A new problem concerning reliability issues is posted on this web site periodically, and a solution is proposed. Use this page to select interesting problems by title.




Making Sense With Sparse Data
Poisson distributions allow use of sparse data to make sense from data that looks like nonsense.




Why It’s Important To Sometimes Use Crow-AMSAA Plots and Weibull Plots Together
An example is shown to demonstrate what both tools can tell you the complete information.




Process Reliability Plots For Solving the Most Important Production Problems First Using Weibull Probit Analysis
An example of how to show problems in different colored Weibull plots for different problems.




Excel Simulation For Mean Time Between Failures, Confidence Intervals, Number Of Samples To Test, Warranty Failures, Weibull Analysis, and Monte Carlo Test Results,
This simulation can accommodate 10 Weibull failure modes and answer the question of expected warranty failures and other issues mention in the title.  An Excel program is available for download but expect the download time to be at least 15 minutes.



Process Safety Valves And Rupture Disk Test Results
Process safety valves and rupture disks protect against overpressure.  They are important process safety devices.  Process safety problems occur infrequently but with severe $Consequences. Whereas personal safety devices are involved in more frequent failures but with less severe $consequences.  Engineers must understand the probability of failure and the $consequences to reduce the $Risks = (probability of failure)*($Consequences).  Engineers must keep the $Risks within their signature authority.  Weibull analysis of test results defines the probability of failure.  Examples are discussed along with the $Consequences to make business decision.



Safety Integrity Levels (SIL) Standards Are Appropriate For Many Reliability Issues
SIL standards are about managing risks which is a subject for determining the amount of reliability required for making financial decisions using life cycle costs techniques.




A Few Profitable Processes vs Many Marginally Profitable Processes.  Why? Updated 07/17/11
How to tell where to search for the underlying causes for problems and how to go about fixing the problems with comparisons to 1st quartile processes.




Why Are A Few Profitable Processes Highly Reliable With Small Variations In Output And Many Marginally Profitable Process Are The Opposite?
Barringer process reliability plots help explain the difference when the processes are designed by the similar engineering companies using similar equipment and operated by competent people?




Effective Exception Reports For Special Causes
Barringer process reliability plots are effective tools for separating common cause problems from special cause problems.  They become more effective when the exception reports for deviation of output is properly defined.  Examples of effective reports are shown and also problem reports.




Cable Splice Failures
Electrical cable splices are causing major failures at a chemical plant.  Each failure cost ~US$500,000. Weibull analysis shows the failure mode is wear-out and not chance failure modes expected by the local experts.  Corrective actions, based on the wear-out failure mode, has avoided any failures in the time period of 1994 to 2010 with millions of $’s of cost avoided.




Shear Ram Blowout Preventer Forces Required Updated 07/10/13
Shear ram test results and system requirements are presented to meet May 2010 USA Department Of The Interior requirements considering risk—this was originally presented as a case study in The New Weibull Handbook but extended here because of the BP blowout problem in the Gulf Of Mexico.




Can You Use Weibull Analysis On Repairable Items?
The short answer is yes.  A longer answer is provided.




How To Calculate Maintainability Values Updated 03/02/09
An example of repair data is show by hand calculation and by probability plot for finding maintainability values for use in reliability, availability, and maintainability (RAM) models.




Use Periods Of Low Production Output to Improve Process Reliability And Consistency
Improve process consistency during periods of low output when the problems stand out like a sore thumb to get prepared for larger production requirements and reduce costs.




Weibull Probability Paper for Hand Plots
Weibull probability paper with coaching notes for making a few quick hand plots




Compressors And Silent Root Causes For Failure
The number one silent root cause killer of compressors (both reciprocating and centrifugal) in chemical plants, refineries, and gas processing plants is inadequate knockout drum design.




Little r and Big R
Reliability strategic issues of big R and tactical issues of little r are described in relationship to Juran’s explanation of quality with his big Q and little q details for making improvements.




Special Cause Variations, Common Cause Variations, and Process Reliability Plots
Barringer Process Reliability Plots Tell You The Problems And Skills Needed For Solutions




Summary Of Process Reliability
Question and comments about the technique




Reliability Programs: Successful or Failures? Updated 12/10/07
Why are some programs successful and other failures along with what you must do to make reliability programs successful?




