Weibull analysis great support for maintenance budgeting

Executive Editor Russ Kratowicz, P.E., CMRP, shows you how to use Weibull analysis to support your requests for a greater maintenance budget.

By Russ Kratowicz, P.E., CMRP, executive editor

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We owe a lot to the theoreticians who can start with a blank sheet of paper and noodle their way into something that can be applied to the issue of plant reliability. Consider Jean Baptiste Joseph Fourier, whose work ultimately led to the idea of Fast Fourier Transforms, the technology that made modern vibration analysis possible. Gustav Kirchhoff and Max Planck codified the equations that describe black body radiation, which, of course, forms the basis for the way your infrared camera interprets images. Nearly everything that engineers get involved with on the plant floor is the end of a chain of developments and improvements on something that started with the pencil scratchings of some brilliant person a long time ago.

Then, there are the mathematician types, those who know more about the possible combinations and permutations of those 10 digits than anyone. Sometimes they invent a protocol that provides us with a crystal-clear approach to answering a question with more precision than we ever thought possible. One such example is Waloddi Weibull, who developed an algorithm that finds application to reliability and failure analysis. This month, we’re going to slosh through the digital morass we call the Web in search of practical, zero-cost, noncommercial, registration-free resources that will help you prove, unambiguously, that your plant reliability initiatives are helping to keep your plant competitive in this global market. Remember, we search the Web so you don't have to.

The big picture

Weibull analysis can be a daunting exercise if you’re not prepared for it. A quick side trip to Wikipedia is a good place to begin exploring and learning how to apply it to maintenance and engineering. Open up http://en.wikipedia.org/wiki/Weibull_distribution, for a page that’s heavy with the theoretical and abstract mathematics underlying the analysis. Before your eyes glaze over, though, take advantage of the “External links” section at the extreme bottom of the page. Here you can read a biography about Weibull. Pay particular attention to the last few lines of this story, which appear just above the author’s contact information and the bibliography. Another external link will let you read a reprint of Weibull’s original 1951 paper, in which he methodically derives the mathematics behind his approach using some degree of rigor. The link to Mathpages concludes with a numerical example that shows how to do Weibull analysis with pencil and paper. The article about using Microsoft Excel for Weibull analysis includes a worked out numerical example and walks you through the process, step by step. You also can download the Excel spreadsheet used in the example.

Plot the data

If you’re going to perform Weibull analysis the old-fashioned way, you’ll need several sheets of something called, amazingly enough, Weibull paper. It’s graph paper that features nonlinear axes, not something you’re going to find in the local stationery store. Just mark up a sheet of plain-vanilla graph paper to get the appropriate axis configuration or, because this is the 21st century, you can use your computer and printer. If you elect the latter option, Graph paper printer is the name of a software package that you can install on your PC or network. It has three features to recommend it. First, it’s totally free. Second, it can be used to generate nearly every type of graph or chart you’ve ever seen in your life. As the author claims, the software prints “graph papers, music manuscripts and pattern papers, with user-defined sizes and colors.” Third, loading it to your machine adds no DLL files and leaves the registry unchanged. One can’t expect a free, digital wonder to be any more unobtrusive than that. This work of art is brought to you through the kind generosity of Dr. Philippe Marquis, biologiste des hopitaux, in Metz, France. Pay a visit to http://pharm.kuleuven.be/pharbio/gpaper.htm for the self-explanatory instructions for downloading. The only potential drawback is that the graph layouts are dimensioned in metric units.

Practical examples

Barringer & Associates Inc., Humble, Texas, is a reliability consultant and purveyor of reliability software. The company’s Web site (www.barringer1.com) has much relevant information for the plant professional, more than I have space to highlight here. You’ll need to explore it on your own. But, you might want to start by opening the home page and scrolling down to the section called “Handy Tools & Information” and click the entry titled “Problems of The Month.” This gives you links to a selection of articles that explain how Weibull analysis can be applied to pump seals, relief valves, process reliability and other practical concerns in the typical plant setting. Look for the article about NASA. It’s a study in the simplicity of two points determining a line on a Weibull chart. In spite of the fact that only two space shuttles have experienced fatal crashes, Weibull analysis uses that pair of data points to predict when the next will occur, assuming NASA keeps the craft flying while maintaining its current reliability trend. Then, check out the link to “Free (Or Low Cost) Software” to investigate, among other things, the RAPTOR software from the military that models reliability, availability and maintainability.

Case in point

A protocol related to Weibull analysis goes by the name Crow-AMSAA. It was originally developed for the U.S. Army Materiel Systems Analysis Activity, hence the AMSAA acronym. And, it was Dr. Larry H. Crow who realized it could be represented as a Weibull process. Because you didn’t ask how to build a watch, I now direct your attention to a case study that used the Crow-AMSAA technique to analyze the forced outages and reliability at a New Zealand power-generating station. The first six pages of this 22-page presentation cover the background and justification for the work. It’s on that seventh page that the data analysis begins and continues through subsequent pages to explain how and why various conclusions became obvious. It might not be incredibly detailed, but it gives a flavor of the power of quantifying reliability gains or losses. The paper is posted at www.plant-maintenance.com/articles/Crow-AMSAA.pdf for your edification.

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