STATISTICAL PROCESS CONTROL (SPC) & STATISTICAL QUALITY CONTROL (SQC)
DEMMING'S 14 POINTS:
Dr. Edward Demming, one of the famous quality advocates,
summarized, in 14 points, what he believed to be necessary to obtain excellence within a
corporation. These 14 points have gained world- wide acceptance.
1. Create constancy of purpose toward improvement of product and service.
2. Adopt the new philosophy. We are in a new economic age.
3. Cease dependence on inspection to achieve quality.
4. End the practice of awarding business on the basis of initial cost.
5. Improve constantly and forever every activity.
6. Institute training and education on the job, including management.
7. Institute leadership.
8. Drive out fear.
9. Break down barriers between departments.
10. Eliminate slogans and exhortations.
11. Eliminate work standards that prescribe numerical quotas.
12. Remove barriers that rob workers of their right to pride of workmanship.
13. Institute a vigorous program of education and self-improvement.
14. Put everybody in the company to work in teams to accomplish the transformation.
DEMMING'S THINKING:
1. Management is responsible for improving the system.
2. Systems are complex: managers can't figure out all on their own the sources of problems.
3. Problems can be divided into two sources:
 local
Some workers, some of the time, … - also called Special Cause, Bias
 system
Continual, inherent within the process – also called Random, Common Cause
Managers first need to determine if a problem is local or system:
Managers must use the workers to determine this.
Workers and management must speak a common language for communicating this
information. The common language is statistics and the type of problem can be identified
using statistical process control.
GOALS OF SPC:
understand the process
eliminate special cause variation
reduce common cause variation and maintain a process that is in "statistical control" and has
high "process capability".
SPC FOR CHEMISTS
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DEFINITIONS:
1. Statistics: a body of methods by which useful conclusions can be drawn from numerical
data. (Not simply facts stated as numbers.)
2. Process: a systematic series of actions directed to some end.
SPC: refers to controlling a process (e.g., chemical manufacture) based on responding to
process data with statistical techniques and tools.
SQC: refers to controlling the quality of a product based on responding to laboratory data with
statistical techniques and tools.
3. Quality Assurance (Program): refers to a laboratory program that assures management,
customers, government, etc. that the lab data is proven and of known quality. A lab may
demonstrate quality control (and thereby give assurance to customers) as follows:
a) include a standard of know concentration along with each batch of samples analyzed and
plot this result on a control chart
b) calibrate instruments on a regular basis and retain proof of this
c) with every product shipment, retain samples that are properly labeled (e.g., analyst, date,
time, method number, instrument used) – these can be checked at a later date if needed
d) demonstrate prevention of falsification of data (e.g., run blind samples, keep data
recorded in bound note books)
4. Blind Sample: refers to a sample of known concentration submitted as a routine sample
without the analyst's knowledge
5. Accuracy: defines the difference between the measured value and the true value
6. Precision: is repeatability of a measurement.
(repeatable) but be quite inaccurate.
An analysis may yield precise results
Quantifying Accuracy: requires that the true value be known. The average ( x ) of several
measurements (xi) is reported as a percentage of the true value (T).
E.g.: An analyst began with ‘0’ concentration of analyte and added measured amounts of a
known standard. The data and accuracy might be reported as follows…
mg Ca+2 added
mg Ca+2 recovered
1
20
22
2
20
20
3
20
24
n=3
xI = 66
x
66
 22
n
3
Average % Recovery :
x
i

x
22
100%  100%  110%
T
20
The average % recovery on 3 analyses = 110%
If the analyst repeated the procedure and obtained the following data, what is true about the
accuracy and the precision with regard to the second set of data?
mg Ca+2 added
mg Ca+2 recovered
1
20
14
2
20
21
3
20
25
n=
xI =
It is important to determine both accuracy and precision of a method.
SPC FOR CHEMISTS
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7. Error: like accuracy, is determined with reference to a true value, i.e., error = inaccuracy. In
the previous example, the average % error could be reported as +10% in the first case and
0% in the second case.
8. Variation: like precision, deals with repeatability of data and also stability of a process, i.e.,
variation = instability = imprecision
Errors and variation can arise from two kinds of causes:
1. Special Causes: (assignable, bias, local variation), error/variation results in one direction
(either + or -) and can be traced to an assignable, special cause, e.g., miscalibrated
instrument. It can be detected by running known standards and recalibrating.
2. Common Cause: (random, system variation) error/variation results randomly (without bias) in
both directions (+ and -) and in varying magnitude – due to unknown causes. Random
variation is chronic (continual), e.g., normal fluctuations in instruments, natural variation in raw
materials.
Statistics is more applicable to measuring and controlling variation from common cause (random)
than from special causes. (bias).
Exercise