Reliability Tools Updated 11/22/07
What reliability tools are available? 
Why should I use them? 
When should I use them?
Where should I use them?




Weibull Analysis of Pump Seals Updated 11/4/07
How to give the data a voice for business decisions




Reliability And Data
MTBF, MTTF, Weibull probability plots, and cost considerations—how to give your data a voice for making decisions.




Remaining Life In Pressure Relief Valves
Given you have pressure relief valves that have survived without failure for 24 months, how much longer can they survive to achieve the desired reliability of 95%?




Corrosion Problems, Inspection Data, And The Gumbel Lower Distribution
How to make sense of corrosion data taken from an operating pressure vessel and make a risk decision for run/don’t-run using ASME and API fitness for service criteria.




PVE % A Goodness Of Fit Criteria By Wes Fulton Updated 5/2/06
Correlation coefficients and estimates of P-values for goodness of fit.o




Benign Failures Updated 1/16/05
Correct definition of failures and suspensions (censored data) is very important for a creditable reliability analysis—watch out for inspection euphemisms and the use of rubber rulers in defining failures




Process Reliability Punch List  Updated 5/2/05
How to show different product grades on a process reliability plot




Load-Strength Interference Updated 1/11/07
How to calculate the reliability of products knowing a load distribution and a strength distribution




Find Annual Costs Using Life Cycle Cost Calculations With Planned Replacements Updated 2/19/08
Monte Carlo simulation of Weibull life and costs with optimum replacements




Find Annual Costs For Life Cycle Cost Calculations  Updated 3/14/05 
Monte Carlo simulation of Weibull life and costs with a fix when broken strategy




Risk Based Decisions Updated 12/25/08 
How to build a practical risk based decision matrix for everyday risk matrix decisions




Mean Time Between Stupid Events  Updated 10/15/07
A politically incorrect failure criteria that everyone understands




Failure Forecast For The World’s Most Unsafe Railroad  Updated 5/18/05
Crow-AMSAA forecast of future failures and visual demonstration of failures avoided by corrective action programs




Forecast Of The Next Space Shuttle Failure  Updated 10/29/04
Carlo-AMSAA forecast of future space shuttle failures using data from the Challenger and Columbia failures




Fabled Mercedes Reliability Or Is Mercedes Reliability Just A Fable?  Updated 10/29/04
ML 320 SUV failure forecasts of future tow-in incidents based on my personal vehicle data using Crow-AMSAA methods to validate Mercedes reliability issues so you can decide if Mercedes vehicles are reliable or unreliable




Can Reliability Software Solve Other Statistical Problems?  updated 6/02/2004
WinSMITH Weibull and WinSMITH Visual reliability software is used to solve problems from the literature for 1) corrosion pit depths, 2) stress corrosion cracking (SCC) in aluminum, 3) stress corrosion cracking in stainless steel, 4) tank bottom pit depths, 5) tree diameters, and 6) pipe corrosion problems.




Use Data To Show You’ve Made A Maintenance Improvement With Crow-AMSAA Plots
Crow-AMSAA reliability growth plots graphically show improvements made and failures avoided by use of new methods to prove the changes were effective.




Process Reliability Line Segments
Process reliability Weibull plots often have a variety of line segments that provide useful information about hidden factories




How Many Heat Exchanger Tubes Should I Inspect?  updated 5/05/2004
How many tubes should be inspected to estimate the number of failures in the tube bundle




Are RCM Programs Justified?  updated 4/3/2005
Crow-AMSAA plots can demonstrate if your RCM has made improvements or are you just talking about making improvements




Death Of Soldiers In Iraq During Gulf War II with Crow-AMSAA Forecast
updated 12/25/2008
Crow-AMSAA plots are made from fatalities in the Iraq war to forecast future need for body bags and cusps on the curves show improvements/deterioration in combat deaths.




Make Repairs On Overtime?  updated 1/04/2004
How much risk can you tolerate for failures:
      $Risk = (probability of failures)*($Consequence for the failure)




Will It Last Until The Next Turnaround 
Conditional reliability calculations define the probability of failure and $Risk are calculated




Reliability And Life Cycle Cost updated 1/18/2003
Know when to accept the risk and when to reject the risk—finding the lowest long term cost of ownership




Crow-AMSAA Reliability Growth Plots updated 5/22/2004
Show me, don’t tell me, how failures are occurring with time




Waloddi Weibull’s ASME Size Distribution Of Fly Ash Problem #2
Three parameter Weibull plots for fly ash data




Waloddi Weibull’s ASME Yield Strength Problem #1 updated 10/2/2001
Three parameter Weibull plots for yield strength’s to show the failure free zone




Maintainability updated 02/17/2009
What is it and how do I find it?




