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Home » Archives for Larry George

Larry George — Active Contributor

Author of Progress in Field Reliability? articles.


This author's archive lists contributions of articles and episodes.

About Larry George

UCLA engineer and MBA, UC Berkeley Ph.D. in Industrial Engineering and Operations Research with minor in statistics. I taught for 11+ years, worked for Lawrence Livermore Lab for 11 years, and have worked in the real world solving problems ever since for anyone who asks. Employed by or contracted to Apple Computer, Applied Materials, Abbott Diagnostics, EPRI, Triad Systems (now http://www.epicor.com), and many others. Now working on actuarial forecasting, survival analysis, transient Markov, epidemiology, and their applications: epidemics, randomized clinical trials, availability, risk-based inspection, Statistical Reliability Control, and DoE for risk equity.

by Larry George Leave a Comment

Estimate Reliability Functions Without Life Data

Estimate Reliability Functions Without Life Data

ASQC Reliability Review, Vol. 13, March 1993

This paper shows how to estimate field reliability functions from ships and returns. It offers to estimate field reliability functions from your data. It suggests how you can use these estimates to improve service and inventory management. [Links to Google Sheet and user guide follow the paper.]

You can estimate field reliability functions without life data. You don’t need to know each part’s time to failure. In fact, if you don’t know times to failures, you have to estimate field reliability functions from ships and returns, unless you have a sample of times to failures, and some of the sample failed.

[Read more…]

Filed Under: Articles, on Tools & Techniques, Progress in Field Reliability?

by Larry George 1 Comment

Kolmgorov-Smirnov Two-Sample Test for Censored Data

Kolmgorov-Smirnov Two-Sample Test for Censored Data

Submitted to ASQC Reliability Review, Nov. 1996

A client wanted to compare the Kaplan-Meier (nonparametric maximum likelihood) estimators of the reliabilities of the old and new products. That is, he wanted me to test reliability functions, Ho: R1(t)=R2(t) for all nonnegative t vs. Ha: R1(t)≠R2(t) for some nonnegative t.

Because I’m lazy and fixed in my ways and because I thought it would be easier to explain, I chose the Kolmgorov-Smirnov (K-S) test [Gnendenko]. It’s convenient, practically every statistics text has the tables, and I can program tables and the test statistic easily. The test uses the maximum absolute difference between the Kaplan-Meier estimates of the two reliability functions. Reject Ho if maximum absolute difference, Dmn=max|R1(t)-R2(t)| exceeds a critical value, where m and n are the two sample sizes.

[Read more…]

Filed Under: Articles, on Tools & Techniques, Progress in Field Reliability?

by Larry George 1 Comment

Uncertainty and Resource Allocation in the URC

Uncertainty and Resource Allocation in the URC

 This article appeared in 1983 in the ORSA Applied Probability SIG under the pseudonym “Anonymous” 

In another country far away, there were power plants that generated cheap electricity by unclear means. Since operation of the plants involved some risk, the Unclear Regulatory Commission was established to license power plants for operations. The URC decreed that any plant could have a license if its probability of an unclear accident was smaller than 0.000001 per year. The plant operators said they were uncertain. 

[Read more…]

Filed Under: Articles, on Tools & Techniques, Progress in Field Reliability?

by Larry George 1 Comment

Kaplan-Meier Reliability: What Could Possibly Go Wrong?

Kaplan-Meier Reliability: What Could Possibly Go Wrong?

SAS, JMP, R-”Survival”, Minitab, ReliaSoft, XLStat, and perhaps other statistics programs offer the Kaplan-Meier nonparametric reliability estimator as a default. Take credit for using nonparametric reliability estimation and avoiding unwarranted assumptions. What could go wrong using the Kaplan-Meier estimator?

  • Cohorts could be non-stationary, random processes! 
  • Failures could be recurrent process counts, not dead-forever! 
  • Lifetime data depends on the censoring process(es); e.g., competing risks!
  • Greenwood’s variance estimator errs! Covariances are missing!
  • Alternative estimators could be more efficient than Kaplan-Meier!

Are you using all the information in data available from population data required by GAAP? If you don’t have lifetime data, use periodic failure counts. This article describes an example where the Kaplan-Meier estimator from grouped lifetime data is less efficient than using periodic failure counts, even though you don’t know which cohort they came from! 

