, I'd check whatever documentation there is for that routine.

Also consider that if it is a two sided 95% confidence interval, that translates to a 97.5% single sided upper confidence level, since you really only care about the worst case, highest estimate of the failure rate.
 

Miner

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Thanks for the replies. When you say R.95 Lowe bound (400 hours) then shouldnt it be 0.907 (1-0.092693). How did you get 0.954? I have also attached the weibull parameteres and the estimated Beta is 7.27 so a rapid wear out mechanism, Is it common for electric motors? Unfortunately I do not have any historical estimates of the Beta as this is a new suppliers' motor we are testing. The failure mode is same in all the machines and it is 'Carbon brushes worn out'.

I do see the 6 central data values being very tightly grouped together but is it correct to say that only one point @ 590 hours can give low confidence in our results as i would always expect some variation. What else i can learn from these results which can tell me about the reliability of the motors.

Our two software packages are giving slightly different results. Due to the small sample size, I am using a Least Squares Estimate. Are you using Maximum Likelihood? Also, I am using a 1-sided confidence interval, not a 2-sided CI. This is because you are not really interested in the upper limit.

AC or Brushless DC motors would not have the rapid wearout because the typical failure modes would be bearing failure or insulation breakdown. However, a DC motor with brushes would indeed for brush wearout. However, brushes are considered to be a routinely replaceable item, so I would use the reliability data to establish the PM interval for replacing the brushes, then continue your reliability testing on these same motors by replacing the brushes each time they fail and continue to run until the next failure modes appear. Ignore the brush failures during this latter analysis.

Regarding the spread of data, it is difficult to draw any conclusions with only 8 data points. This is not a criticism. Reliability testing is often done with small sample sizes for many reasons. The two extreme values have a strong influence on the shape parameter, beta (look at the slope of the line if the two outer points were removed), but that does not mean that they are incorrect.
 

tahirawan11

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I am using JMP software to perform the analysis and it offers two methods to calculate Conf. levels. 1. Wald and 2. Likelihood but both the methods gives me same results. And i agree that I am only interested in the Lwr. limit (worst case scenario).

The motors we are using are AC motors and the motors will be used in vacuum cleaners for consumer market. The product is for low price market so it is important that the motors do not fail in first 400 hours to avoid any warranty claims. On the other hand if brushes were to replace after failures can we still use weibull analysis to analyse data for non repairable system or analyse it using weibull analysis for repairable system?
 

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Miner

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It appears that JMP only uses the maximum likelihood approach for estimating the parameters like beta (not the CIs). It also doesn't appear to provide an option for 1-sided CIs.

Regarding the motors: AC motors do not have brushes (see schematic), so it is either a DC motor, or the reason for failure is not due to brush wear. If it is a consumer market, few consumers would be knowledgeable enough to replace the brushes (if DC), and if it is low price, few would have it repaired, so there would be no point to analyzing it as a repairable system.

All vacuum motors that I have seen have always been AC (no brushes), so it is most likely due to bearing failure or insulation failure from the heat generated when the beater bar jams.
 

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