Let\'s revisit problem 1 of Homework 2. Now that you learned about Weibull distr
ID: 3207754 • Letter: L
Question
Let's revisit problem 1 of Homework 2. Now that you learned about Weibull distributions, you start doubting your assumption of random failures (exponential distribution) for the projector bulb failures. Your expectation is that the bulbs should have an increasing failure rate. Basically, an increasing failure rate implies an underlying degradation mechanism with time, or in other words, the older the bulb the more likely it is to fail. Using Weibull++ and a 2-parameter Weibull model confirm or refute your new expectation. If the model is no longer an exponential distribution (as assumed in Homework 2)and using the same failure times that were: 513, 649, 740, 814, 880, 944, 1009, 1078, 1161 and 1282 hours. Estimate the mean life of the bulbs. Estimate the B10 life of the bulbs. Estimate the reliability of the bulbs after 200 hours of operation. Assuming 1,000 bulbs will be fielded, estimate how many would fail after 200 hours. Estimate the warranty time for the bulb if you do not want failures during the warranty period to exceed 2%.Explanation / Answer
3.1) Using 2-parameter weibull model, we can state that as the older the bulb gets, more likely is it to fail.
3.2) Mean life of bulbs=5070/10=507
3.3) To estimate the B10 life of bulbs (i.e. the time by which 10% of bulbs would fail), we get 570 i.e. Approximately 10% of the population will get failed after 570 hours of operation
3.4) Reliability of the bulbs after 200 hours of operation is 0.998406 or 99.84%.
3.5) In this case, first we need to calculate the probability of how many bulbs would fail after 200 hours of operation and multiply by 1000. The probability of failure is 0.16%. Multiplying it by 1000, we get 1.6 or approximately 2 bulbs would fail after 200 hours of operation.
3.6) Reliable life would be selected as 0.98 in this case and the answer would come to 377 hours
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