A warranty claim is a shipment, then a failure, then a reporting and adjudication delay, so a count of claims received in a calendar month mixes every cohort at every age and is always incomplete at the recent end. The structure that makes it readable is a development triangle indexed by ship cohort and months in service, the same object general insurance uses for reserving, and Mack's 1993 result gives you a standard error on the development factors. Where a warranty expires on age or usage, whichever comes first, the effective coverage of a cohort depends on the usage mix inside it, so channel mix moves the claim curve without any change in reliability. At expiry the failures continue and the payer changes, which is why a parts plan built on claim counts falls off a cliff the machines do not.
The quality review in November has a chart on it that everybody likes. Claims per thousand units for machines shipped in the third quarter are running about 40 percent below the cohort before them, and the supplier change made in June is getting the credit. By the following March that cohort has caught its predecessor and gone slightly past it. The June change has been rolled out across two more lines on the strength of a number that was never real, and nobody reopens the November slide.
Nothing about the machines changed between November and March. Claims that had not yet been reported arrived, and the cohort filled in.
A claim is a shipment, a failure and two delays
Four events sit between a machine leaving the factory and a row appearing in your warranty data. The unit ships and eventually enters service. Something fails. The customer presents the machine, which frequently means waiting for the next scheduled service rather than calling on the day. The dealer or service partner files, the claim is adjudicated, and it lands in the system.
Each of those steps has a distribution attached to it, and the series you observe is the convolution of the shipment curve, the time-to-failure distribution and the reporting delay. Lawless set this structure out in the International Statistical Review in 1998 and it has not needed revising.
The delays are ordinary and larger than people expect. Dealers batch submissions to a weekly or monthly cycle. Adjudication takes its own cycle. High-value claims often require the failed part to be returned and inspected before approval, which can add a month by itself. Campaign work and goodwill approvals sit in yet another queue. In vehicle and equipment programmes a median reporting delay of one to three months is unremarkable, with a tail running considerably longer, and the tail is disproportionately made of the expensive claims.
The result is that a calendar-month claim count answers a question nobody asked. It mixes a three-month-old cohort with a thirty-month-old one, applies whatever reporting completeness the recent months happen to have, and gets reported as performance.
The triangle that makes the recent months readable
Index the data two ways instead of one. Rows are the ship cohort, meaning the month of manufacture or in-service date. Columns are months in service. Each cell holds the claims for that cohort at that age. Every month of new data adds one diagonal to the grid, and the newest cohorts have only a few columns filled.
That object is the development triangle that general insurance has used for reserving for decades, and the standard estimator is the chain ladder. Compute the ratio of cumulative claims at age k plus one to cumulative claims at age k, average it across the cohorts old enough to have both, and apply the resulting factors to the immature cohorts to project them forward. Mack's 1993 paper in the ASTIN Bulletin gives the distribution-free standard error for those estimates, which turns the projection into an interval you can argue with rather than a single number that gets quoted as fact.
Work the arithmetic on the November chart. A cohort of 10,000 units shipped in July has 180 claims recorded by month four. Across the mature cohorts, 62 percent of the eventual first-year claims for a cohort are recorded by month four. The projection is 180 divided by 0.62, which is 290. Reporting 180 as that cohort's performance understates it by more than a third, and the understatement shrinks as the cohort ages, which is exactly the pattern that makes a fix look like it worked and then quietly stop working.
There is a better version available if your data supports it. Kalbfleisch and Lawless showed in Technometrics in 1991 how to estimate the reporting delay distribution directly, using the failure date recorded on each claim against the date the claim was processed. That gives you the delay distribution as a measured object rather than something inferred from the shape of the triangle, and it separates a genuine change in failure rate from a change in reporting speed. Most warranty systems capture both dates on every claim and almost nobody looks at the difference between them. Wu's 2012 review in Quality and Reliability Engineering International is the place to start on the wider set of methods that build on this.
Age or usage, whichever comes first
Most equipment and vehicle warranties have two limits. Three years or 100,000 kilometres. Two years or 4,000 operating hours. The coverage ends at whichever arrives first, and Blischke and Murthy's 1994 treatment of two-dimensional warranty policies is the reference for the mechanics.
The planning consequence is that the effective warranty period in months is a property of the customer rather than of the policy. A fleet operator running 60,000 kilometres a year exits a three year, 100,000 kilometre warranty after twenty months. A retail buyer at 12,000 kilometres a year runs the full thirty-six. Two cohorts with identical reliability will produce different claim curves purely from their usage mix, and usage mix moves with the sales channel mix, which moves with commercial decisions made in a different building.
