Desired failure rate, reliability analysis, confidence levels
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A "one-shot" device can be used only once; after use, the device (e.g. a nuclear weapon, space shuttle, automobile air bag) either is destroyed or must be rebuilt. The destructive nature of a one-shot device makes repeated testing either impractical or too costly. Hence, the reliability of such a device must be determined with minimal testing.
Consider a one-shot device that has some probability p of failure. Of course, the true value of p is unknown, so designers will specify a value of p which is the largest defective rate that they are willing to accept. Designers will conduct n tests of the device and determine the success and failure of each test. If the number of the observed failures x, is less than or equal to some specified value k, then the device is considered to have the desired failure
2 rate. Consequently, the designers want to know the minimum sample size needed so that observing K or fewer defectives in the sample will demonstrate that the true probability of failure for the one-shot device is no greater than p.
a. Suppose the desired failure rate for a one-shot device is p = 0.10. Suppose also that designers will conduct n = 20 tests of the device and conclude that the device is performing to specifications if K =1 (i.e., if 1 or no failure is observed in the sample). Find p(x≤1)
b. In reliability analysis, 1- p(x≤ K) is often called the level of confidence for concluding that the true failure rate is less than or equal to p. Find the level of confidence for the one-shot device described in part (a). In your opinion, is this an acceptable level? Explain.
c. Demonstrate that the confidence level can be increased by either (1) increasing the sample size n or (2) decreasing the number K of failures allowed in the sample.
d. Typically, designers want a confidence level of 0.90, 0.95, or 0.99. Find the values of n and K to use so that designers can conclude with at least 95% confidence that the failure rate for the one-shot device of part (a) is no greater than p = 0.10.
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Solution Summary
The desired failure rate, reliability analysis and confidence levels are examined.
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"
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