Flood Data and Gumbel Largest Distributions updated 6/19/2001
Houston, Texas flood data with prediction of 100 year flood depths at gaging station near downtown using a single maximum flood depth per year




Process Reliability Plots With Flat Line Slopes updated 8/17/2002
A Monte Carlo simulation shows how small effects can destroy predicted output in a production processes




Weibull Beta Slopes For Ball Bearings updated 7/11/2001
What’s the “right” Weibull slope value, beta, to use for ball bearings




Heat Exchanger IRIS Wall Thickness and Gumbel Smallest Distributions updated 1/07/2007
How to predict end of life from ultrasonic wall thickness inspection data with minimum wall thickness for each tube




Spare Equipment updated 1/26/2001
How and why to add spare equipment




Timing of Maintenance Replacements updated 1/26/2001
Gives replacement concepts and a Monte Carlo simulation is available for no-cost download to illustrate failure intervals




Screen Sizes For Pulverized Materials updated 6/14/2002
WinSMITH Weibull makes a probability plot for sieve data




Automating Monthly Weibull Production Plots From Excel Spreadsheets
updated 8/14/2001
Batch processing using WinSMITH Weibull cuts time when many plots are required




Key Performance Indicators From Weibull Production Plots updated 6/19/2001
Weibull production Monte Carlo simulation to find how KPI’s relate to demonstrated production output




April 1998—Production Reliability Example With Nameplate Ratings updated 6/19/2001
How to find reliability losses along with efficiency and utilization losses to quantify the hidden factory




March 1998—Nameplate Capacity updated 6/19/2001
How to find the nameplate capacity of a production process using Weibull analysis




February 1998—Coefficient of Variation updated 11/1/2002
Why is the coefficient of variation helpful for process reliability issues and Weibull plots




January 1998—Six Sigma updated 8/14/2001
Six sigma—how is it calculated and used in manufacturing plus preliminary info for Weibull plots




Waste Disposal System Failures And Crow-AMSAA Plots updated 1/20/03
Crow/AMSAA plots used for business decisions and for determining the turnaround period for an actual waste disposal system




Total Productive Maintenance Results updated 1/9/03
Crow/AMSAA (formerly known as Duane AMSAA) plots for no-TPM and TPM programs show failures avoided




How Much Life Is Lost From Specific Pump Practices updated 6/5/05
Losses for each pump practice are quantified




Demonstrated Life Of Pump Components From Pump Practices updated 3/31/98
Inherent reliability of pump components are derated in a reliability model based on findings of from the pump practices survey




Pump Practices And Component Life Multipliers updated 3/31/98 with more information
Best practices, better practices, and good practices for pump installation and use based on a survey of expert users




Monte Carlo Reliability Model Of A Pressure Vessel
Log-normal plots of random stresses, S-N curves, Miner's rule to failure via Monte Carlo models, pressure vessel wall thickness versus age to failure




Pipe Wall Thickness & Risk Based Inspection  updated 5/31/2001
Weibull plots, characteristic life versus time plots, parameter as function of engineering variables




Production Output/Problems updated 6/19/2001
Weibull plots of production data as a business tool to find the process reliability




Tank Bottom Corrosion
Weibull plots, log-normal plots, normal plots, and likelihood ratio confidence limit plots




Remaining Coke Drum Life updated 5/31/2001
Weibull plots and likelihood ratio confidence limit plots

  A few words of caution:

E-mail comments, criticisms, and corrections to: Paul Barringer.  Also, if you have a problem suitable for future listings, submit a problem statement for consideration. Problems include reliability issues and costs receive priority.  

 Technical tools are only interesting toys for engineers until results are converted into money and time for the business. Want to get the interest of your management team? Complete your analysis with a bottom line converted into $'s and time!

You can download a PDF file of these topics by clicking here.

Last revised 8/1/2016
© Barringer & Associates, Inc., 2001

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