Weibull analysis great support for maintenance budgeting

Aug. 11, 2008
Executive Editor Russ Kratowicz, P.E., CMRP, shows you how to use Weibull analysis to support your requests for a greater maintenance budget.

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.

For product selection

Weibull analysis helps if you need to choose the most reliable product, assuming that the competing vendors provide life cycle test data or you subject the designs to your own run-to-failure field testing. A Web resource that explains how this is done is operated by Quanterion Solutions Inc., Utica, N.Y. For a concise description of the input data and the interpretation of the analytical results, with none of those perhaps confusing intervening mathematical machinations, go to http://quanterion.com/ReliabilityQues and click on the link to the article titled “Which Design is More Reliable? Weibull Provides Answers!” Be forewarned, the several offers of free stuff you’ll see on this site require you to register your e-mail address, if not your entire identity.

Bedtime reading

Weibull analysis is only one of many approaches to modeling your reliability data. The good folks at The Statistical Engineering Division of NIST’s Information Technology Laboratory, Gaithersburg, Md., know about all of them and is willing to impart its collective wisdom to those of us who fund their efforts through our taxes. In fact, the Laboratory has an online handbook that should serve you well if you’re into numbers and maintenance statistics. Put on your reading glasses and crack the cover on www.itl.nist.gov/div898. Listed under the “Products and Services” heading at the center of the page is a link to the “NIST/SEMATECH Engineering Statistics Handbook.” This is a biggie - you’ll wind up with more than 3,100 pages if you download the entire PDF version, an action definitely not recommended. Instead, use the search feature on the left side. Enter “weibull” and look for the entry named “ Weibull Distribution.” Then, read about Weibull and take advantage of the many links to cross-referenced pages.

You’ll definitely want to investigate the software offerings also shown under the “Products and Services” heading. When the page opens, take a look at Dataplot, a software package for graphical analysis on data you furnish. When you get to the Dataplot home page, click on “Dataplot Summary” to see the 17 broad categories of analysis it will handle. And each category has a string of subcategories and finer gradations. Even if you have no practical application for the software, at least tell some college engineering undergrad about it.

From your peers

The concepts underlying Weibull analysis provide powerful objective evidence about the efficacy of the current maintenance philosophy the plant is using. Despite the fact that the technique has been available for some time, its reliance on heavy mathematics and the user’s uncertainty about its applicability to a given situation can be off-putting. Well, friends, there’s no sense trying to reinvent the Weibull wheel when many of your associates in industry have gone this way before you. How would you like to tap into an online forum dedicated to Weibull and related issues? It’s there for the asking. Simply ask your desk rodent to go in the direction of www.reliasoftforums.com/archive for the Q&A hosted by ReliaSoft Corp., Tucson, Ariz. Click on “Weibull and Life Data Analysis” and you’ll be able to access more than 120 forum threads, each of which begins with a question from a user. These threads sometimes have only one answer from someone in the company’s technical support group. Others generated a lively debate. You can read for free, but if you want to participate, the cost will be a loss of your anonymity.

Another reliability-based forum comes from the Reliability Information Analysis Center (RIAC), a part of the Department of Defense (DoD). As its mission statement says, RIAC provides “the information, tools, training and technical expertise in the engineering disciplines of reliability, maintainability, quality, supportability and interoperability (RMQSI) to support accurate decision-making and implement cost-effective solutions throughout all phases of a product or system life cycle.” That’s government speak for products that are, of course, military assets. Anyway, to see the forum postings you’ll need to score a direct hit on http://theriac.org and click on “RIAC Forum” found under “Help Desk” on the left side of the page. The most relevant of the choices might be those about data analysis and testing, maintainability and supportability, reliability models and non-electrical component reliability.

References galore

ReliaSoft has a related Web site, www.weibull.com, which has several points of interest for the industrial reliability sleuth. For example, the content listed under “More Reliability References” is freely available. You might want to explore the “Blueprint for Implementing a Comprehensive Reliability Engineering Program.” It’s a 30-page Adobe document that is truly comprehensive in its scope and would be helpful to anyone wanting to learn more about improving a reliability program. The link to “Military Handbooks and Standards” will give you access only to the Mil-specs related to reliability. They’re listed in numerical order, not alphabetical order, so searching by topic is unnecessarily more difficult than it needs to be. The case studies aren’t universally useful because they’re based on success stories in which the company’s software figures prominently.

Take a look at the “Free Downloads” at the bottom center of the page. The offers of evaluation software and free reliability software tools will require you to register. The training and example guides are essentially user manuals for the company’s software products. But, should you elect to try your hand at graphical reliability analysis using pencil and paper, this site lets you download blank exponential, Weibull, log-normal and normal graph paper. Opening the link to the graph paper also gives you access to rank tables.

E-mail Executive Editor Russ Kratowicz, P.E., CMRP, at [email protected].

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