Identify the following causes of variation as Special or Common
a) spectrophotometer calibration off
_______
b) spectrophotometer unsteady
_______
c) forgot to add one reagent to all samples and standards
_______
d) it is unusually humid during analysis and samples are hydroscopic
_______
e) temperature gauge on distillation column is reading 5 low
_______
f)
sloppy analytical technique
_______

% Recovery is a measure of ……………………………….

Calculate the average % recovery and average % error in the following analysis
mg Cr+3 added
mg Cr+3 recovered
1
50
57
2
50
55
3
50
50
n=
xI =

Match the following….
1
precision
A
imprecision
2
variation
B
closeness to true value
3
error
C
repeatability
4
accuracy
D
inaccuracy
SPC FOR CHEMISTS
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STATISTICS FOR SPC
Variation (imprecision, instability, degree of repeatability) is described in statistics by the standard
deviation
If a large homogeneous sample is analyzed many times (say ‘n’ times), all results will not be
identical but will vary over a ‘range’.
Range = [highest value – lowest value].
Normally the values will cluster about the ‘average value’.
Average = x =
( x1  x 2     x n )  x i

n
n
Exercise
Calculate the average and range of the following measurements.
a) 1.31, 1.32, 1.30, 1.36, 1.37
b) 1.30, 1.41, 1.36, 1.35, 1.32
c) 1.29, 1.36, 1.37, 1.30, 1.33
d) 1.34, 1.30, 1.30, 1.38, 1.36
When every part is measured, the arithmetic average ( x ) is called the Mean (), pronounced ‘mu’.
The majority of the values will be very close to the average ( x ) and fewer values will be far from
x . If the values are plotted as a frequency distribution (a plot of number of times a value is
obtained versus the value itself), the plot will approximate that shown below and is called a ‘Normal
Distribution’, ‘Gaussian Curve’ or a ‘Bell Curve’.
Normal Distribution
# of
times
xI
occurs
34%
34%
14%
14%
2%
2%
-3
-2
-1
0
1
2
3
x
magnitude of xi
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The most useful measure of dispersion is not range but rather standard deviation.
Standard deviation:
sx 
(x
 x)2
i
n 1
n = number of data points in the sample
(xi - x ) is the difference between an individual datum and the
sample average
sx is the standard deviation of the sample
Think of standard deviation as being the average range or average deviation from the mean.
When all parts are measured, the standard deviation calculation becomes…
x 
(x
i
 x)2
n
n = number of data points (usually called the population, ‘N’)
x = average (usually called the population mean, ‘’)
x = standard deviation of the population (pronounced sigma)
When the sample size, n, is large (n > 30), both formulas give approximately the same value.
Regarding the Normal Distribution:
 68.26% of all data points lie within  1 of the mean
 95.46% of all data points lie within  2 of the mean
 99.73% of all data points lie within  3 of the mean
Thus for data which closely follows the normal distribution:
Any single analytical result has a 68% probability of being within  1 standard deviation of the
mean.
Any single analytical result has a 95.5% probability of being within  2 standard deviations of the
mean.
Any single analytical result has a 99.7% probability of being within  3 standard deviations of the
mean.
Exercise
During her shift, a chemist measured 20 viscosity readings (shown below) on a large sample of
solution.
365.3
365.7
366.0
366.0
366.0
366.3
366.0
365.3
363.0
365.3
364.3
366.3
365.0
365.0
365.3
364.0
366.0
361.3
365.7
363.3
Use the data to calculate …
a) the sample average
b) the range of the data
c) the standard deviation
d) Within what limits (range) will

68% of the data lie?

