Accendo Reliability

Your Reliability Engineering Professional Development Site

  • Home
  • About
    • Contributors
  • Reliability.fm
    • Speaking Of Reliability
    • Rooted in Reliability: The Plant Performance Podcast
    • Quality during Design
    • Way of the Quality Warrior
    • Critical Talks
    • Dare to Know
    • Maintenance Disrupted
    • Metal Conversations
    • The Leadership Connection
    • Practical Reliability Podcast
    • Reliability Matters
    • Reliability it Matters
    • Maintenance Mavericks Podcast
    • Women in Maintenance
    • Accendo Reliability Webinar Series
  • Articles
    • CRE Preparation Notes
    • on Leadership & Career
      • Advanced Engineering Culture
      • Engineering Leadership
      • Managing in the 2000s
      • Product Development and Process Improvement
    • on Maintenance Reliability
      • Aasan Asset Management
      • AI & Predictive Maintenance
      • Asset Management in the Mining Industry
      • CMMS and Reliability
      • Conscious Asset
      • EAM & CMMS
      • Everyday RCM
      • History of Maintenance Management
      • Life Cycle Asset Management
      • Maintenance and Reliability
      • Maintenance Management
      • Plant Maintenance
      • Process Plant Reliability Engineering
      • ReliabilityXperience
      • RCM Blitz®
      • Rob’s Reliability Project
      • The Intelligent Transformer Blog
      • The People Side of Maintenance
      • The Reliability Mindset
    • on Product Reliability
      • Accelerated Reliability
      • Achieving the Benefits of Reliability
      • Apex Ridge
      • Metals Engineering and Product Reliability
      • Musings on Reliability and Maintenance Topics
      • Product Validation
      • Reliability Engineering Insights
      • Reliability in Emerging Technology
    • on Risk & Safety
      • CERM® Risk Insights
      • Equipment Risk and Reliability in Downhole Applications
      • Operational Risk Process Safety
    • on Systems Thinking
      • Communicating with FINESSE
      • The RCA
    • on Tools & Techniques
      • Big Data & Analytics
      • Experimental Design for NPD
      • Innovative Thinking in Reliability and Durability
      • Inside and Beyond HALT
      • Inside FMEA
      • Integral Concepts
      • Learning from Failures
      • Progress in Field Reliability?
      • R for Engineering
      • Reliability Engineering Using Python
      • Reliability Reflections
      • Testing 1 2 3
      • The Manufacturing Academy
  • eBooks
  • Resources
    • Accendo Authors
    • FMEA Resources
    • Feed Forward Publications
    • Openings
    • Books
    • Webinars
    • Journals
    • Higher Education
    • Podcasts
  • Courses
    • 14 Ways to Acquire Reliability Engineering Knowledge
    • Reliability Analysis Methods online course
    • Measurement System Assessment
    • SPC-Process Capability Course
    • Design of Experiments
    • Foundations of RCM online course
    • Quality during Design Journey
    • Reliability Engineering Statistics
    • Quality Engineering Statistics
    • An Introduction to Reliability Engineering
    • Reliability Engineering for Heavy Industry
    • An Introduction to Quality Engineering
    • Process Capability Analysis course
    • Root Cause Analysis and the 8D Corrective Action Process course
    • Return on Investment online course
    • CRE Preparation Online Course
    • Quondam Courses
  • Webinars
    • Upcoming Live Events
  • Calendar
    • Call for Papers Listing
    • Upcoming Webinars
    • Webinar Calendar
  • Login
    • Member Home

by Larry George Leave a Comment

Convert a Constant Failure Rate to Operating Hours

Convert a Constant Failure Rate to Operating Hours

Someone asked, “…if you can give me quick explanation: For Example, EPRD 2014 part, Category: IC, Subcategory: Digital, Subtype1: JK, Failure Rate (FPMH) = 0.083632 per (million) calendar hours! How do you convert that to operational hours?” I.e., time-to-failure T has exponential distribution in calendar (million) hours with MTBF 11.9571 (million) hours.

