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# According to the article “Optimization of Distribution ISBN: 9780321629111 32

## Solution for problem 96E Chapter 2

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 96E

According to the article “Optimization of Distribution Parameters for Estimating Probability of Crack Detection” (?J. of Aircraft?, 2009: 2090–2097), the following “Palmberg” equation is commonly used to determine the probability ?Pd?(?c?) of detecting a crack of size ? ? n an aircraft structure: where ?c?* is the crack size that corresponds to a .5 detection probability (and thus is an assessment of the quality of the inspection process). a.? ?Verify that Pd(c*)= .5 b.?? hat is Pd(2c*)= when ?= 4 ? c. ?Suppose an inspector inspects two different panels, one with a crack size of ?c?* and the other with a crack size of 2?c?*. Again assuming ?= 4 and also that the results of the two inspections are independent of one another, what is the probability that exactly one of the two cracks will be detected? d.? ?What happens to? Pd?(? as ? ?? ?

Step-by-Step Solution:

Answer: Step 1 of 4 The probability Pd(c) of detecting a crack of size c in an aircraft structure: (c/c ) P dc) = 1 + (c/c ) where c* is the crack size that corresponds to a 0.5 detection probability (and thus is an assessment of the quality of the inspection process). * a. We need to verifP (d ) = 0.5 (c /c ) P (c ) = d 1 + (c /c ) = 1 1 + 1 = 1 2 = 0.5 Hence, P (c ) = 0.5 d Step 2 of 4 b. Now, we need to determineP d2c ) when = 4 * (2c /c ) P (dc ) = 1 + (2c /c ) 2 = 1 + 2 4 = 2 4 1 + 2 16 = 1 + 16 16 = 17 = 0.9411 * Hence, P d2c )= 0.9411

Step 3 of 4

Step 4 of 4

##### ISBN: 9780321629111

This full solution covers the following key subjects: crack, size, Probability, detection, aircraft. This expansive textbook survival guide covers 18 chapters, and 1582 solutions. Since the solution to 96E from 2 chapter was answered, more than 438 students have viewed the full step-by-step answer. The answer to “According to the article “Optimization of Distribution Parameters for Estimating Probability of Crack Detection” (?J. of Aircraft?, 2009: 2090–2097), the following “Palmberg” equation is commonly used to determine the probability ?Pd?(?c?) of detecting a crack of size ? ? n an aircraft structure: where ?c?* is the crack size that corresponds to a .5 detection probability (and thus is an assessment of the quality of the inspection process). a.? ?Verify that Pd(c*)= .5 b.?? hat is Pd(2c*)= when ?= 4 ? c. ?Suppose an inspector inspects two different panels, one with a crack size of ?c?* and the other with a crack size of 2?c?*. Again assuming ?= 4 and also that the results of the two inspections are independent of one another, what is the probability that exactly one of the two cracks will be detected? d.? ?What happens to? Pd?(? as ? ?? ?” is broken down into a number of easy to follow steps, and 146 words. Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111. The full step-by-step solution to problem: 96E from chapter: 2 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9.

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