[Read more…]

Filed Under: Articles, on Tools & Techniques, Progress in Field Reliability?

by Larry George 1 Comment

Reliability Estimation Efficiency? Without Lifetime Data?

Reliability Estimation Efficiency? Without Lifetime Data?

What is the efficiency of your reliability estimators and failure forecasts? Compare naïve forecasts: guess, AFR, MTBF, or times series extrapolations such as ARIMA, GMDH, and AI, vs. forecasts based on reliability estimators. With grouped lifetime data, the Kaplan-Meier estimator is statistically efficient, under a condition often ignored! With lifetime data you could use maximum likelihood estimators like Weibull or Kaplan-Meier from (a sample of?) grouped lifetimes. Without lifetime data you could estimate reliability from population ships and returns counts from data required by GAAP! This article compares efficiency and cost of forecasts based on alternative data and estimators.

[Read more…]

Filed Under: Articles, on Tools & Techniques, Progress in Field Reliability?

by Larry George Leave a Comment

What MTBF Do You Want?

What MTBF Do You Want?

Originally published in the ASQC Reliability Review, Vol. 15, No. 3, Sept. 1995 

This article shows reductio ad absurdum in action. Yes you can achieve any MTBF you want, by mixing products with Weibull life distributions, but you won’t want the consequences. The article also shows the absurdity of specifying MTBF, alone. 

[Read more…]

Filed Under: Articles, on Tools & Techniques, Progress in Field Reliability?

by Larry George Leave a Comment

Renewal vs. Generalized Renewal Process?

Renewal vs. Generalized Renewal Process?

How to distinguish a renewal process from a “generalized” renewal process? Compare observed monthly returns vs. actuarial returns forecasts using actuarial return rate estimates of TTFF and TBF (Time To First Failure and Time Between Failures). A geophysicist masquerading as an Apple reliability engineer said, “It’s too hard to figure out the probability that a return came from a computer made in an earlier year.”  It’s harder if returns could be second, third, or???

[Read more…]

Filed Under: Articles, on Tools & Techniques, Progress in Field Reliability?

by Larry George 5 Comments

Multiple-Failure-Mode Reliability Estimation

Multiple-Failure-Mode Reliability Estimation

“It is the policy of my Administration to respond to the coronavirus disease 2019 (COVID-19) pandemic through effective approaches guided by the best available science and data” [Biden Executive order, 2021]. That epidemic inspired the simultaneous nonparametric estimation of survival functions from case to recovery and case to death, without lifetime data (figure 1)!

Why not do the same for multiple-failure-mode data? This article shows nonparametric, multiple-failure-mode, maximum likelihood reliability estimation in a spreadsheet. Data are system first-failure times and the corresponding failure modes that caused the first system failures (table 1). However those data are dependent. I will explain the likelihood function, lnL, and how to find the maximum likelihood reliability estimates for all failure modes simultaneously.

[Read more…]

Filed Under: Articles, on Tools & Techniques, Progress in Field Reliability?

by Larry George 4 Comments

Statistical Software Problem?

Statistical Software Problem?

When a system fails for the first failure in one mode at time t, this data is right censored data for other failure modes! How to estimate reliability functions for all failure modes from first failure data?

Google AI says, “’Competing risks’ refers to a statistical scenario where a subject can experience failure from multiple possible causes, but once one failure occurs, it prevents the observation of any other potential failures, essentially creating “multiple failure modes” that compete with each other to be the first event observed; this means analyzing the probability of a specific failure type needs to account for the possibility of other competing failures happening first.” “Use appropriate statistical methods: Employ statistical models specifically designed for competing risks analysis…” 

[Read more…]

Filed Under: Articles, on Tools & Techniques, Progress in Field Reliability?

by Larry George Leave a Comment

Fred’s Bicycles and Kaplan-Meier Error?

Fred’s Bicycles and Kaplan-Meier Error?

The Kaplan-Meier reliability estimator errs on Fred’s bicycle ships and failure data! The Kaplan-Meier estimate was computed from Fred’s bicycles’ grouped failure data in the body of a “Nevada” table. It disagrees with the reliability estimate from ships cohorts and monthly failures (without knowing which cohort the failures came from). It disagrees with least squares nonparametric reliability estimates. All but the Kaplan-Meier estimate agree! Which would you prefer?

