Weibull distribution for heat exchanger tubes

[beck admiralty]

Hi,

I am doing a project on heat exchanger. And I need to figure out how many tubes from the exchanger are needed to be inspected to ensure that the data resulted is reliable. Is Weibull Distribution can be applied to do such a prediction? Is there any good reference to find out more information about that. Coz, this far, I only find that Weibull can only be used to predict the failure, but still have to inspect the entire badge. But it is time consuming and costly.

Thanks,

beck

[Pantelis]

Weibull analysis is not limited to failure data. Now with regards to your heat exchangers, what exactly are you doing with each inspection (and what kind of data do you have related to each inspection). Are you measuring some type of quantity, looking at an event (failed/not failed)…

[Dennis Craggs]

The usage of statistical distribution is not limited to failure data. Weibull analysis can be used to describe the distribution of variables, i.e., diameter, wall thickness, length, hardness, ... Of course, other distributions may be used, i.e., the Normal, LogNormal, and others. The distribution which best describes the data should be used.

[beck admiralty]

Actually, what I am doing is I am trying to find out the minimum tubes that are needed to be inspected. Let say, from 1000 tubes, maybe I only need to inspect 30%? 40%? or maybe 55% of the total 1000 tubes? I do not know. So I am trying to find out that percentage. I am looking at event(failed/not failed) with a few different faliure modes. So, by using the Weibull, I can find out the percentage from the total tubes. Is it possible to do such a calculation?

Thanks,

beck

[Pantelis]

Its possible. What are you measuring (what is the random variable)?

[Dennis Craggs]

If the consequence of failure is severe, such as a boiler explosion, then perhaps you should inspect all of the tubes. If the consequence is less severe, a sampling plan may be acceptable. But, what is being measured or checked? Is it an Attribute or Variable?

If an attribute, such as the presence of a crack in the tube and there is no tolerance for cracks, then the analysis is go/nogo. With a finite population (1000) the hypergeometric distribution and associated sampling plans are acceptable. Check Dodge-Romig tables. Then you need to define producer and consumer risks and an AQL.

If the characteristic is a variable, such as the length of a crack and there is a maximum acceptable crack length, then a variable distribution may be used, i.e., Weibull, Normal, LogNormal..., but then you need a specification limit.

Working with variable measurements will be a lot easier than working with attributes. Also, query the design and manufacturing engineers very carefully. Engineers are very crafty and creative at converting variable measurements to attribute measurements. (I am an engineer so I know.)

[beck admiralty]

hm, actually i am new to weibull things. so i don't really familiar with all the terms. i do not really understand what random variable means. But I am measuring based on the wall thickness of the tubes. Currently, I have The New Weibull Handbook with me, any reference chapter in this book to do such a calculation?

[beck admiralty]

so, anyone can show me how to get such a calculation? i mean to find out the percentage. I cannot find such a calculation from the handbook.

[Dennis Craggs]

What failure mode is anticipated?

If it is major, like a boiler failure or explosion with potential loss of life, then perhaps a 100% inspection is required rather than a sample, assuming the wall thicknesses may be measured in a non-distructive manner.

If the failure mode is a simple violation of specification limits, then a sample is appropriate provided you are taking variable measurements, like your wall thickness. This is appropriate even if the measurement process is distructive.

The objective is to calculate upper and lower population limits (LPL and UPL) that will contain the population of tube wall thicknesses. Mentally picture the bell shape curve of thickness measurements contained within the specification limits.

If the data is normally distributed, you could try a k-factor analysis. In k-factor analysis, you start with the sample size (n), sample mean (xbar), sample standard deviation (sigma), and the upper specification limit (USL) and lower specification limit (LSL). The sample size is flexible, perhaps n = 20. You don't need large sample sizes if you are analyzing variable data.

You want to estimate limits that will contain P% of the population to C% confidence. For 1000 tubes, you may want to select P=99.9 and C=90%.

These population limits need to be contained within the specification limits as follows:

LSL < Xbar - K*sigma < Xbar + K*sigma < USL

where the LPL = Xbar - K*sigma
and the UPL = Xbar + K*sigma

Twenty is a reasonable sample size for many situations. I don't have a k-factor table available right now, but I will respond tomorrow with the information for the parameters proposed above. Also, provide the technical reference.

This is test planning. Without prior knowledge of the distribution of wall thicknesses, one has to make assumptions. I start with the normal. Since wall thickness conforming to specification is important, we bootstrap our knowledge by taking a small sample. From the sample, we can do further analysis: K-factor analysis, infer the type of distribution; use Weibull and confidence limits to define population limits; compare the data and distribution to specification limits, etc... Once we have data, a whole new world of analysis opens up.

[Dennis Craggs]

A technical reference for the K-factor analysis is Experimental Statistics Handbook 91, United States Department of Commerce, National Bureau of Standards, Section 1-8 and Tables A-6 and A-7. The statistical models that were used to generate the tables are quite involved and require an indepth literature search.

An online technical resource is the Engineering Statistics Handbook at http://www.itl.nist.gov/div898/handbook/