95% of the data lie?

99% of the data lie?
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Understanding Standard Deviation:
The standard deviation of a group of data is one sixth (1/6) of the total range of data that were
measured. For example:
a) An analyst reports the concentration of PO4-3 in a sample as x = 50.0 ppm; sx = 1.0 ppm
Thus, the average result was 50.0 units
1/6 of the total range of data was 1.0 unit
The total range of data was 50.0  3.0 units, i.e., 47  53 ppm.
b) Analysis of Fe+3 yielded x = 10.0 ppm, sx = 0.1 ppm
Thus the average result was 10.0 units
1/6 of the total range of data was 0.1 units
The total range of data was 10.0  0.3 units, i.e., 9.7  10.3 ppm
Quantifying Precision (Relative Standard Deviation):
It is important for chemists to quantify the degree of precision in their work. This is done when
various methods of analysis are being evaluated and compared. It might also be used to
compare the work of two different analysts performing the same method.
In the previous data for PO4-3 and Fe+3 analysis, which analytical test gave greater precision?
In a) the sx = 1.0 on an average of 50.0
In b) the sx = 0.1 on an average of 10.0
To quantitatively compare precision of methods, calculate sx as a percentage of x .
For a) we have
1.0
100%  2%
50.0
For b) we have
0.1
 100%  1%
10.0
The result indicates that method b) is twice as precise as method a). The calculated values (2%
and 1%, respectively) are called relative standard deviation (RSD).
RSD 
sx
 100%
x
RSD gives the sx as if the average ( x ) were 100 units.
RSD is used in validating new laboratory analytical methods and in Round Robin studies. In
Round Robins, a large homogenous sample is divided in portions. Portions are sent to different
labs and tested by different analysts. The chemists performing the analysis do not know the
correct concentration of analyte. All results are collected and laboratory performance is
evaluated.
Exercise
You have just analyzed a product storage tank in order to certify this material for shipment to a
customer. All parameters are well within specification except PO4-3, which is measured at the
specification limit of 50 ppm. Based on past analysis (and method validations) the RSD of this
method is 4.0%. Is this product ‘on spec’? Hint: Use the established RSD to determine the
concentration range within which the true value will lie.
Standard Deviation for Multiple Samples:
Statistically it is true that the average ( x i ) of a set of samples (xi ) will be closer to the true value
(true population mean) than only 1 sample.
Therefore the standard deviation of a number of averages (s x i ) will be lower than the standard
deviation of a number of single samples (sxi).
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S x I can be calculated as follows:
s xi 
sx
sxi
s xi
= standard deviation of averages of subgroups (sets) of samples
= standard deviation of a group of single samples
n = number of samples in the subgroup
n
In the last exercise, by only analyzing 1 sample of the storage tank (xI = 50 ppm), you must report
that the true value lies in the range of 50  6 ppm ( 3), i.e., between 44 and 56 ppm.
If you resample the storage tank and, for example, if the average of the 2 samples is also 50 ppm,
you can now use s x to calculate the range, as follows.
s xi 
sx
n

