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Inspection is not always a neutral clock. If unstable specimens are examined more often, the visit process carries information about the material state and can distort naive exit maps.
Open the chapter contents · Polymer Science root · Gold Standard of Education · How X Works
Chapter contents
Choose the route closest to the question, or read from Chapter 1 for the complete argument. The chapters remain open on the page; these grouped routes are an index.
Route 1 · Frame the problem
Route 2 · Work the ledgers
Route 3 · Transfer the method
Route 4 · Check limits and evidence
Route 5 · Ask and continue
CHAPTER 1 OF 12 · FRAME THE PROBLEM
1. The observation schedule can select the evidence
A fixed protocol inspects every specimen at the same planned times. An adaptive protocol may add scans after clouding, stress whitening or a rapid modulus change. The extra observations are scientifically useful, but they make observation intensity depend on the evolving state.
A naive analysis that treats every recorded image as an independent snapshot over-represents specimens that generated more visits. Informative inspection is a sampling problem layered on top of interval-censored exits and uncertain mechanisms.
CHAPTER 2 OF 12 · FRAME THE PROBLEM
2. Represent visits as a counting process
For each specimen, define a visit-count process N(t) that increases whenever an inspection occurs. Its intensity can depend on protocol, past observations, latent material state and time since the previous visit.
The exit process records first departure from a regime or another event of interest. A joint model links visit intensity and exit risk through observed history, shared latent effects or both. The chosen link is an assumption to test, not a fact revealed by the data.
CHAPTER 3 OF 12 · WORK THE LEDGERS
3. A fixed-and-triggered inspection ledger
Imagine eight polymer films followed for 60 minutes. Four remain visually stable and four develop early warning signs. Triggered visits supplement the common 0, 30 and 60 minute schedule.
| Film group | Films | Visits per film | Observed exits |
|---|---|---|---|
| Stable | 4 | 3 | 1 |
| Warning signs | 4 | 7 | 3 |
| All films | 8 | 40 visits | 4 exits |
| Fixed schedule only | 8 | 24 planned visits | Exit status still specimen-level |
The warning group contributes 28 of 40 visits despite containing half the films. A visit-level percentage therefore describes the observation process as much as the material population.
CHAPTER 4 OF 12 · WORK THE LEDGERS
4. Worked size bias from unequal visit intensity
Suppose high-risk specimens form 40% of a population and average six visits, while lower-risk specimens form 60% and average two. The proportion of all visits contributed by high-risk specimens is 0.4×6 divided by 0.4×6 + 0.6×2, which equals 2.4/3.6, or about 67%.
| Quantity | High risk | Lower risk | Combined |
|---|---|---|---|
| Population share | 40% | 60% | 100% |
| Visits per specimen | 6 | 2 | — |
| Visit-weighted mass | 2.4 | 1.2 | 3.6 |
| Share among visits | 67% | 33% | 100% |
The correction is not simply to delete triggered visits. Their timing contains evidence. The analysis must retain that evidence while acknowledging why it was collected.
CHAPTER 5 OF 12 · WORK THE LEDGERS
5. Three modelling routes answer different questions
A history-adjusted approach conditions visit intensity on recorded past observations. Inverse-intensity weighting reweights observations by the probability of being seen. A shared-latent-effect joint model lets unobserved susceptibility influence both visits and exits.
Each route requires positivity: relevant specimen histories must retain a nonzero chance of observation. Weighting becomes unstable when some histories are almost always or almost never inspected. Latent-effect models replace that difficulty with stronger structural assumptions.
CHAPTER 6 OF 12 · TRANSFER THE METHOD
6. Join the visit and exit likelihoods carefully
A complete contribution can include the scheduled and triggered visit times, measurements at those visits, an interval containing the exit and right-censoring when no exit is seen. The likelihood must distinguish administrative end of follow-up from a material-dependent loss of observation.
When inspection is destructive, the visit can change or terminate the specimen’s future. That is not merely informative timing; it is an intervention on the observation unit and may need a multistate or competing-event design.
CHAPTER 7 OF 12 · TRANSFER THE METHOD
7. Changed-context transfer: adhesive bond monitoring
Transfer the method to adhesive joints monitored by acoustic emission. A burst can trigger more frequent imaging, while joints with quiet signals remain on the fixed schedule. Joint modelling can prevent burst-triggered inspection density from being mistaken for a larger population of unstable joints.
The transfer check asks whether the trigger has a fixed threshold, whether inspections alter loading, and whether quiet failures can occur. A visit model cannot rescue a sensor that is blind to an important failure route.
CHAPTER 8 OF 12 · TRANSFER THE METHOD
8. Connect observation timing to prior polymer guides
The joint timing-and-cause guide keeps interval and mechanism uncertainty together. The interval-censoring guide explains why an event remains inside its inspection bracket.
Use the competing-exit guide when the first observed departure can occur by several physical mechanisms.
CHAPTER 9 OF 12 · CHECK LIMITS AND EVIDENCE
9. Limits and misconceptions
Joint modelling does not prove why an inspection occurred. Trigger logs, protocol versions and technician notes are still evidence. If unrecorded judgement drives visits, results can remain sensitive to assumptions about that hidden process.
More frequent observation can narrow event intervals without increasing the number of independent specimens. It can improve timing precision and worsen selection bias at the same time. Those two effects should not be collapsed into one quality score.
CHAPTER 10 OF 12 · CHECK LIMITS AND EVIDENCE
10. Practical evidence checklist
Archive the planned schedule, actual visit times, trigger reason, past measurements available at each decision, missed visits, dropout reason, destructive tests and protocol changes. Plot visit intensity against recorded warning signals before fitting a joint model.
Compare fixed-schedule analyses, history-adjusted weights, weight truncation, shared-effect models and sensitivity scenarios for unrecorded triggers. Report specimen-level and visit-level counts separately.
CHAPTER 11 OF 12 · ASK AND CONTINUE
11. Frequently asked questions
Are irregular visits always informative?
No. Equipment availability or a random rota can create irregularity unrelated to material state. The mechanism, not irregularity alone, determines informativeness.
Can I analyse only scheduled visits?
That can be a useful benchmark, but it discards timing evidence and may still be biased if scheduled visits are missed selectively.
Does a joint model recover the true latent state?
No. It estimates under declared observation and dependence assumptions that require diagnostics and sensitivity analysis.
CHAPTER 12 OF 12 · ASK AND CONTINUE
12. Sources and next reading
Liang, Lu and Ying develop joint analysis with informative observation times. Han and colleagues model informative visits and dropout together. Dai and Pan study survival and longitudinal outcomes with informative observation times. The polymer ledgers above are original teaching examples.
Continue through the Polymer Science root, the joint timing-and-cause guide and hidden semi-Markov regime guide. The Gold Standard of Education and How X Works provide the wider route.
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