I learned actuarial methods working for the USAF Logistics Command. We used actuarial rates to forecast demands and recommend stock levels for expensive engines tracked by serial number, hours, and cycles. I had a hunch that actuarial methods could be applied to all service parts, without life data. [Read more…]
Search Results for: martingale
What if Ships Cohorts Were Random?
The Kaplan-Meier reliability estimator is for dead-forever products or parts, given individual lifetime data or a “Nevada” table of periodic ships cohorts and their grouped failure counts. This estimator presumes that ships cohorts are NOT random. Production, sales, installed base, and cohort case counts are random! What does that do to Kaplan-Meier reliability estimates? What is the nonparametric reliability function estimator if ships cohorts are random?
[Read more…]Kaplan-Meier Estimator for Renewal Processes?
The New-Products manager asked me, “Your actuarial failure rate estimates (from vehicle registrations, bills-of-materials, and automotive aftermarket store sales) are for dead-forever parts with at most one failure. What if auto parts could be renewed or replaced more than once?” Chagrined, I wrote a spreadsheet program to estimate actuarial rates for renewal processes, without life data. But what is the corresponding estimator from grouped, cohort renewal counts like the Kaplan-Meier estimator for grouped, cohort failure counts?
[Read more…]Time Series Forecasts for Service Parts?
Do you want easy demand forecasts or do you want to learn and use the reliabilities of service parts and make demand forecasts and distribution estimates, without sample uncertainty? Would you like to do something about service parts’ reliability? Would you like demand forecast distributions so you could set inventory policies to meet fill rate or service level requirements? Without sample uncertainty? Without life data? Don’t believe people who write that it can’t be done!
Reliability of Breast Implants
Dear Larry
Thank you for your data request for breast implant data and apologies for the delay in responding. The data available is:
- The number of women receiving implants, by year, by major manufacturer
- Number of Explants: All Manufacturers (inc. Others and Unknown Brands)
My colleagues have been copied into this email to show your request has been actioned. I hope this is helpful. [Read more…]
Covariance of Renewal Process Reliability Function Estimates Without Life Data?
Email from www.smartcorp.com advertised how to forecast inventory requirements using time-series analyses: single and double exponential smoothing, linear and simple moving average, and Winters models. SmartCorp compares alternative times-series forecasts in a “tournament” that picks the best forecast. Charles Smart says forecasting, “…particularly for low-demand items like service and spare parts — is especially difficult to predict with any accuracy.”
Time series forecasts also quantify variance. Excel’s time-series FORECAST() functions do exponential smoothing, account for seasonality and trend, and “pointwise” confidence intervals. Pointwise means only one confidence interval is valid at a time; not a confidence band on several forecasts!
Uncertainty in Population Estimates?
Dick Mensing said, “Larry, you can’t give an estimate without some measure of its uncertainty!” For seismic risk analysis of nuclear power plants, we had plenty of multivariate earthquake stress data but paltry strength-at-failure data on safety-system components. So we surveyed “experts” for their opinions on strengths-at-failures distribution parameters and for the correlations between pairs of components’ strengths at failures.
If you make estimates from population field reliability data, do the estimates have uncertainty? If all the data were population lifetimes or ages-at-failures, estimates would have no sample uncertainty, perhaps measurement error. Estimates from population field reliability data have uncertainty because typically some population members haven’t failed. If field reliability data are from renewal or replacement processes, some replacements haven’t failed and earlier renewal or replacement counts may be unknown. Regardless, estimates from population data are better than estimates from a sample, even if the population data is ships and returns counts!
[Read more…]Forecast Parts’ Demands, Without Life Data, for a Nonstationary Process
In the 1960s, my ex-wife’s father set safety stock levels and order quantities for Pep Boys. He used part sales rates and the Wilson square-root formula to set order quantities.
Why not use the ages of the cars into which those parts go, to forecast part sales and recommend stock levels? Imagine you had vehicle counts (year, make, model, and engine) in the neighborhoods of parts stores, catalogs of which parts and how many go into which cars, and store sales by part number.
[Read more…]Credible Reliability Test Planning
How to allocate subsystems’ MTBF requirements with testing? Name-withheld-to-protect-the- guilty proposed “Top-Down” reduction in subsystem MTBF requirements; the more subsystems (in series) that you test, the lower the subsystem required MTBF! “The correct formula is
1/MTBF(subsystem requirement) = 1/MTBF(system requirement) –
((# of subsystems in series – # of subsystems tested)/MTBF(subsystem).”
This “Top-Down…” method is uncited and not found in Internet search.
[Read more…]Please Enter Forecast_____
Reliability-based forecasts can be made from field data on complaints, failures, repairs, age-replacements (life limits), NTFs (no trouble found), WEAP (warranty expiration anticipation phenomenon), spares, warranty claims, or deaths. Some spares inventory forecasting software says… “Please enter forecast______” No kidding. 1800 years ago Roman Jurist Ulpian made actuarial pension cost forecasts for retiring Roman Legionnaires. Would you like actuarial forecasts? Their distributions? Stock recommendations?
[Read more…]Renewal Process Estimation, Without Life Data
At my job interview, the new product development director, an econometrician, explained that he tried to forecast auto parts’ sales using regression. His model was
sales forecast = SUM[b(s)*n(t-s)] + noise; s=1,2,…,t,
where b(s) are regression coefficients to be estimated, n(t-s) are counts of vehicles of age t-s in the neighborhood of auto parts stores. The director admitted to regression analysis problems, because of autocorrelation among the n(t-s) vehicle counts, no pun intended.