2

2
2
 1.4
1.41
Now after averaging 2 sample results, the true value lies in a smaller range, i.e.,
[50  3()] = [50  3(1.4)] = [50  4.2] = 45.8  54.2 ppm
Exercise
As an extension of the
analysis in the storage tank, calculate the range within which the
true value lies for the following cases…
a) n = 4, x = 50.0, sx = 2
b) n = 9, x = 50.0, sx = 2
PO4-3
Confidence Limits:
On a given day you may run a single analysis on a process sample using a proven method for
which you have already calculated the standard deviation of the method. It would be correct to
say that your single value has a 95% probability of being within  2 of the true value. This is
called the 95% confidence limit.
For example, with  = 1 unit and a single measurement of 100 units, we can state with 95%
confidence that the true concentration is 100  2 units (2), i.e., 98 to 102 units
We can also state with 99% confidence that the true concentration is 100  3 units (3), i.e., 97 to
103 units.
If we make such statements many times, we will be wrong about 5 times per 100 (at 95%
confidence limit) or only about 1 time per 100 (at the 99% confidence limit)
Exercise
Your established analytical method has  = 0.5 ppm and you obtain a single measurement of 8.0
ppm. How would you report to your boss the true concentration of the sample using the 95% and
99% confidence limits?
SPC FOR CHEMISTS
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QUALITY CONTROL CHARTS
Where Control Charts are Used:
 incoming raw materials, e.g., assay, delivery time, errors in orders
 the process itself, e.g., concentration of impurities, production rates
 maintenance, e.g., repair time, corrosion/wear rate of tanks
 marketing/sales, e.g., customer complaints, product delivery time
 laboratory, e.g., concentration of secondary standards, recovery on spikes/standards
 every where in manufacturing and research industries
Types of Variation:
Special Causes (bias)
temporary, assignable, fixable, e.g.,
 seasonal effects
 instrument calibration is off
 ‘off-spec’ raw material
Common Cause (random)
continual, chronic, system, e.g.,
 poorly trained worker
 fluctuations in machinery
 normal variation of ‘on-spec’ raw material
How to Reduce Variation:
Fundamental Point: Special causes and random causes of variation are treated differently.
Juran’s 85% Rule: 85% of variation is random error in the system and can only be remedied by
management make changes to the system. 15% of variation is special cause and is fixable by
the worker.
Steps in an SPC Program:
1. Identify the cause of variation in order to remedy it. This is not always obvious; often it is
elusive because manufacturing operations are complex - many interrelated variables.
Statistical Control Charts distinguish between Common causes and Special causes of
variation.
2. Remove special causes, e.g., recalibrate the instrument, store standards to minimize
deterioration, etc. Once a process is free of special causes, it is said to be STABLE even
though it still has variation due to random causes.
3. Estimate the Process Capability.
4. Establish and carry out a plan to monitor, improve and assure the quality of the process, e.g.,
charting, maintenance, training and record keeping, in order to constantly and forever reduce
variation.
Usefulness of Control Charting:
1. detects special causes of variation
2. measures and monitors common causes of variation
3. know when to look for problems and adjust or when to keep hands off
4. know when to make a fundamental change.
Setting up an Xi Chart (Individuals Chart):
It is generally recommended that one standard (xi) be run with each batch of samples or if large
batches are run simultaneously, one standard for each 10 - 20 samples.
When 20 - 25 analyses of standards have been gathered, calculate x and sx.
On suitable graph paper (or a predesigned SPC chart) construct a chart with the y-axis as
concentration and the x-axis numbered sequentially (sample #'s or dates)
SPC FOR CHEMISTS
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Draw horizontal lines across the chart as follows…
1. a solid line at y = x (mean)
2. a dashed line at y = x + 3sx (upper limit of xI values, called Upper Control Limit, UCL)
3. a dashed line at y = x - 3sx (lower limit of xI values, called Lower Control Limit, LCL)
After calculating UCL and LCL ( x  3sx), see if any points exceed these limits. They should not
be included in constructing the Xi chart limits as these points due to special causes (not common)
and will skew the chart. Discard these out of control points and calculate new values for x , sx,
UCL and LCL. This is not cheating.
Again check the data to ensure that all data lies within the new UCL and LCL. If not repeat the
discarding and recalculating of data until all points are within UCL and LCL.
If you repeatedly cannot draw a control chart with all data within the limits, it indicates that the
process is out of control, plagued with special causes of variation and you cannot utilize a control
chart until you eliminate these special causes.
Recall that only 1 result per 100 should lie beyond the control limits, i.e., >99% of all data lies
within x  3sx if random variation is the cause. Such a process (or data set) is said to be
IN CONTROL.
If data exceeds the control limits more frequently, this is due to special causes of variation and
the process (or data set) is said to be OUT OF CONTROL.
Using and Interpreting Xi Charts:
1. Continue to plot new data on the Xi chart in real time (as the data is measured/collected).
2. Circle any data points that are out of control (out of the limits). Any out-of-control point
should be immediately suspect for special causes of variation and investigation undertaken.
3. Check for special causes (bias) if…
a) 7 or more consecutive points are on the same side of x
b) 7 or more consecutive points are rising or falling
Periodically calculate the x and sx for a new set of data (minimum 25 points). If it differs from the
values first calculated, draw new lines for x , UCL and LCL forward from that point.
X Charts:
When standards (or samples) are analyzed in replicate (duplicate, triplicate, etc.) each time
period (day, shift, etc.) an X chart is constructed. This is the same as an Xi chart except that
each point ( x I) plotted on the chart is the average of several data points (called a subgroup).
 one point per period is a subgroup size of n = 1 (this generates an Individuals (X I) chart)
 two points per period is a subgroups size of n = 2
 three points per period is a subgroup size of n = 3, etc.
x is simply the average of all subgroup averages ( x I)
x
x
i
# of subgroups
UCL and LCL for X charts are calculated as x  3 s x , where s x = average standard deviation.
That is, for each subgroup of data (e.g., each day's data) a standard deviation is calculated (s x).
The average standard deviation ( s x ) is the arithmetic average of sx for all subgroups.
A simpler method for constructing XI and X charts is discussed later.
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Range Charts (R charts):
Range is the difference between the highest and lowest data points in a group.
Control charts are constructed with a range chart immediately below the Xi or X chart.
When more than 1 data point per day is analyzed and x I values are plotted on an X chart, the
range is the difference between the highest and lowest xI in that period (subgroup).
When only 1 data point (xI) per period is plotted on the Xi chart then a 'moving range' can be
plotted on a moving range chart. The moving range is the absolute value of the difference
between (usually) two consecutive xI values, e.g., between today's reading and yesterday's
reading. Moving range charts will have one less point than the corresponding Individuals chart.
Constructing an R Chart:

 R  & draw it as a solid horizontal line
1.
Calculate the arithmetic average of the ranges  R 
2.
UCLR can be calculated as R  3sR (like UCLx) but more often it is calculated using a formula
derived from the normal distribution, i.e., UCLR = D4 R , where D4 is a factor obtained from
tables used in constructing control charts. UCLR is drawn as a dotted line on R charts.
LCL is often not used for range charts, rather the zero line serves as LCL.
3.

i
n 
R Charts:
Advantages:
Range charts can be used when no XI or X chart can be constructed for example, when
standards are unavailable or too unstable to retain and analyze repeatedly. Instead the actual
unknown samples are split and analyzed in replicate and the range (xlargest - xsmallest), R values, and
UCLR are calculated and plotted on an R chart.
Disadvantage:
Range charts do not detect bias (special cause variation) because this is cancelled out when the
difference between analysis is calculated, leaving only random (common) causes of variation. The
range chart shows the precision of the values.
Constructing Control Charts - The Shortcut Method:
In order to simplify control chart construction (avoid calculating standard deviation) various factors
can be used. For example, for an X and R chart, the following calculations apply.
UCLx = x + A2 R
UCLR = D4 R
LCLx = x - A2 R
LCLR = D3 R
x and R are the arithmetic averages you calculate from your data sets.
A2, D3, and D4 are read from tables (see SPC manual)
Select A2, D3, and D4 according to the subgroup size (n) of the data set and the type of chart being
prepared. For example, duplicate standard analysis each day corresponds to a subgroup size of
n = 3 and in this case an X chart can be prepared using the following factors…
for n = 3:
A2 = 1.693
D4 = 2.574 D3 = no value
Note that factors A2, D3, and D4 are calculated from a perfect Gaussian distribution. UCL and LCL
calculated from these factors will exactly match those calculated from x  3 s x only when the data
is also normally distributed, randomly sampled and many data points are averaged. Otherwise
some differences will occur. In most cases the differences will be negligible.
SPC FOR CHEMISTS
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Exercise
The tabulated data are measurements of Fe content (ppm) in anhydrous HF. The subgroup size
n = 3. Use the data to perform the following tasks.
a) Calculate the control limits for an X and R chart.
b) If there are any out of control points assume they are related to special causes and recalculate
the limits.
c) What happened to the control limits as out-of-control points were removed?
d) Plot a control chart of the data once all of the points are in control.
Subgroup
Average
Range
Subgroup
Average
Range
1
298
34
11
251
80
2
282
40
12
250
8
3
211
127
13
258
100
4
220
81
14
286
110
5
233
95
15
255
93
6
319
33
16
223
132
7
380
219
17
285
134
8
214
60
18
292
236
9
275
90
19
255
87
10
182
55
20
298
45
a) A2 = ………….
D3 = …………….
D4 = ………………
x = ………….
UCLx = …………
LCLx = ………………
R = …………
UCLR = …………
LCLR = ……………..
Process Capability (Capability Index):
Process capability (Cp) is simply the ability of a process to meet a customer's product specification
(assuming the process is centered on target). A process must be in control (random variation only)
before Cp can be calculated.
Cp =
customer' s tolerance range of specification  upper spec.- lower spec. U - L



