ProdSpec

Product announcement: Field Reliability Estimator version 3.0  April 19, 2013

Revised June 28, 2018 to correct link to M/G/Infinity article

Revised March 5, 2019 to include estimation of reliability functions for competing risks

Now you can estimate field reliability for all products and service parts, dead forever or repairable, dependent or not, with or without life data, without unwarranted assumptions. Field reliability is what really happens, in the hands of customers, in the field. The picture below shows some actionable features of field reliability: infant mortality, warranty expiration returns, inspection, preventive maintenance, retirement, and premature wearout. Actions include: provide early warning of problems, statistical process control on returns, diagnose and size problems, estimate warranty reserves, forecast service requirements, determine spares to satisfy service level requirements, compare new and renewed lives, evaluate effects of fixes, and recognize obsolescence. Not shown in the picture is dependence, which you might exploit for better service or improved throughput.

People say, "You need age-at-failure data and survivors’ ages to estimate age-specific field reliability." This is called, “adopting a narrative,” define the status quo as success and ignore evidence that suggests otherwise. This also leads to a sales principle, “It’s hard to sell something that constitutes an admission that what buyers had been doing is wrong.” Nevertheless, you don’t need to track products or parts by serial number to get ages at failures and field reliability. Ships (sales, installed base, and so on) and returns counts (complaints, failures, service actions, repairs, spares sales, and so on) are statistically sufficient to compute nonparametric reliability estimates. Generally accepted accounting principles require ships and returns counts, and they are population counts, so reliability estimators are population estimates with NO sample uncertainty. 

Problem Solving Tools’ Field Reliability Estimator makes nonparametric estimates of age-specific field reliability and failure rate (actuarial) functions. All information in your ships and returns data is preserved (Walter Shewhart’s rule #1), and no unwarranted assumptions are required. Methods compute maximum likelihood and least squares nonparametric estimators, even if some data is missing or censored. The Field Reliability Estimator also computes estimates from all data subsets, in order of accumulation, to identify production problems, to make broom charts, and to identify improvement or bad lots, if any. There are versions for reparable systems that estimate reliability functions of TTFF (Time To [age at] First Failure), and TBF1, TBF2,…(Times Between Failures), dependent or not. Dependence is quantified by covariances of TTFF and TBFs using copulas.

The Field Reliability Estimator is accurate (asymptotically unbiased) and precise (minimum variance). It has no sample uncertainty because it uses population data, not a sample. Its information content (entropy) has the same order of magnitude as age-at-failure estimators with equivalent censoring while requiring approximately one-thousandth the data storage (mainframe vs. PC).

The Field Reliability Estimator is a collection of Excel workbooks. For more information, specifications, free samples, or software, please contact Problem Solving Tools, pstlarry077@gmail.com. If you would like to read the original article that led to the Field Reliability  Estimator, read  https://sites.google.com/site/fieldreliability/home/m-g-infinity-service-distribution. If you would like to see A(H7N9) survival analysis in action, ask for the Ebola.xlsm workbook.

[Under "Files, Workbooks, Etc." you will find Mathematica files named NPmle.* that implement the estimator in this article. Either open NPmle.nb in Mathematica or execute NPmle.cdf using http://www.wolfram/com/cdf-player. If there is a problem, let me know. Nov. 10, 2016] 

Suppose you want survivor or reliability function estimates for competing risks, alternative failure modes, without life data. See the RD Congo Ebola Survival Analysis, https://sites.google.com/site/fieldreliability/eboladrcongo2018, for alternative methods using case reports (cohorts or installed base) and death and recovery counts. The alternatives are: 

1. Maximum likelihood assuming deaths and rcoveries are both outputs M(t)/G/infinity counts   

2. Least squares estimation assuming transient Markov chain with three states: in treatment, dead, or recovered. 

Wouldn’t it be nice to know what’s really happening to your products and their parts in the field?