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Let's say I have a segment of pipe of length $X$ that I want to test the integrity of by way of a hydrostatic pressure test. That is, I isolate the ends of the pipe and pump water into it until it a very high pressure is attained and hold that pressure on the line for an amount of time. If the pipe does not burst, leak, etc. during the test, then I say the pipe passed. Else the pipe failed. Let $Y$ = {pass, fail} = {1, 0}. Thus $Y$ is a discrete, binary, random variable.

However I don't want to test the whole line. I only want to test a sample interval of the line. Let $Z$ = the length of the interval sampled, $Z < X$.

Assuming the sample interval of pipe passes the hydrostatic pressure test, how large must $Z$ be so that I can assume the entire line of length $X$ would pass a hydrostatic pressure test with 95% confidence? Do I need to give a confidence interval? If so, let's say +/-5%.

Assume the probability of failure is uniform along the entire length, $X$. Also, by 95% confidence, I mean my confidence level is 95%. My degree of belief is 95%. And by +/-5% confidence interval, I mean the margin of error is +/-5%. Please forgive me if I am using these terms incorrectly. Please feel free to educate me. Thanks for your help.

kjetil b halvorsen
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Mark B
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    What do you really mean by "95% confidence ... +/-5%"? It reads like you are discussing a confidence interval for a confidence interval! – whuber Nov 20 '14 at 21:14
  • Confidence Level = 95%. Confidence Interval = +/-5%. Am I thinking about this incorrectly? – Mark B Nov 20 '14 at 21:18
  • Please explain what *you* mean by the two terms "confidence level" and "confidence interval." (It sounds like you may be using one or both of them in unconventional ways.) – whuber Nov 20 '14 at 21:20
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    Confidence Level = Degree of belief. How "sure" I can be. Confidence Interval = Margin of error. – Mark B Nov 20 '14 at 21:22
  • Forgot to say that the pipe is assumed to have uniform probability of failure along the entire length, $X$. – Mark B Nov 20 '14 at 21:41
  • You ought to place those definitions and that assumption prominently in your post, Mark, because (1) the definitions differ from the usual ones and (2) the assumption--although likely necessary for doing any calculations--is probably not physically correct. (One should at least entertain the possibility of different failure rates near joints.) You also probably need to assume that the failure probabilities exhibit no correlation along the length--which also might not be physically correct. – whuber Nov 20 '14 at 21:46
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    Thank you. I made your suggested edits. I am aware that the uniform distribution assumption is probably not physically correct. However that what I am willing to start with. I am certainly open to entertaining other failure rates as my project evolves. Thanks again for your help. – Mark B Nov 20 '14 at 22:02
  • I think we need some strong assumptions about the failure generating process. – Glen_b Nov 20 '14 at 23:59

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