manufacturing ability
process variability
6
6
 = the standard deviation established from previous shipments (the process history).
6 = the range of concentrations which included 99.7% of all previous shipments.
If the process is not centered (on target), the process output will be less than its ‘capability’
indicates. It is possible to have an excellent Cp but produce 100% NC product.
Exercise
A customers specs for hydrofluoric acid = 70.0 - 72.0 % HF. Previous product shipments averaged
71.0% with a  = 0.333. Calculate the process capability for meeting the customer's specification.
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If Cp = 1, then the supplier can meet the customer's specification on 99.7% of the shipments.
If Cp < 1, then the supplier can produce off spec. material (more than 0.3% of the shipments).
If Cp > 1.33, then the process can demonstrate 99.999% conformance to customer specs.
North American auto makers generally require that their suppliers maintain a Cp of  1.33
Capability Ratio: (CR) is simply the inverse of Process Capability. For example, a Cp of 1.33 is
equivalent to a CR of 1/1.33 = 0.75. A Capability Ratio of 0.75 means that the process spread
occupies 75% of the tolerance. The lower the CR the more capable the process.
CPU, CPL and Cpk:
 upper spec. - x  U - x
CPU = 

3

 3
or
 x - lower spec.  x - L
CPL = 

3
3


CPU is the ‘Upper Process Capability’, i.e., the process capability to meet the upper spec. limit.
CPL is the ‘Lower Process Capability’, i.e., the process capability to meet the lower spec. limit.
Cpk is equal to the lower of CPU and CPL. Cpk is a better measure of process capability than Cp
of CR since Cpk takes into account the actual process center compared to the target.
For 1-sided specifications: Calculate CPU for specifications which are maximums and calculate
CPL for specifications which are minimums. In such cases, both CPU and CPL may be referred to
as Cpk since they are numerically equal.
One-sided specifications are common in the chemical industry where a customer's specification is
a maximum impurity (spec. =  25 ppm As) or minimum assay (spec. =  50 % NaOH).
Exercise
Calculate the process capability for the following data.
1. Arsenic determinations on past shipments average 19.0 ppm with  = 2.0. The customer's
specification is 25 ppm max. Calculate the capability of the process in meeting the spec.
2. NaOH assay of past shipments averaged 51.0% with sx = 0.50. The customer's spec. is 50.0%
min. Calculate the capability of the process in meeting the spec.
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PRINCIPLES FOR CONTROL CHARTING IN A CHEMICAL PROCESS/LABORATORY:
Suggestions for what should be charted:
 Chart the concentration of key reagents (those used to certify product shipments), i.e.,
secondary standards, e.g., 1.0N NaOH for acidimetric titration. Normality is routinely checked
against primary standard (e.g., KHP). Normality changes of stock reagent are posted and
causes for change are investigated, e.g., different analyst (different technique), deterioration of
reagent (NaOH absorbs CO2 - Nitrogen pad NaOH reagents)
 Known standards are run with each batch of product samples. Of course this is done for
calibration of spectrophotometers, etc., however the instrument reading (e.g., Absorbance) of
the standard is also plotted on a control chart. This may reveal trends or fluctuations in
method, technique or instrumentation which can be investigated and rectified. The R chart will
show the common cause variation of the method and the x chart will reveal special cause
problems. Charting shows trends that are not apparent from raw data.
 Chart analysis of a finished product. This will allow determination of Cp or Cpk. This also
gives the range of the assay of the product. Customers want this info. You must decide which
parameter to plot. A typical product certification may have 8 to 10 parameters (specifications).
You probably don't have time to plot all parameters. Discuss with the customer/management
which parameters are critical, e.g., concentration of main component and certain impurities
(H2O, As, Fe, SO4-2, PO4-3, H2SiF6, grease, color, particle size distribution, etc., etc.)
 Chemical process operators will chart variables of the chemical process, e.g., furnace
temperature, reboiler temperature on the distillation column, pressure on carbonating tower,
etc. With modern computer-controlled processes pressure, temperature and flow readings are
continuously fed to data processing software which immediately plots and displays data in
control charts for the process operators. By monitoring the process (not just the product)
quality control is achieved by prevention rather than detection. Operators can distinguish