Did the questioner mean how to convert calendar-hour MTBF into operating-hour MTBF? David Nichols’ article does that for 217Plus MTBF predictions, based on “the percentage of calendar time that the component is in the operating or non-operating (dormant) calendar period, and how many times the component is cycled during that period.” I.e., MTBF/R where R is the proportion of operating hours per calendar hour. 

There could be reasons for converting to operating hours. For example, A “War Readiness Spares Kit” [Glazener and Tinder] recommends spare parts required to support a flying-hour program plan in case of war and deployment away from the spare parts’ inventory. The flying-hour program specifies aircraft war-time operating hours, so an actuarial parts demand forecast requires their actuarial failure rates in operating hours [Hess, Hogge, Kamins and McCall, Long and Engberson]. 

What if the Proportion R is Random?

Suppose the operating rate R = operating hours per calendar hour has a uniform distribution on [a, b] with 0<a<b<1. The failure rate function of operating time-to-failure, X=T*R (T = calendar-hour time to failure), is NOT constant; it is toonasty a formula for publication here. The formula was computed using Mathematica. 

Figure 1 graphs the failure rate function from 1100 simulated times to failures in operating hours. The calendar time-to-failure T has exponential distribution with constant failure rate of 0.08362 per (million) hours, and the proportion of operating time R has uniform distribution between 0.25 and 0.75. The formula in figure 1 is for a quadratic-polynomial trend line, an approximation to the nasty formula. The non-zero coefficients for the quadratic and linear terms are not zero indicating operating time failure rate is NOT constant. 

Figure 1 is the simulated (1100 repetitions) failure rate function in operating-hours with operating hours per calendar hour R distributed uniformly on [0.25, 0.75].
Figure 1 is the simulated (1100 repetitions) failure rate function in operating-hours with operating hours per calendar hour R distributed uniformly on [0.25, 0.75].

For this example, the operating time failure rate function of T*R changes from 0.180306 (at age 1) to 0.15665 (at age ~10 (million) operating hours). The operating-time failure rate at age 1 is about twice the calendar time failure rate initially because there is a 50% chance of operating in the first calendar period. 

The MTBF in operating hours is 11.957*(a+b)/2 = 5.98752. (11.957 is the calendar-hour MTBF of an exponential distribution with (constant) failure rate 0.083632.) Nichols’ article says MTBF in operating hours is MTBF(calendar)/E[R]=MTBF(calendar)/((a+b)/2). That’s probably not true for other distributions of T, times-to failures, and R, operating hours per calendar hour.

“Constant Failure-Rate Models may be Hazardous to your Design” [Bowles, ReliaSoft]. Age-dependent failure rate (FR) function means the simple series system MTBF prediction, 1/(1/FR1 + 1/FR2 + … + 1/FRk), for k independent components, is wrong! What if a system is not in series? What if not all parts have same distributions of operating hours/calendar hours? What if parts’ operating hours/calendar hour are differently distributed, statistically dependent, or all of the above? [Schenkelberg]

Alternatives

  1. Use the MTBF software and constant failure rates to compute MTBF in calendar time and convert it to MTBF/E[R] (E[R] is expected value of R.) Warn customers that that formula is correct only if calendar-hour failure rate is really constant, and if operating hours per calendar are uniformly distributed!
  2. Send data on parts, their failure rates (calendar hours), and data on their operating hours/calendar hour to pstlarry@yahoo.com. I will estimate the distribution of R and plug it into an Excel workbook or Mathematica, and send back the inconstant failure rates per operating hour. If you send system reliability block diagram, I will (try to) compute or simulate system reliability and MTBF.
  3. Use MTBF prediction software as if operating-hour failure rates are constant/E[R], E[R] = the average operating hours per calendar hour, so that you can compare your lies with others’. Warn consumers of your operating-hour MTBF predictions and of your assumptions, explain the consequences, and ask for data on operating hours/calendar hour.
  4. Give up on MTBF predictions based on untenable assumptions and use field reliability data to estimate reliability and MTBF, or, if you’re trying to predict for a new product without field reliability data, ask for “Credible Reliability Prediction” [George], because it shows how to use field reliability of previous generations of products and parts.

