SPC Control Chart and Distribution

Mix.install([
  {:plotly_ex, "~> 0.3"},
  {:kino, "~> 0.18"}
])

Section

The control chart (left, 70% width) shows measurements with UCL/LCL and a centre line drawn as scatter traces so they appear in the legend. Points outside the control limits are highlighted as violation markers.

The distribution histogram (right, 20% width) uses orientation: "h" so bins run along the shared y-scale. It has its own independent yaxis2 anchored to xaxis2, with tick labels hidden to avoid duplication.

alias Plotly.{Figure, Scatter, Histogram}

:rand.seed(:exsss, {10, 20, 30})

n = 30
process =
  for i <- 1..n do
    base = (for _ <- 1..12, do: :rand.uniform()) |> Enum.sum() |> Kernel.-(6.0)
    if i > 20, do: base + 1.5, else: base
  end

mean  = Enum.sum(process) / n
sigma = :math.sqrt(Enum.sum(Enum.map(process, fn v -> (v - mean) * (v - mean) end)) / n)
ucl   = mean + 3 * sigma
lcl   = mean - 3 * sigma

violations =
  process
  |> Enum.with_index(1)
  |> Enum.filter(fn {v, _i} -> v > ucl or v < lcl end)

viol_x = Enum.map(violations, fn {_v, i} -> i end)
viol_y = Enum.map(violations, fn {v, _i} -> v end)

Figure.new()
|> Figure.add_trace(
  Scatter.new(
    x: Enum.to_list(1..n),
    y: process,
    mode: "lines+markers",
    name: "Data",
    line: %{color: "blue", width: 2},
    marker: %{color: "blue", size: 8, symbol: "circle"}
  )
)
|> Figure.add_trace(
  Scatter.new(
    x: viol_x,
    y: viol_y,
    mode: "markers",
    name: "Violation",
    marker: %{color: "rgb(255,65,54)", size: 12, symbol: "circle-open", line: %{width: 3}, opacity: 0.5}
  )
)
|> Figure.add_trace(
  Scatter.new(
    x: [0.5, n + 0.5, nil, 0.5, n + 0.5],
    y: [lcl, lcl, nil, ucl, ucl],
    mode: "lines",
    name: "LCL/UCL",
    line: %{color: "red", dash: "dash", width: 2}
  )
)
|> Figure.add_trace(
  Scatter.new(
    x: [0.5, n + 0.5],
    y: [mean, mean],
    mode: "lines",
    name: "Centre",
    line: %{color: "grey", width: 2}
  )
)
|> Figure.add_trace(
  Histogram.new(
    y: process,
    orientation: "h",
    name: "Distribution",
    xaxis: "x2",
    yaxis: "y2",
    marker: %{color: "blue", line: %{color: "white", width: 1}}
  )
)
|> Figure.update_layout(
  title: "SPC Control Chart and Distribution",
  xaxis: %{domain: [0, 0.7], zeroline: false},
  yaxis: %{zeroline: false},
  xaxis2: %{domain: [0.8, 1]},
  yaxis2: %{anchor: "x2", matches: "y", showticklabels: false}
)
|> Plotly.show()