[Read more…]

Filed Under: Articles, on Tools & Techniques, Progress in Field Reliability?

by Larry George Leave a Comment

Kaplan-Meier Ignores Cohort Variability!

Kaplan-Meier Ignores Cohort Variability!

The Kaplan-Meier reliability estimator is the nonparametric, maximum likelihood estimator from right-censored, grouped lifetime data. It has been used since publication, most statistics programs do it, and it has been taught since I was in school. I give away a spreadsheet version. 

Lifetime data requires tracking individual subjects or units from their start to failure, death, or censoring. Data may be collected periodically grouped by cohorts: monthly sales, ships, or other collections of individuals, subjects, or units and each cohort’s lifetimes. Data could be displayed in a “Nevada” table with random cohorts in one column, and each cohort’s lifetimes grouped in periodic age-at-failure intervals in columns to the right [Schenkelberg].

[Read more…]

Filed Under: Articles, on Tools & Techniques, Progress in Field Reliability?

by Larry George 1 Comment

MTBF Correlation vs. Causation: MIL-HDBK-217G

MTBF Correlation vs. Causation: MIL-HDBK-217G

People claim poor correlation of predicted and observed MTBFs. That is understandable because handbook failure rates and fudge factors for quality and environment were derived from unknown populations or samples. People also claim there is no basis for applying statistics or probability to MTBF predictions. MTBF predictions use failure rate averages that lack statistical causation. Why not incorporate Paretos in MTBF predictions?

Paretos are fractions of equipment failures caused by each type of part or subsystem. They represent what really happens. Incorporating Paretos requires statistics to adjust MTBF predictions. That causes Paretos in MTBF predictions to match field Paretos. A 1992 ASQ Reliability Review article “MIL-HDBK-217G” proposed using observed Paretos to adjust handbook MTBF predictions with a “Reality” factor.

[Read more…]

Filed Under: Articles, on Tools & Techniques, Progress in Field Reliability?

by Larry George 1 Comment

MIL-HDBK-217G (George) Reality Factor

MIL-HDBK-217G (George) Reality Factor

Originally published in the ASQ Reliability Review, Vol. 12, No 3, June 1992

Insert these pages into your copy of MIL-HDBK-217. The boldface text is changed to MIL-HDBK-217E [1], section 5.2, on parts count reliability prediction. The changes explain how to use “Paretos,” proportions of parts failing in the field, to compute a reality factor that makes predicted Paretos match field Paretos. You can use field Paretos to calibrate predictions for new equipment. You probably have field Paretos on related parts used in your other equipment, which is now in the field. Remember, the field determines reliability.

[Read more…]

Filed Under: Articles, on Tools & Techniques, Progress in Field Reliability?

by Larry George 2 Comments

What Price Kaplan-Meier Reliability?

What Price Kaplan-Meier Reliability?

The Kaplan-Meier estimator is the maximum likelihood, nonparametric reliability estimator for censored, grouped lifetime data. It’s traditional. It’s in statistical software. Greenwood’s variance formula is well known. Could Kaplan-Meier be improved: smaller variance, better actuarial forecasts, seasonality, separate cohort variability from reliability? Could you estimate reliability without life data and preserve privacy?

[Read more…]

Filed Under: Articles, on Tools & Techniques, Progress in Field Reliability? Tagged With: Field data analysis

by Larry George 1 Comment

Semi-Nonparametric Reliability Estimation and Seasonal Forecasts

Semi-Nonparametric Reliability Estimation and Seasonal Forecasts

I estimated actuarial failure rates, made actuarial forecasts, and recommended stock levels for automotive aftermarket stores. I wondered how to account for seasonality in their sales? Time series forecasts account for seasonality but not for age, the force of mortality accounted for by actuarial forecasts. I finally figured out how to seasonally adjust actuarial forecasts. It’s the same method, David Cox’ “Proportional Hazards” model, used to make “Semi-Parametric” estimates and “Credible Reliability Predictions”.

[Read more…]

Filed Under: Articles, on Tools & Techniques, Progress in Field Reliability? Tagged With: Statistics non-parametric

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