Conclusions

Converting constant calendar-time failure rate, with random operating time per calendar-time unit, yields inconstant an operating-time failure rate function. That invalidates simple reliability and MTBF predictions that depend on constant failure rates.

Send data on field reliability and operating rates per unit time (please describe) to pstlarry@yahoo.com, and I will send back nonparametric field reliability and failure rate function estimates, operating rate distribution estimates, and convert between operation and calendar time scales. 

If you want the failure rate function per operating hour for non-exponential time-to failure in calendar hours or R = operating hours/calendar hour with a non-uniform distribution, let me know. Send samples of operating hours per calendar hour or specify distribution of R.

I wonder how EPRD came up with (constant) Failure Rate (FPMH) = 0.083632 per million calendar hours for an IC?

References

Bowles, John, “Caution, Constant Failure-Rate Models may be Hazardous to your Design,” IEEE Transactions on Reliability, Volume: 51, Issue: 3, Sept. 2002, http://ieeexplore.ieee.org/document/1028412/

L. L. George, Credible Reliability Prediction, 2nd Edition, August 2022

Charles U. Glazener  and Alan J. Tinder, “War Readiness Spares Kit Composition: A Systems Approach,” AFIT/SLSR 30-76B, Air Force Institute of Technology, AD A032426. Nov. 1976

Hess, Tyler, “Cost Forecasting Models for the Air Force Flying Hour Program,” AFIT/GCA/ENV/09-M07, Air Force Institute of Technology, http://www.dtic.mil/dtic/tr/fulltext/u2/a499658.pdf, March 2009

Hogge, Lewis J., “Effective Measurement of Reliability of Repairable Air Force Systems, AFIT/GSE/ENV/12-S02DL, Air Force Institute of Technology,https://pdfs.semanticscholar.org/a005/9387c34417acc0a6223be7eaed2dbb3d9476.pdf, September 2012 

Kamins, Milton, and J. J. McCall, Jr., “Rules for Planned Replacement of Aircraft and Missile Parts, RAND Research Memorandum RM-2810-PR, November 1961

Long, William S. and Douglas H. Engberson, “The Effect of Violations of the Constant Demand Assumption on the Defense Logistics Agency Requirements Model,” AFIT/GLM/ILAL/94S-15,http://www.dtic.mil/dtic/tr/fulltext/u2/a285272.pdf, 1994

Nichols, David, “Convert a RIAC 217 Plus Reliability Prediction Calendar Hour-Based Failure Rate to an Operating Hour-Based Failure Rate,” Journal of the Reliability Information Analysis Center, 2nd Quarter 2009

ReliaSoft, “Limitations of the Exponential Distribution for Reliability Analysis,”http://www.reliasoft.com/newsletter/4q2001/exponential.htm, 4th quarter 2001

Schenkelberg, Fred, “The Constant Failure Rate Myth,” http://nomtbf.com/2015/09/the-constant-failure-rate-myth/, Sept. 2015

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

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 survival analysis, epidemiology, and their applications: epidemics, randomized clinical trials, risk-based inspection, and DoE for risk equity.

« Symptoms Of Oxygen Deficient Atmosphere
Project Manager Lessons Learned: Bad Technical Decision »

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Articles by Larry George
in the Progress in Field Reliability? article series

Join Accendo

Receive information and updates about articles and many other resources offered by Accendo Reliability by becoming a member.

It’s free and only takes a minute.

Join Today

Recent Articles

  • test
  • test
  • test
  • Your Most Important Business Equation
  • Your Suppliers Can Be a Risk to Your Project

© 2025 FMS Reliability · Privacy Policy · Terms of Service · Cookies Policy