Process Summary and Capability

Related modules

mqr.plot.ishikawa
mqr.process (and mqr.plot.process)
mqr.plot.correlation

Detailed examples

nklsxn/mqr-guide

Fishbone diagram

A fishbone diagram can be constructed with the tools in matplotlib, though constructing all the lines by hand is a bit tedious, so MQR includes a convenience function to create the plot.

The plot can create only two levels of “bones”, including the “spine”. The top-level result is given in the argument problem and the two levels of causes are given in the argument causes.

This is a general diagram.

problem = 'Problem'
causes = {
    'Method': ['Time consumption', 'Cost', 'Procedures', 'Inefficient process', 'Sampling'],
    'Machine': ['Faulty equipment', 'Compatibility'],
    'Material': ['Raw materials', 'Supplier', 'Shortage'],
    'Measurement': ['Calibration', 'Performance', 'Bad measurements'],
    'Environment': ['Bad conditions'],
    'People': ['Lack of training', 'Managers', 'Labor shortage', 'Procedures', 'Sales strategy'],
}

with Figure(8, 5) as (fig, ax):
    mqr.plot.ishikawa(problem, causes, ax=ax)

A more specific example for, say, the variability in the yield strength in a dimension of an injection molded plastic part might be like this.

problem = '$\\mathbf{var}\\ \\sigma_y$'
causes = {
    'method': [
        'gate location', 'shear rate', 'hold pressure',
        'hold time', 'gate-wall ratio', 'location in batch mould'],
    'machine': [
        'time since service', 'time since sensor calibration',
        'warm-up time', 'mold surface texture'],
    'material': ['pellet material', 'colour (dye)', 'supplier'],
    'measurement': ['gauge capability', 'gauge calibration'],
    'environment': ['humidity at pellet hopper', 'ambient temp (cooling time)'],
    'people': ['removal technique', 'removal force'],
}

with Figure(8, 5) as (fig, ax):
    mqr.plot.ishikawa(problem, causes, ax=ax)

Often the defaults and matplotlib’s spacing algorithms will present a tidy diagram. The Ishikawa defaults in MQR can be viewed at

mqr.plot.defaults.Defaults.ishikawa

{'head_space': 2.0,
 'bone_space': 8.0,
 'bone_angle': 0.7853981633974483,
 'cause_space': 1.0,
 'cause_length': 2.0,
 'padding': (1.0, 1.0, 1.0, 1.0),
 'line_kwargs': {'linewidth': 0.8, 'color': 'k'},
 'defect_font_dict': {'fontsize': 12, 'weight': 'bold'},
 'cause_font_dict': {'fontsize': 9, 'weight': 'bold'},
 'primary_font_dict': {'fontsize': 9},
 'bone_rise': 7.0,
 'bone_run': 7.000000000000001}

For this diagram, split the long lines and increase the bone-space and cause-space. To split a line, insert a new-line character “\n” (backslash-n).

causes = {
    'method': [
        'gate location', 'shear rate', 'hold pressure',
        'hold time', 'gate-wall ratio', 'location in\nbatch mould'],
    'machine': [
        'time since service', 'time since\nsensor calibration',
        'warm-up time', 'mold surface texture'],
    'material': ['pellet material', 'colour (dye)', 'supplier'],
    'measurement': ['gauge capability', 'gauge calibration'],
    'environment': ['humidity at pellet hopper', 'ambient temp\n(cooling time)'],
    'people': ['removal technique', 'removal force'],
}

ishikawa_kws = {'bone_space': 15.0, 'cause_space': 2.0}

with Figure(8, 5) as (fig, ax):
    mqr.plot.ishikawa(problem, causes, ax, ishikawa_kws)

Summary statistics

Summary statistics are organised into the following types.

mqr.process.Summary

A set of samples from a process, optionally including specifications for the dimensions which are used to calculate capability.

mqr.process.Specification

A target, and lower and upper limits.

mqr.process.Sample

Measurements from a single dimension in a process/product shown with a set of common descriptive statistics.

mqr.process.Capability

Formed from a sample and a specification, contains process potential, capability, and expected defect rates.

Summary

Of those types, Summary and Specification must be constructed manually. The other two are created automatically when Summary is created with Specifications.

