Larry George — Active Contributor

“Component D” had some failures in its first 12 months. How many more would fail in 36-month warranty? ASQ’s Quality Progress Statistics Roundtable published the data and Weibull analysis. The data included left-censored failure counts collected at one calendar time. The Weibull analysis included actuarial failure forecasts. This article describes nonparametric alternatives to Weibull and quantifies extrapolation uncertainty. The nonparametric forecasts are larger than the Weibull forecasts. Alternative extrapolations of nonparametric failure rates from data subsets quantify uncertainty. [Read more…]

I learned actuarial methods working for the USAF Logistics Command. We used actuarial rates to forecast demands and recommend stock levels for expensive engines tracked by serial number, hours, and cycles. I had a hunch that actuarial methods could be applied to all service parts, without life data. [Read more…]

Ergodicity means that cross-section probabilities equal longitudinal lifetime probabilities. (“Ergos” is Greek for “work.” Think of “ergonomics”.) Ergodicity means that we can estimate age-specific field reliability functions from cross-section data: ships (installed base) and returns (complaints, failures, service parts’ sales, etc.). Ships and returns provide information about lifetimes. Returns are the superpositions of failures of products or their parts started at different times. What does ergodicity have to do with toilet paper? [Read more…]

Andrew Vázsonyi led an interesting life. He collaborated with mathematician Paul Erdös, he was co-founder of The Institute of Management Sciences, and he wrote “Which Door has the Cadillac: Adventures of a Real-Life Mathematician”. Around 1970, Andrew Vázsonyi interviewed for a teaching job in Sauder School of Business, University of British Columbia. During the job interview, he taught us Gozinto Theory. [Read more…]

Myron Tribus’ UCLA Statistical Thermodynamics class introduced me to entropy, -SUM[p(t)ln(p(t))]. (p(t) is the probability of state t of a system.) Professor Tribus later advocated maximum-entropy reliability estimation, because that “…best represents the current state of knowledge about a system…” [Principle of maximum entropy – Wikipedia] Caution! This article contains statistical neurohazards.

Claude Shannon wrote that entropy (log base 2) represents information bits, “…an absolute mathematical limit on how well data from the source can be losslessly compressed onto a perfectly noiseless channel.”  [Beirlant et al.]

Maximum likelihood estimation is one way to estimate reliability from data. It maximizes the probability density function of observed data, PRODUCT[p(t)], e.g., for observed failures at ages t. It is equivalent to maximize -SUM[ln(p(t)]. Maximum entropy reliability estimation maximizes entropy -SUM[p(t)ln(p(t)]. That’s same as maximizing the expected value, -SUM[p(t)ln(p(t)], of the log likelihood -ln(p(t). Fine, if you have life data, ages at failures t censored or not. [Read more…]

Ralph Evans was editor of the IEEE Transactions on Reliability from 1969 until 2004. He was a very good editor for my 1977 article, and he used me as a reviewer, because I was critical of BS and academic exercises. Ralph moved to University Retirement Community, Davis, CA. He died in 2013, https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6587564. I wish I’d known he lived nearby so I could have visited and argued with him.

Ralph’s editorials [1 and 2] pled, “Data, Data, Oh Where Art Thou Data?” He wrote, “Field-data are largely garbage. I believe they deserve all the negative thinking possible.” “True field-data are wonderful-much better than fancy equations. Unfortunately, they are very difficult to get. Thus data from the field are largely garbage because they do not represent what really happened.” [Read more…]

My wife and I were in Firestone-Walker Brewery (Buellton, California) after Solvang Danish Days. (That’s me playing in the Solvang Village band.) My wife was comparing an Adam Firestone photo on the wall with a man at a table. I was admiring a woman seated near the bar with balletic posture. The balletic woman picked up a pizza and delivered it to the man and sat with him. My wife went over and asked the man if he was Adam Firestone? He was, with his sister Polly. While my wife chatted with them, I did not engage, because I was responsible for FORD recalling the Firestone tire sizes that Firestone did NOT recall. [Read more…]

Would you like the reliability of all your products and their service parts, without assumptions, in real environments, and with all premature failures, complaints, repairs, warranty expirations, preventive maintenance, changes, warranty extensions, etc.? Field reliability tells what really happens! [Read more…]