# How to Interpret Shewhart Control Charts Control Chart Philosophy TCQF

```How to Interpret Shewhart
Control Charts
TCQF
October 9, 2012
David E. Stevens
KPTWARE
Control Chart Philosophy
“There is no such thing as constancy in real life. There is, however, such
a thing as a constant-cause system. The results produced by a constantcause system vary, and in fact may vary over a wide band or a narrow band.
They vary, but they exhibit an important feature called stability. Why apply
the terms constant and stability to a cause system that produces results that
vary? Because the same percentage of these varying results continues to fall
between any given pair of limits hour after hour, day after day, so long as the
constant-cause system continues to operate. It is the distribution of results
that is constant or stable. When a manufacturing process behaves like a
constant-cause system, producing inspection results that exhibit stability, it is
said to be in statistical control. The control chart will tell you whether your
process is in statistical control.”
W. E. Deming, “Some Principles Of The Shewhart Methods Of Quality
Control”, Mechanical Engineering, Vol. 66, pp. 137-177, March 1944
Distribution Of BKLD Results
From Constant-Cause System
Distribution Characteristics
Normal Dist.
Mean: 8000
Std. Dev.: 100
Average
95% , + or - 2 Std. Dev.
99%, + or - 3 Std. Dev.
Upper Control Limit, 3 Std. Dev.
8300
8200
Upper Warning Limit, 2 Std. Dev.
Individuals Control Chart
8000
7800
7700
Target
Lower Warning Limit, 2 Std. Dev.
Lower Control Limit, 3 Std. Dev.
Distribution Variation
Monitoring
BKLD
8009
8151
8094
7957
7999
7807
Two-Point Moving Range
.
142
57
137
42
192
Range = Largest Value - Smaller Value
Distribution Of Two Point
Moving Range
Two Point Moving Range
Control Chart
Upper Control Limit: 368.6
Target: 112.8
Lower Control Limit: 0
BKLD Control Chart
Ways A Process Can Be
Out Of Control
Sustained, Average Shift,
Constant Standard Deviation
Irregular, Average Shifts,
Constant Standard Deviation
Constant Average,
Change In Standard Deviation
Trend Up Or Down In Averages,
Constant Standard Deviation
Irregular Changes In Average And
Standard Deviation
Sustained Shift in Population
Mean with Constant Variation
Irregular Shift in Population
Mean with Constant Variation
Mean with Constant Variation
Change in Variation With No
Change in Population Mean
Irregular Shifts in Population
Mean and Variation
Control Chart Rules: Bonnie Small
(Others: Western Electric, AT&T)
n
n
Individual/Mean Control Chart
n A point exceeds either the upper or lower control chart limit
n Two points between the upper or lower warning limit and the
upper or lower control chart limit, respectively
n Seven successive points are all on the same side of the
target line
Variation Control Chart
n A point exceeds upper control limit
n Points which are consistently above the target line indicate
that the process capability has increased and that the
Individual or Mean Control Chart limits are too narrow for the
process
n Points which are consistently below the target line indicate
that the process capability has decreased and that the
Individual or Mean Control Chart limits are too wide for the
process
Control Chart Simulator Demo
Program available for
FREE
at www.kptware.com
How Well Can A Control Chart
Detect A Sustained Process Shift
n Example
using:
n Subgroup
Size of 1*
n Subgroup Size of 5**
n Western Electric Control Chart Rules
Rule One: Any one point falls outside three-sigma control
limits
n Rule Two: Two out of three successive points are outside
the two-sigma limits
n Rule Three: Four out of five successive points are
outside the one-sigma limits
n Rule Four: Eight successive points on the same side of
the center line
n
* Simulation by Jim Stuart, Eastman
** See Donald Wheeler Reference
Subgroup Size of 1
Subgroup Size of 5
K is the number of sampling periods
Table values are the probability of detecting a given shift
Plotting Rare Event Data
n
Traditional Individual & Moving Range Chart
n
n
n
n
n
n
n
Concern: Lower Limit below zero
P Chart
C Chart
U Chart
Concern: Large amount of data needed to establish accurate
control limits
New Charts in Minitab
n
G-Chart
n
n
n
Plots number of opportunities between rare event (Count Distribution)
Based on Geometric distribution
T-Chart
n
n
Plots time between rare event (Continuous Distribution)
Based on Weibull distribution
Note: Charts need to be constructed on “Stable Process”
IR Chart for OR Acquired Staph
Infections
This is simulated data from a stable process. Note LCL is below zero
and the out-of-control points.
G Chart for OR Acquired Staph
Infections
This is simulated data from a stable process.
G Charts
n When
to Use
n Known
# opportunities between defects
n No “floor” or “ceiling
n Constant rate expected
n Low Probability
n Low to moderate volume
n Chart
Tests
n 3-sigma
n9
in a row
n Benneyan (consecutive 0’s)
See link to paper by Benneyan on construction of G Charts
http://www1.coe.neu.edu/~benneyan/papers/g_chart_overview/
T Chart of Earthquakes in
Washington State
Data is time in days between event.
T Charts
n When
to Use
n Date/Time
of (or between) defects known
n No “floor” or “ceiling”
n Constant rate expected
n Low Probability
n Low to moderate volume
n Stable # opportunities over time
n Chart
Tests
n 3-sigma
n9
in a row
References
n
n
n
n
n
n
“Statistical Method from the Viewpoint of Quality
Control”, Walter A. Shewhart (Edited and with a New
Foreword by W. Edwards Deming), Dover Pub., 1986
“Statistical Quality Control”, Grant & Leavenworth,
McGraw-Hill, 1980
“Quality Control and Industrial Statistics”, A.
Duncan,Irwin, 1986
“Detecting a Shift in Process Average: Tables of the
Power Function for Xbar Charts”, D. Wheeler, JQT,
Vol. 15, No. 4, Oct. 1983
Minitab G and T Charts
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