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Statistical Process Control (SPC)
Overview Data Characteristics Nature or Shape of the Distribution Representative Value - Mean Measure of Variation - Standard Deviation Pattern of Change with respect to Time
Quality Control Consistency (limited variation from unit to unit)
Definitions
Process Data Chronologically arranged data.
Statistically Stable ( Within Statistical Control ) Only random variation, no patterns or cycles.
Variation Random Variation - Due to chance, inherent in any process. Assignable Variation - Results from identifiable causes.
Concept of Statistical Quality Control
Only when a process is statistically stable can the data be treated as if it came from a single population.
One method of maintaining quality is to reduce the amount of assignable variation.
Minimum Assignable Variation implies a stable process; a stable process is indicative of a quality product or service.
Data charts are useful tools for monitoring the stability of a process, and hence help maintain quality.
SPC - Data Charts
Run Chart Sequential plot of individual data values over time. Control Charts (Quantitative & Qualitative) Sequential plot of average values over time. Control values indicate central tendency and the limits of acceptable excursions. Upper Control Limit ( UCL ) Center Line Lower Control Limit ( LCL ) Quantitative ( R, X, s ) Qualitative ( p, c )
Control Charts
Quantitative Control Charts R Charts - Monitor Variation (Range) s Charts - Monitor Variation ( Standard Deviation) X Charts - Monitor Means (Averages)
Qualitative Control Charts p Charts - Monitor Proportions of Characteristic Value c Charts - Monitor Number of Characteristic Values Note: p Charts & c Charts are often used to track the proportion or number of defective items per lot.
R Charts (Range)
R Charts are used to monitor variation (plots of sample ranges, not individual values) Notation n = size of each sample R = mean of sample ranges Control Limits ( 99.7 % confidence intervals { 3 SD’s} ) Upper Control Limit (UCL) = D 4 R Center Line = R Lower Control Limit (LCL) = D 3 R
s Charts (Standard Deviations)
s Charts are used to monitor variation (plots of sample standard deviations)
Notation n = size of each sample s = mean of sample standard deviations
Control Limits ( 99.7 % confidence intervals { 3 SD’s} )
Upper Control Limit (UCL) = B 4 s Center Line = s Lower Control Limit (LCL) = B 3 s
X Charts (Means)
X Charts are used to monitor sample means (plots of sample means, based on ranges) Notation n = size of each sample X = mean of sample means = mean of all samples Control Limits ( 99.7 % confidence intervals { 3 SD’s} ) Upper Control Limit (UCL) = X + A 2 R Center Line = X Lower Control Limit (LCL) = X - A 2 R
X Charts (Means)
X Charts are used to monitor sample means (plots of sample means, based on standard deviations)
Notation n = size of each sample X = mean of sample means = mean of all samples
Control Limits ( 99.7 % confidence intervals { 3 SD’s} )
Upper Control Limit (UCL) = X + A 3 s Center Line = X Lower Control Limit (LCL) = X - A 3 s
p Charts (Proportion)
p Charts are used to monitor attribute’s proportionality (plots of sample attribute proportions) Notation n = size of each sample p = pooled estimate of attribute’s overall proportion Control Limits ( 99.7 % confidence intervals { 3 SD’s} ) Upper Control Limit (UCL) = p + 3 [ p ( 1 - p ) / n ]1/ Center Line = p Lower Control Limit (LCL) = p - 3 [ p ( 1 - p ) / n ]1/
c Charts (Count)
c Charts are used to monitor attribute’s numerical quantities (plots of sample attribute numbers)
Notation n = size of each sample c = pooled estimate of attribute’s overall quantity
Control Limits ( 99.7 % confidence intervals { 3 SD’s} )
Upper Control Limit (UCL) = c + 3 c 1/ Center Line = c Lower Control Limit (LCL) = c - 3 c 1/
Out-of-Control Criteria
Obviously apparent non-random pattern, trend, or cycle.
Outlying point beyond upper or lower control limit.
Run-of-#-Points Rule Eight consecutive points above or below the centerline.
Six consecutive points all increasing or all decreasing.
Fourteen consecutive points alternating above and below the center line.
