Shotgun repair is trying to fix a system problem by replacing parts until the problem goes away. It is often done without regard to parts’ age-specific reliability information. Should you test before replacement? Which test(s) should you do? In which order? How long? Which part should you replace next if the test gave no indication of what’s wrong? What if test indication is imperfect or the fault is intermittent? What if there are more than one part failure?

Which of these six failure rate functions do your products and their service parts have? You don’t know? You don’t have field reliability lifetime data by product name or part serial number? That’s OK. Lifetime data are not required to estimate and classify failure-rate functions, including attrition and retirement. GAAP requires statistically sufficient field reliability data to classify failure rate functions for RCM.

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.

Suppose installed base or cohorts in successive periods have different reliabilities due to nonstationarity? What does that do to forecasts, estimates, reliability predictions, diagnostics, spares stock levels, maintenance plans, etc.? Assuming stationarity is equivalent to assuming all installed base, cohorts, or ships have the same reliability functions. At what cost? Assuming a constant failure rate is equivalent to assuming everything has exponentially distributed time to failure or constant failure rate. At what cost?

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.

As I rode, I thought, how could I use reliability statistics to optimize a solar-tube production line? Then I noticed a brass glint in the scrub brush. It didn’t look like trash, so I stopped and found an old brass oil lamp like Aladdin’s. Naturally, I rubbed it. There was a flash and a puff of smoke, and out popped the genie who said, “Yes master, by the powers vested in me, I grant you three wishes.”