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WECOrules.jl

A Julia package that implements the Western Electric Company's eight rules for detecting process change. In statistical quality control, these rules are often used along with control charts to determine whether an industrial process remains nominally within process control limits. Failures are deemed to be reasons to investigate and resolve potential problems with the industrial process.

The Eight Rules

A process is deemed out-of-control if:

  1. A single data point more than three standard deviations from the nominal value.
  2. Nine sequential data points above (or below) the nominal value.
  3. Six sequential data points monotonically increasing (decreasing).
  4. Sixteen sequential data points alternating up and down.
  5. Two of three data points above (or below) that are over two standard deviations from the nominal value.
  6. Four of five data points above (or below) that are more than one standard deviation from the nominal value.
  7. Fifteen data points within one standard deviaiton of the nominal value.
  8. Eight sequential data points that are more than one standard deviation from the nominal value.

where the nominal value is the value deemed optimal for a measured property of the process. One standard deviation is determined from prior observations of the process.

weco(
  df::DataFrame, 
  nominal::Real, 
  onesigma::Real; 
  timestamp=:Date, 
  value=:Value, 
  result::Union{Missing,Function}=missing
)::DataFrame
  • The package takes a DataFrames package DataFrame containing time-sequence data.
  • The nominal and onesigma values are specified.
  • The timestamp data is by default in the :Date column
  • The value data is by default in the :Value column
  • The result argument can be a function that can compute an optional 9th column with a go/no go decision based on the previous eight rule columns. The function takes a DataFrame row argument and can be based on any data in df or the :Rule? columns. The default result function returns true if all the rules evaluate true or missing and false otherwise.

Example result function:

mot(v) = ismissing(v) || v
allrules(r) = all(mot.((r[:Rule1], r[:Rule2], r[:Rule3], r[:Rule4], r[:Rule5], r[:Rule6], r[:Rule7], r[:Rule8])))

The method creates a new DataFrame with eight additional Union{Boolean,Missing} columns - one for each of the tests called :Rule1, :Rule2, ..., :Rule8. The columns contain true if the data point in the row datum is "in control" according to the rule and false if the row is "out-of-control" according to the rule. If there is a reason that the rule can't be evaluated then the value will be missing.

If Gadfly has been imported then the method shewhart(...) will plot a Shewhart-like control chart.

shewhart(
  df::AbstractDataFrame, # DataFrame containing columns :Date & :Value (or below)
  nominal::Real, # Nominal value for :Value column
  onesigma::Real; # Nominal 1σ variation in :Value column
  timestamp::Union{Symbol,AbstractString}=:Date, # Alternative to :Date
  value::Union{Symbol,AbstractString}=:Value, # Alternative to :Value
  result::Union{Missing,Function}=missing
)

The plot method first calls weco(df,...) to apply the rules. It plots "passing" data points in green, "failing" in red according to the result function. It also plots yellow horizontal lines at the nominal±2σ level and red horizontal lines at the nominal±3σ levels.