My wife says I am wasting my time trying to change reliability statistics, so I polled the www.linkedin.com Reliability Leadership…, ASQRRD, IEEE Reliability, “Biostatistics, and No MTBF groups. The polls claimed that “Life data, censored or not, is required to estimate MTBF, reliability function, failure rate function, or survivor function. TRUE? FALSE? or DON’T KNOW.” I am grateful for the responses.
It’s normal to collect a random sample of a random variable to estimate its distribution function. The Lifetime Data Analysis Journal says that it is… “An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data.” IEEE1413.1-2002 5.2.1 reliability prediction guide says times to failures and “accumulated operating time for all items that have not failed” are required. CFR Title 21 Volume 8 Subpart B Section 821.20 “Devices Subject to Tracking”, requires times-to-failures for implantable medical devices. Www.Weibull.com says times to failure are required.
Approximately 91% of poll replies were “TRUE”. There were no “DON’T KNOW” replies, so respondents seemed to know despite 9% disagreeing. There seem to be a lot of people who “KNOW BUT AREN’T TELLING”!
Table 1. Results of LinkedIn groups’ polls. “Impressions” count clicks on poll pages.
| Group | ASQRRD | IEEERel | RelLea | BioSta | Total | |
| Members | 875 | 4730 | 3328 | 24620 | 17986 | 51539 |
| TRUE | 0 | 63 | 3 | 53 | 9 | 128 |
| FALSE | 1 | 6 | 1 | 4 | 1 | 13 |
| DON’T KNOW | 0 | 0 | 0 | 0 | 0 | 0 |
| TRUE% | 0% | 91% | 75% | 93% | 90% | 91% |
| FALSE% | 100% | 9% | 25% | 7% | 10% | 9% |
| Total votes | 1 | 69 | 4 | 57 | 10 | 141 |
| Proportion | 0.11% | 1.46% | 0.12% | 0.23% | 0.06% | 0.27% |
| “Impressions” | 40 | 2350 | 124 | 5765 | 390 | 8669 |
The correct answer is FALSE! Lifetime data is available “hidden” or “masked” in counts: births and deaths, ships and returns, SARS, Ebola or COVID-19 infections, recoveries, or deaths, covered calls, breast implant and explants, etc.; even in HIV+->AIDS->death counts.
Counts are statistically sufficient to make nonparametric estimates of MTBF, reliability, failure rate, or survivor functions, often with several failure modes simultaneously, censored or not. Often, ships and returns counts are implicit in revenue and cost data required by generally accepted accounting principles. Often, counts are population data, so estimates from them have no sample uncertainty. Furthermore, it is possible to quantify the uncertainty in MTBF, reliability, failure rate, and survival function estimates without life data.
In 1990 at Apple Computer, Mike Johanns regarded computer’s lives as service times in M/G/infinity self-service systems: M stands for Poisson inputs and G stands for the hidden distribution of times-to-failure. Mike told me to do a literature search for “Self-Service Queues” and “Statistics.” The only hit was my 1973 paper. The reliability estimation methods also work for nonstationary Poisson inputs M(t)/G/infinity systems [Nelson and Leemis].
Table 2. Ships and returns counts and least-squares reliability function estimate for a low-power mouse. Return counts in 3rd column are mixed from shipped cohorts in same month and previously.
| Months | Ships | Returns | Age | Reliability |
| Feb-87 | 20182 | 94 | 1 | 0.9832 |
| Mar-87 | 58169 | 303 | 2 | 0.9832 |
| Apr-87 | 84833 | 527 | 3 | 0.9764 |
| May-87 | 110037 | 1056 | 4 | 0.9764 |
| Jun-87 | 95356 | 1326 | 5 | 0.9764 |
| Etc. | ||||
| Jun-89 | 12950 | 1634 | 28 | 0.9449 |
See www.accendoreliability.com articles and examples. See https://sites.google.com/site/fieldreliability/ for snarky opening page and links to books and articles.
L. L. George and A. Agrawal, “Estimation of a Hidden Service Distribution of an M/G/Infinity Service System,” Naval Research Logistics Quarterly, vol. 20, pp. 549-555, 1973
B. L. Nelson and L. M. Leemis, “The Ease of Fitting but Futility of Testing a Nonstationary Poisson Processes from One Sample Path,” 2020 Winter Simulation Conference (WSC), Orlando, FL, USA, pp. 266-276, doi: 10.1109/WSC48552.2020.9383930, 2020
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