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. 

The well-known variance of the Kaplan-Meier reliability function estimator [Greenwoood, Wikipedia] can drastically under-or over-estimate variance. The covariances of the Kaplan-Meier reliability pairs at different ages are ignored or neglected. Variance errors and covariance neglect bias the variance of actuarial demand forecasts. Imagine what errors and neglect do to confidence bands on reliability functions.

My first task at Apple Computer was to recommend the warranty duration for the Apple II computer. Apple didn’t have a warranty! So, I looked at competitors’ warranties and recommended the same, one year. I wish I had known Apple’s computers’ and service parts’ reliabilities before that recommendation; I would have used actuarial forecasts of warranty returns to compare alternative warranties. Apple’s hardware warranty is still one year. Is that equitable to Apple, its customers, and society?

Imagine observing inputs and outputs of a self-service system, without individual service times. How would you estimate the distribution of service time without following individuals from input to output? The maximum likelihood estimator for an M/G/Infinity self-service-time distribution function from ships and returns counts works for nonstationary arrival process M(t)/G/Infinity self-service systems, under a condition. A constant or linearly increasing arrival (ships) rate satisfies the condition. If you identify outputs by failure mode then you could estimate reliability by failure mode or quantify reliability growth, without life data. [Read more…]

ANSI-IES TM-21 standard method may predict negative L70 LED lives. (L70 is the age at which LED lumens output has deteriorated to less than 70% of initial lumens.) Philips-Lumileds deserves credit for publishing the data that inspired an alternative L70 reliability estimation method based on geometric Brownian motion of stock prices in the Black-Scholes-Merton options price model. This gives the inverse Gauss distribution of L70 for LEDs. 

COVID-19 Case Fatality Rate (CFR) is easy to estimate: CFR=deaths/cases. Regression forecasts of COVID-19 cases and deaths are easy but complicated by variants and nonlinearity. Epidemiologists use SIR models (Susceptible, Infectious, and “Removed”) to estimate Ro. These are baseball statistics. Reliability people need age-specific reliability and failure-rate function estimates, by failure mode, to diagnose problems, recommend spares, plan maintenance, do risk analyses, etc. Markov models use actuarial transition rates.

Age-specific reliability of a standby system depends on components’ failure rates. Reliability computation is interesting when part failure rates depend on age, which is what motivates having a standby system. A Markov chain, approximates the age-specific reliability and availability, which are complicated to compute exactly, unless you assume constant failure rates. Why not use age-specific (actuarial) rates? They are Markov chain transition rates.