Worked examples — Testing — unit, integration, system, acceptance, smoke, regression

This page is a drill. The parent note told you what the six test types are. Here we throw every awkward case at you — every "which test do I use?", every degenerate input, every limiting number — and work each one fully. First guess, then read.

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The scenario matrix

Think of every question this topic can ask as living in one of these cells. The worked examples that follow each carry a [Cell X] tag so you can see the whole space get covered.

Cell	Case class	What makes it tricky	Example
A	Classify a test (unit vs integration)	the "mocked DB" trap	Ex 1
B	Classify a test (system vs acceptance)	Verification vs Validation	Ex 2
C	Classify a test (smoke vs regression)	both "re-run checks"	Ex 3
D	Cost-of-delay — normal $n$	$\text{Cost}=c{k}^n$	Ex 4
E	Cost-of-delay — degenerate $n=0$	"caught immediately" edge	Ex 4
F	Cost-of-delay — limiting large $n$	why cost explodes	Ex 4
G	Suite trust — normal case	$P=p^n$	Ex 5
H	Suite trust — degenerate $p=1$ or $n=1$	perfect / single test	Ex 5
I	Suite trust — limiting $n\to \infty$	why flaky top of pyramid is poison	Ex 5
J	Real-world word problem	pick tests + estimate savings	Ex 6
K	Exam-style twist	"all tests green" but wrong product	Ex 7
L	Ordering a pipeline	fail-fast arithmetic	Ex 8

The two formulas you will lean on (from the parent, restated so nothing is assumed):

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Cells A–C — classification (no arithmetic, pure judgement)

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Cells D–F — cost of delay across all $n$

The figure below draws $\text{Cost}(n)=c{k}^n$ with $c=1$, $k=10$. Notice the vertical axis is logarithmic — a straight line there means explosive growth.

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Cells G–I — suite trust across all $p$ and $n$

The next figure plots $P_{\text{trust}}=p^n$ against the number of tests $n$, for three reliabilities $p$. Watch the top curve collapse as tests accumulate.

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Cell J — a real-world word problem

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Cell K — the exam-style twist

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Cell L — ordering a pipeline (fail-fast arithmetic)

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Recall Quick self-test on the matrix

Test with mocked DB is which type? ::: A unit test — no real seam runs. System test answers which V&V word? ::: Verification — built the product right. Acceptance test answers which V&V word? ::: Validation — built the right product. Cost of a bug caught immediately, c=\50, k=10$?:::$50\cdot10^0 = $50$.Costafterescaping3stages,samenumbers?:::$50\cdot10^3 = $50{,}000$.Suitetrustfor$n=500$testseach$p=0.999$?:::$0.999^{500}\approx 0.61$—about39\%false-redrisk.As$n\to\infty$withany$p<1$,$P_{\text{trust}}\to$?:::$0$ — flaky tests compound to worthlessness. Why does smoke run first in a pipeline? ::: To fail-fast and avoid wasting minutes on the full suite.