Create a summary of a process from a DataFrame.

data = pd.read_csv(mqr.sample_data('study-random-5x5.csv'))
data.head()

	run	part	operator	replicate	KPI1	KPI2	KPI3	KPO1	KPO2
0	0	A1	Op A	1	152.234	19.952	15.190	159.717	2.619
1	1	A1	Op A	2	149.571	19.914	15.101	159.380	2.116
2	2	A1	Op A	3	150.542	19.735	12.951	162.806	4.656
3	3	A1	Op B	1	148.946	19.661	13.979	159.633	2.031
4	4	A1	Op B	2	148.948	20.171	13.784	163.127	5.880

Pass the measurements from the DataFrame to the mqr.process.Summary constructor.

summary = mqr.process.Summary(data.loc[:, 'KPI1':'KPO2'])
summary

	KPI1	KPI2	KPI3	KPO1	KPO2
Normality (Anderson-Darling)
Stat	0.34262	0.23807	1.1871	0.19191	0.70216
P-value	0.48587	0.77799	0.0040861	0.89435	0.065132
N	120	120	120	120	120
Mean	149.97	20.003	14.004	160.05	4.0189
StdDev	1.1733	0.24530	0.75645	2.0489	1.5634
Variance	1.3767	0.060174	0.57221	4.1979	2.4442
Skewness	0.23671	-0.31725	-0.63426	-0.12055	0.087372
Kurtosis	0.34013	-0.032887	0.37921	-0.16922	-0.18837
Minimum	147.03	19.234	11.639	154.89	-0.37200
1st Quartile	149.22	19.833	13.642	158.87	2.9020
Median	149.97	20.011	14.033	160.03	3.9265
3rd Quartile	150.56	20.174	14.481	161.35	5.2163
Maximum	153.27	20.505	15.460	164.51	8.2830
N Outliers	5	1	4	1	0

Samples are automatically created as part of a Summary, and can be retrieved using indexing syntax.

vstack(
    f'median = {summary['KPO1'].median}',
    summary['KPI2'],
)

median = 160.025

	KPI2
Normality (Anderson-Darling)
Stat	0.23807
P-value	0.77799
N	120
Mean	20.003
StdDev	0.24530
Variance	0.060174
Skewness	-0.31725
Kurtosis	-0.032887
Minimum	19.234
1st Quartile	19.833
Median	20.011
3rd Quartile	20.174
Maximum	20.505
N Outliers	1

Specifications and capability

If specifications (mqr.process.Specification) are passed to Summary then capabilities will be included in the summary. They are stored in the Summary.capabilities attribute.

specs = {
    'KPI1': mqr.process.Specification(150, 145, 155),       # cp=cpk~1.33
    'KPI2': mqr.process.Specification(20.25, 19.00, 21.50), # cp~1.67, cpk~1.33
    'KPI3': mqr.process.Specification(14.00, 11.72, 16.28), # cp=cpk~1.00
    'KPO1': mqr.process.Specification(160, 148, 172),       # cp=cpk~2.00
    'KPO2': mqr.process.Specification(2, -7.6, 11.6),       # cp~2.00, cpk~1.67
}

summary = mqr.process.Summary(data.loc[:, 'KPI1':'KPO2'], specs)
summary.capabilities

	KPI1	KPI2	KPI3	KPO1	KPO2
USL	155.	21.5	16.3	172.	11.6
Target	150.	20.2	14.0	160.	2.00
LSL	145.	19.0	11.7	148.	-7.60
Cpk	1.41	1.36	1.00	1.94	1.62
Cp	1.42	1.70	1.00	1.95	2.05
Defectsst (ppm)	20.4	21.8	2.58e+03	0.00476	0.620
Defectslt (ppm)	123.	97.8	2.62e+03	0.939	11.5

Graphical summaries

These routines (from mqr.plot.process) operate on the types from mqr.process.

The histogram and box plot for a sample and also a confidence interval for its mean can be shown on a plot with

with Figure(5, 5, 3, 1, height_ratios=(4, 1, 1)) as (fig, axs):
    mqr.plot.process.summary(summary['KPO1'], axs)

If a summary was created with specifications, MQR can show sample capabilities graphically. If the target capability is different from 2.0 (the default), pass the target as cp, which truncates the tails of the fitted density function so that if it fits in the tolerance region, then the sample has at least the specified capability.

with Figure(6, 10, 5) as (fig, axs):
    for ax, name in zip(axs, ['KPI1', 'KPI2', 'KPI3', 'KPO1', 'KPO2']):
        mqr.plot.process.capability(summary, name, cp=5/3, ax=ax)

Correlation

Use mqr.plot.correlation to show a detailed correlation plot. The plot includes histograms on the diagonal, scatter plots and fitted lines on the lower triangle, and statistics on the upper triangle. Pass show_conf=True to include confidence intervals on the correlation coefficients. Significant correlations are shown in bold.

with Figure(6, 6, 5, 5) as (fig, axs):
    mqr.plot.correlation.matrix(data.loc[:, 'KPI1':'KPO2'], axs, show_conf=True)