between common causes and special causes of variation. They are quickly alerted to special
problems and can begin to investigate and adjust the process. In response to random variation
an operator will know when to just allow the system to fluctuate naturally. It avoids a common
operations error called 'over controlling'.
Who Decides and Who Does the Charting?:
Ultimately management is responsible for the QC system. However, management will involve
employees representing many areas of the process.
Often a company will establish a quality team made up of key members such as an internal
quality assurance officer, an SPC specialist, a process engineer, a laboratory foreman, a process
operator, a maintenance foreman, etc. This group will usually make key decisions as to where
charting would be most valuable.
The process operators must have significant input into what measurements will be taken (how often
and when) since the operators are usually the ones to take measurements and plot the data. The
operator must be trained to interpret the control chart so they can respond to the chart results and
improve the process.
Some Benefits of Control Charting:
It is often found that control charting gives operators greater better process control, increased
accountability to management, greater pride in his/her work. It gives credibility to the operator's
recommendations to management re: the need for repairs.
Many industries must be able to demonstrate process capability in order to win and keep customer
contracts. The ISO and QS standards have gained world-wide recognition in recent years and as
a result many companies have invested considerable resources toward QA/QC (training, quality
specialist positions, and equipment).
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TOOLS FOR QUALITY IMPROVEMENT:
Organizational:
1. Flow chart
2. Cause and Effect (fishbone, Ishikawa) diagram
3. Check Sheet
4. Pareto chart
Statistical:
5. Time-ordered plot (run chart)
6. Histogram (dot plot)
7. Statistical control charts (variables & attribute charts)
8. Scatter plot
Flow Charts:
Purpose: show parallel and sequential operations in a logical figure and show a graphical
representation of dependencies.

They are commonly used in manufacturing processes to show the flow of material through a
plant. They may also be used to track paper work and action sequences associated with
delivery of a service, e.g., delivery of a product, delivery of a certificate of analysis to a
customer, etc.

Operations are classed as either bottleneck or non-bottleneck


A bottleneck operation can have less than or equal to capacity

A non-bottleneck operation has capacity that exceeds demand
Flow chart principles:
1. The cost of operating a bottleneck is equal to the cost of operating the whole system, since
time lost at a bottleneck is time lost to the whole system.
2. Increased productivity for the bottleneck is increased productivity for the whole system
3. Time wasted or lost at a non-bottleneck is of no consequence, since, short of a completed
and total breakdown, it will have absolutely no impact upon the throughput of the system.
4. Time saved at a non-bottleneck is worthless since it does not translate into increased
productivity for the system as a whole.
(Source: Wheeler & Chambers: Understanding Statistical Process Control, 1986)
Conventions used in drawing flow charts:
circle = starting point
diamond = decision point
box = action taken
trapezoid = end of process
rectangle with rounded sides = discussion point, meeting, phone call, etc.
Draw a flow diagram for getting to work in the morning.
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Cause and Effect Diagrams: (Fishbone/ Ishikawa diagrams)
Most people are overwhelmed by the number of factors that are possible problem causes.
Dr. Kaoru Ishikawa used a ‘fault tree’ approach to organize information.


Procedure:





Brainstorm: gather together many different people closely associated with the process
Everyone is encouraged to contribute
No discussion, evaluation or criticism of suggestions at this stage
Suggestions not limited to factors in participants own work area
Concentrate on eliminating the problem; don’t excuse the problem

After a list is generated, like items are combined in separate lists, redundant items are
eliminated and voting is carried out to prioritize the remaining items.
Construction of Diagram:
1. Choose the problem. Write it at the end of a horizontal arrow
2. List all factors that influence the effect
3. Arrange and stratify factors: use principal factors as branches. Consider the main
categories of variation in a process, i.e., machinery, materials, methods, measurement,
environmental factors, and people
4. Draw stems to branches for various sub-factors
5. Check diagram to see that it is complete.

