This case study reconstructs the use case that originally motivated
the package: monitoring daily COVID-19 mortality in Recife, capital of
Pernambuco state, Brazil, during 2020. The challenge is that epidemic
curves are non-stationary by construction — they grow, peak,
and recede. A classical Shewhart chart applied naively to the raw counts
would either miss the early acceleration or fire constant false alarms
during the descent.
The right tool is a regression-based control chart with automatic
phase detection: fit a model to the trend, place limits around the fit,
and let runs rules announce when the trend itself has changed.
The data
cvd_recife is a tibble shipped with the package. (Run
source("data-raw/build_all.R") once if the dataset is not
yet built locally.)
data(cvd_recife)
head(cvd_recife)
#> # A tibble: 6 × 3
#> date new_deaths .t
#> <date> <int> <int>
#> 1 2020-03-28 4 1
#> 2 2020-03-29 0 2
#> 3 2020-03-30 0 3
#> 4 2020-03-31 0 4
#> 5 2020-04-01 1 5
#> 6 2020-04-02 1 6
Columns: date, new_deaths, .t
(an integer 1..N row index, useful when a model needs a numeric
predictor).
A first attempt: classical I-MR
fit_imr <- shewhart_i_mr(cvd_recife,
value = new_deaths,
index = date)
broom::glance(fit_imr)
#> # A tibble: 1 × 8
#> type n phase sigma_hat sigma_method n_violations n_rules pct_violations
#> <chr> <int> <chr> <dbl> <chr> <int> <int> <dbl>
#> 1 i_mr 279 phase_1 5.17 mr 139 2 0.498
The chart fires repeatedly along the entire ascending limb of the
first wave — every “violation” is the chart noticing that today is worse
than yesterday, which is true and is also exactly what we already knew.
The classical chart is the wrong tool: it reports violations of
stationarity, not violations of the underlying public health story.
Why log-log?
The model = "loglog" choice applies the transform \(\log(\log(y/\alpha + 1) + 1)\) to the
response before fitting a linear trend. This is more aggressive than
log — it stabilises variance for very right-skewed,
heavy-tailed counts. For COVID mortality counts, where day-to-day
variability scales sharply with the level, the log-log scale gave the
cleanest residuals in the original analysis. Run
shewhart_box_cox() on your own series to let the data
choose:
shewhart_box_cox(cvd_recife$new_deaths + 1)$lambda_hat
#> [1] 0
If the maximiser is near 0, take logs. If it is near 0.5, the log-log
scale is a reasonable approximation. For values between 0 and 1, a
Box-Cox transformation in that range is the most defensible choice.
A note on the package’s history
The original v0.1 of Shewhart (now
shewhartr) was built specifically for this kind of
analysis, in collaboration with the epidemiology team monitoring
COVID-19 in Recife. The transformation choices, the 7-points-in-a-row
rule, and the start-base / phase-detection structure were all calibrated
for daily mortality counts. That heritage is preserved here as one
application among many, rather than as the package’s organising
principle. For everyday SPC, prefer the classical chart families and the
cleaner default rule (Nelson 2 — 9 points).