If you have telematics or service-visit odometer readings, build the exposure denominator in usage terms and the claim curves become comparable across cohorts. Where you cannot get usage, sales channel is a reasonable proxy and it is stable enough to be worth splitting the triangle on. A single blended triangle across fleet and retail will produce development factors that describe neither.
Movements in the claim rate that have nothing to do with reliability
The claims series is generated by an administrative process as much as by physics, and several ordinary things shift it.
- Adjudication rules. A change to the labour time allowance or to the documentation standard reduces approved claims with no change in failures.
- Goodwill policy. Out-of-warranty repairs approved as goodwill appear in the data attached to old cohorts and inflate their late development.
- Dealer economics. The warranty labour rate relative to the retail rate determines how enthusiastically a network files, and it gets renegotiated.
- Campaign traffic. A recall or a service bulletin brings in machines that would not otherwise have come, and the inspections find unrelated faults, which pulls claims forward from later months.
- The denominator. Units at risk computed from ship date rather than in-service date, with a registration lag of a month or two sitting between them, biases the early-age rates downward for everyone.
The diagnostic for separating administrative movement from reliability movement is to pick a failure mode that adjudication treats consistently, usually a catastrophic failure with a physical part return and no discretion in it, and track its claims per thousand alongside the total. When the total moves and the reference mode holds still, the change happened in the process rather than in the product.
The cliff at expiry that the machines do not have
At thirty-six months the claims for a cohort fall to near zero. The failures carry on at whatever rate the hardware dictates, and quite often at a higher one, since wear-out modes tend to arrive after the warranty window rather than inside it.
Two things follow for anyone using warranty data as a demand input. Forecasting service parts from claims alone will systematically under-forecast any part whose failure distribution peaks past the coverage period, and those are usually the expensive ones. And the volume that continues after expiry is a commercial variable rather than a technical one, because the share you capture depends on your service pricing, your network coverage and how hard the independent channel competes for the work. A ten point movement in post-warranty capture changes a parts forecast far more than a reliability improvement does. The installed base method that carries the forecast past the warranty boundary is a separate piece of work with its own post.
There is a bump immediately before the cliff, and it is worth planning for explicitly. Customers bring machines in for anything marginal in the last few months of cover, so months thirty-four to thirty-six carry elevated claims and elevated parts consumption, and a cohort-indexed forecast predicts that bump while a calendar-month forecast walks into it.
One triangle, two consumers
Finance wants a warranty accrual: expected cost per unit sold, by product line, by month, aggregated. Planning wants claims by part number, by region, by month. Both come out of the same triangle and the argument about who owns it wastes more time than the modelling does.
The failure mode is consistent. The triangle gets built by finance at product-line cost level because that is what the accrual needs, it never produces a part-level output, and parts planning goes back to forecasting off recent claim history, which is the incomplete diagonal the whole exercise was meant to correct. Build it at claim-cause or part-group level, then aggregate upward for the accrual. Aggregating up is arithmetic and disaggregating down is guesswork.
Develop counts and cost separately while you are at it. Expensive claims adjudicate slowly, so a cost triangle develops later than a count triangle built from the same claims, and applying count development factors to cost will understate the reserve on every recent cohort.
Where this stops
The denominator is the weakest part of most warranty datasets. Units at risk needs an in-service date, registration data is incomplete in every channel that sells through intermediaries, and the gap between ship date and in-service date varies by region and by season. An error there moves every rate in the analysis by the same proportion and is invisible in the triangle, since the triangle only sees the claims.
The harder limit is new products. A cohort with no history has no development pattern, so you borrow one from a predecessor, and that borrowing is the dominant source of error in the projection rather than a detail in it. The honest treatment is to take two or three candidate predecessors, project with each, and report the range. A single point estimate for a launch cohort's first-year warranty cost carries a precision it has not earned.
Chain ladder also assumes the development pattern is stable across cohorts, and the things that break that assumption are exactly the things a business does. A new dealer submission system changes reporting speed. A warranty policy change alters what gets filed. A supplier change on a high-volume part shifts the mix of failure modes and therefore the mix of adjudication speeds. When you change the process generating the data, the historical factors describe a system that no longer exists, and the projection stays confidently wrong until enough new cohorts mature to re-estimate them.
Take three years of claims, index them by ship cohort and months in service, and plot the difference between the failure date and the processing date on every row.
More on this in service parts on the DemandLabs platform.