Diagram Analysis: - For each factor…
1.
2.
3.
4.
5.
6.
Is there any record of this cause
Is the factor directly/indirectly controllable
Is there a control chart
Is the factor variable or attribute
Does it affect bias or precision
Has the factor been standardized (Is there a quantified relationship between the factor &
the product quality)
7. Does it interact with other factors

Summary: A framework for collective efforts and for tracking progress.
Draw a cause-and-effect diagram for reasons for poor grades in organic chemistry course.
The Check Sheet: (e.g., product shipment problems)
This simple tool allows one to gather data needed for various decision tools. Commonly, the
vertical axis is the problem(s) encountered and the horizontal axis is a time scale. Inserting a
check mark each time the problem appears gives the frequency of the problem.
Product off spec.
Low Production
Mon.
SPC FOR CHEMISTS
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Wed.
Thurs.
Fri.
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Pareto Chart: - When several causes of NC’s are identified, which should be remedied first?




Focuses attention on problems offering greatest potential for improvement, i.e., separates the
‘vital few’ from the ‘trivial many’
Such focus is necessary due to money/manpower limitations
Helps eliminate distractions, individual agendas
Must also apply common sense. In some cases, the most frequent problem may not be the
most costly or most critical, e.g., solving one or two customer complaints may have greater
payoff than solving the most frequent problem.
Construction:
 Constructed like a dot plot or histogram: Y-axis is number of occurrences, X-axis is various
causes. Is basically a vertical bar graph
 Easily drawn using spreadsheet software, e.g., MS Excel – bar graph
 Occasionally drawn as a pie chart.
NUMBER OF
OCCURREN
CES
REASONS FOR BEING LATE TO CLASS
CAUSES
PIE CHART
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Time-ordered Plots (Run Charts):
ppm PO4-3
Simple plots of data in the order taken can often reveal trends and/or shifts that are not apparent
form tabular data. Data trends, shifts, cycles become apparent. Often the time at which a problem
appeared is identified.
DATE
Dot Plot or Histogram:
Reveal the type of distribution, e.g.,, normal, skewed, bimodal, other.
FREQUENCY
This distribution appears normal. Special causes of variation are probably not present.
PO4-3 MIDPOINT
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Statistical Control Charts:

Variables charts: X & R, X & s, individuals and moving range, median charts

Attributes charts: p chart (proportions faulty), np chart (number faulty), q chart (proportion
good), c & u charts (faults per unit)

These are covered elsewhere in the notes or the Big 3 SPC manual

Useful in operating a process, signaling presence of special causes of variation, and assessing
process capability. They do not identify the cause of the variation. Other tools are needed.
Scatter Plots:
These plots reveal interrelated effects. They may help identify the cause of a variation. For
example, you are trying to determine why the absorbance of your 10ppm standard solution varies
from day to day over a long period of time. Plot absorbance values vs. suspected causes.
A vs. Analyst
1.4
1.2
Absorbance
Absorbance
1.2
1.0
.8
1.0
.8
.6
.6
Tom
Pat
Jim
Joe
A vs. Lab Temperature
1.4
1.2
Absorbance
A vs. Shift
1.4
1.0
.8
.6
18
20
22
24
Lab Temp. ( C )
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Days
Afternoons
Nights
The scatter plots reveal no clear
relationship
between
absorbance
variation and any particular analyst or
shift, however a strong relationship is
indicated between lab temperature and
absorbance of the 10 ppm standard.
Linear regression may also be used for
quantitative data. After entering data (x,y
values) into the 2-variable stats mode of
your calculator, display the ‘r’ value, i.e.,.
the correlation coefficient. This will be a
value between –1 and +1.
 r = +1 indicates a perfect direct
(positive) correlation
 r = -1 indicates a perfect inverse
(negative) correlation
 r = 0 indicates no correlation
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