mqr.spc.rules.

aofb_nsigma

mqr.spc.rules.aofb_nsigma(a, b, n)

Rule monitoring the proportion of samples outside a multiple of sigma.

This function returns an alarm rule that alarms when a out of b statistics in a row are beyond n multiples of the statistic standard error. Only the last sample of the b is marked as an alarm.

This function generates a rule. The result of this function is another function that can be passed to mqr.plot.spc.alarms or combine.

Parameters:

aint

Intensity – the number of statistics in b periods outside n standard deviations required to trigger an alarm.

bint

Period – the number of samples to check for a statistics outside n standard deviations required to trigger an alarm.

nfloat

Threshold in multiples of the standard error.

Returns:

Callable[(ControlStatistic, ControlParams), pandas.Series[bool]]

A function taking a control statistic and the params used to create them, and returning a series with True marking alarms.

Examples

The result of this function can be passed to the plotting routines. This example overlays a “4/5 > 2sigma” rule on an X-bar chart.

data = pd.DataFrame({
    'Xbar': np.array([11, 13, 10, 12, 12, 12, 9, 11, 12])
#                         ^^^^^^^^^^^^^^^^^^ (4/5>=2sigma)
})

params = mqr.spc.XBarParams(centre=10, sigma=1)
stat = params.statistic(data)
rule = mqr.spc.rules.aofb_nsigma(a=4, b=5, n=2)

fig, ax = plt.subplots(figsize=(7, 3))
mqr.plot.spc.chart(stat, params, ax=ax)
mqr.plot.spc.alarms(stat, params, rule, ax=ax)

(Source code, png, pdf)