Download Statistical Process Control (SPC) Definitions Concept of Statistical

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) = D4R
Center Line
=R
Lower Control Limit (LCL) = D3R
s Charts (Standard Deviations)
X Charts (Means)
s Charts are used to monitor variation
(plots of sample standard deviations)
X Charts are used to monitor sample means
(plots of sample means, based on ranges)
Notation
n = size of each sample
s = mean of sample 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} )
Control Limits ( 99.7 % confidence intervals { 3 SD’s} )
Upper Control Limit (UCL) = B4s
Upper Control Limit (UCL) = X + A2R
Center Line
Center Line
=s
Lower Control Limit (LCL) = B3s
=X
Lower Control Limit (LCL) = X - A2R
X Charts (Means)
p Charts (Proportion)
X Charts are used to monitor sample means
(plots of sample means, based on standard deviations)
p Charts are used to monitor attribute’s proportionality
(plots of sample attribute proportions)
Notation
n = size of each sample
X = mean of sample means = mean of all samples
Notation
n = size of each sample
p = pooled estimate of attribute’s overall proportion
Control Limits ( 99.7 % confidence intervals { 3 SD’s} )
Control Limits ( 99.7 % confidence intervals { 3 SD’s} )
Upper Control Limit (UCL) = X + A3s
Upper Control Limit (UCL) = p + 3 [ p ( 1 - p ) / n ]1/2
Center Line
Center Line
=X
Lower Control Limit (LCL) = X - A3s
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 + 3c 1/2
Center Line
=p
Lower Control Limit (LCL) = p - 3 [ p ( 1 - p ) / n ]1/2
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.
=c
Lower Control Limit (LCL) = c - 3c 1/2
Fourteen consecutive points alternating above and below
the center line.