The lifetime of a brake can be modeled as a Weibull Distribution with a ƛ of 1 per 50000 miles. The probability that a brake lasts longer than 30000 miles is 0.8. Find the value of parameter a
Given : P(X>30000) = 0.8
Now we have x= 30000 , = 0.00002
On substituting in F(x), we get c= 1.609
The lifetime of a brake can be modeled as a Weibull Distribution with a ƛ of...
The lifetime of a product can be modeled with a Weibull distribution with δ = 22 and β = 3. a. What is the expected lifetime of the product? b. What is the standard deviation of the product? c. The product costs $15,543 dollars to produce, but is expected to save $1,115 in costs for each year that it functions as advertised. Considering the initial cost, what is the expected savings in costs for this product? d. What is the...
The lifetime of a product can be modeled with a Weibull distribution with δ = 22 and β = 3. a. What is the expected lifetime of the product? b. What is the standard deviation of the product? c. The product costs $15,543 dollars to produce, but is expected to save $1,115 in costs for each year that it functions as advertised. Considering the initial cost, what is the expected savings in costs for this product? d. What is the...
6) The lifetime battery life of a laptop can be modeled as a Weibull variable with parameter λ = 1 per 10 years and parameter a-1.35 a) What is the probability that a laptop will last between 5 and 10 years? b) A merchant sold 40 laptops on a day with a guarantee that any laptop lasting less than 5 years will be replaced by another laptop with a 28% discount. What is the probability that the merchant has to...
The lifetime of bacteria follows the Weibull distribution. The probability that the bacteria lives for more than 10 hours is 0.7 and that it lives more than 20 hours is 0.3. The probability that among 300 bacteria more than 200 live longer than 10 hours can be computed as P(Z>a). What is the value of a?
Suppose that the lifetime of a component (in hours), X, is modeled with a Weibull distribution with B 0.5 and = 3400. Determine the following in parts (a) and (b) Round your answers to three decimal places (e.g. 98.765) a) P(X> 3500) = i b) P(X> 6000|X > 3000) i c) Suppose that X has an exponential distribution with mean equal to 3400. Determine the following probability Round your answer to three decimal places (e.g. 98.765) P(X 6000X > 3000)...
Question 4 Lifetime of a certain component can be represented by 2 parameter Weibull distribution with a-12000 and p Find the mean time to failure and median life of this component.
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The lifetime of a drill bit in a mechanical operation, in hours, has a Weibull distribution with α = 0.5 and β = 2.2. Calculate the probability that the bit will fail after 2.8 hours Answer using 4 decimals.
The life of a semiconductor laser at a constant power can be modeled by a Weibull distribution with a mean of 7000 hours and a standard deviation of 600 hours. (a) What is the probability that a laser fails before 5800 hours? (b) What is the life in hours that 90% of the lasers exceed? (c) What should the mean life equal in order for 99% of the lasers to exceed 10,000 hours before failure? (d) A product contains three...
Gamma, Exponential, Weibull and Beta Distributions (Part 3) 1. The random variable X can modeled by a Weibull distribution with B = 1 and 0 = 1000. The spec time limit is set at x = 4000. What is the proportion of items not meeting spec? 2. Suppose that the response time X at a certain on-line computer terminal (the elapsed time between the end of a user's inquiry and the beginning of the system's response to that inquiry) has...