Chapter 18

CHAPTER # 18:
Statistical Process Control by M. Salman Jamil

 It is tool for quality control merely a scientific, data-driven
methodology for quality analysis and improvement.
 It’s also termed as an industry-standard methodology for
measuring and controlling quality during the manufacturing
process.
 Quality data in the form of Product or Process measurements
are obtained in real-time during manufacturing.
 Graphical explanation helps to determine control limits. Control
limits are determined by the capability of the process, whereas
specification limits are determined by the client's needs.
2

 Pareto analysis is a formal technique useful where many
possible courses of action are competing for attention.
 Pareto analysis is a creative way of looking at causes of
problems because it helps stimulate thinking and organize
thoughts.
 The value of the Pareto Principle for a project manager is that it
reminds you to focus on the 20% of things that matter. Of the
things you do during your project, only 20% are really
important. Those 20% produce 80% of your results. Identify
and focus on those things first, but don't totally ignore the
remaining 80% of causes.
3

 There is need to classify the data according to root cause
problem
 There is need to rank characteristics the financials or other
variable if required
 Collect the appropriate data for particular time frame
 Summarize the data & rank the order for categories in
descending order
 Construct the diagram & find the vital view
This is powerful quality management tool, it helps for
problem solving, identification and progress measurement
as well.
4

Purpose:
Visual illustration of the sequence of operations required to
complete a task
 Schematic drawing of the process to measure or improve.
 Starting point for process improvement
 Potential weakness in the process are made visual.
 Picture of process as it should be.
Benefits:
 Identify process improvements
 Understand the process
 Shows duplicated effort and other non-value-added steps
 Clarify working relationships between people and organizations
 Target specific steps in the process for improvement.
5

 Benefits
• Simplest of all flowcharts
• Used for planning new processes or examining existing one
• Keep people focused on the whole process
 How is it done?
• List major steps
• Write them across top of the chart
• List sub-steps under each in order they occur
6

Cause and Effect Analysis is a technique for identifying all the possible
causes (inputs) associated with a particular problem / effect (output)
before narrowing down to the small number of main, root causes which
need to be addressed.
 Breaks problems down into bite-size pieces to find root cause
 Fosters team work
 Common understanding of factors causing the problem
 Road map to verify picture of the process
 Follows brainstorming relationship
8

 Focusing on causes not symptoms capturing the collective knowledge
and experience of a group
 Providing a picture of why an effect is happening
 Establishing a sound basis for further data gathering and action
 Cause and Effect Analysis can also be used to identify all of the areas that
need to be tackled to generate a positive effect.
 It is also known as a Fishbone or Ishikawa diagram) graphically illustrates
the results of the analysis and is constructed in steps.
 It is usually carried out by a group who all have experience and knowledge
of the cause to be analyzed.
 It graphically display potential causes of a problem & relationship
between potential causes
9

 Use the Check Sheet to distinguish between opinions and
facts
 Use it to gather data about how often a problem is occurring.
 Use it to gather data about the type of problem occurring.
 Record types of writing errors on student writing samples
Examples
 Excuses for late homework
 Observations of the weather
 Items found in a backpack
 Amount of minutes practiced studying math facts
 Amount of minutes spent reading each night
 Amount of time spent completing homework
Prepared By: Muhammad Salman
Jamil 11

14
Purpose:
To determine the spread or variation
of a set of data points in a graphical
form
How is it done?:
 Collect data, 50-100 data point
 Determine the range of the data
 Calculate the size of the class
interval
 Divide data points into classes
Determine the class boundary
 Count # of data points in each class
 Draw the histogram
Stable process, exhibiting bell shape

 Histograms are a useful way to illustrate the
frequency distribution of continuous data. For
example, the data in the table below show the lung
volume of a group of students.
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Lung volume
(litres)
Frequency
2.5–2.9 2
3.0–3.4 5
3.5–3.9 8
4.0–4.4 11
4.5–4.9 9
5.0–5.4 4
5.5–5.9 1

 For some data sets the number of distinct values is too large to
utilize.
 In such cases, we divide the values into groupings, or class
intervals.
 The number of class intervals chosen should be a trade-off
between
(1) choosing too few classes at a cost of losing too much
information about the actual data values in a class and
(2) choosing too many classes, which will result in the
frequencies of each class being too small for a pattern to be
discernible.
 Generally, 5 to 10 class intervals are typical.
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A collection of quantitative data pertaining to a subject or group.
Examples are blood pressure statistics etc.
The science that deals with the collection, tabulation, analysis,
interpretation, and presentation of quantitative data
Jamil 19
Frequency Distribution
Measures of Central Tendency
Measures of Dispersion

The three measures in common use are the:
 Average
 Median
 Mode
Average
There are three different techniques available for calculating the
average three measures in common use are the:
 Ungrouped data
 Grouped data
 Weighted average
20

Jamil 21
Average Un-Grouped Data
Average Grouped Data

 Range
 Standard Deviation
 Variance
The range is the simplest and easiest to calculate of the measures of
dispersion. Range = R = XH – Xl (Largest value - Smallest value in data
set).
These tools are used to determine the dispersion in data, the smaller
the value of standard deviation the better the quality as distribution is
expected around central value. Quality control is one of the important
tool determine through principle control charts. The benefit of standard
deviation is required when there is need to have precise measurement.
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 Population: Set of all items that possess a characteristic of interest
 Sample : Subset of a population
Parameter is a characteristic of a population, it describes a
population. Example: Average weight of the population, e.g.
50,000 cans made in a month.
Statistic is a characteristic of a sample, used to make inferences
on the population parameters that are typically unknown,
called an estimator. Example: average weight of a sample of 500
cans from that month’s output, an estimate of the average
weight of the 50,000 cans.
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 It is symmetrical -- Half the cases are to
one side of the center; the other half is
on the other side.
 The distribution is single peaked, not
bimodal or multi-modal also known as
the Gaussian distribution
 Most of the cases will fall in the center
portion of the curve and as values of the
variable become more extreme they
become less frequent, with "outliers" at
the "tail" of the distribution few in
number. It is one of many frequency
distributions.
24

 The control chart is a graph used to study how a process
changes over time. Data are plotted in time order.
 A control chart always has a central line for the average, an
upper line for the upper control limit and a lower line for the
lower control limit.
 Lines are determined from historical data. By comparing current
data to these lines, you can draw conclusions about whether the
process variation is consistent (in control) or is unpredictable
(out of control, affected by special causes of variation).
26

 A run chart, also known as a run-sequence plot is a graph that
displays observed data in a time sequence. Often, the data
displayed represent some aspect of the output or performance
of a manufacturing or other business process.
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Example Run Chart
0
1
2
3
4
5
6
7
8
1 3 5 7 9 11 13 15 17 19 21 23 25
Day
CRBSI/1000LineDays

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 It helps in determining the trend of data & indicate the variation of
quality.
 The variation helps to understand central tendency and set of
observation related to central tendency and dispersion in data.
 It help in assigning limits at different level of quality adjustments.

Following are the most commonly used variable control charts:
To track the accuracy of the process
Mean control chart or x-bar chart
To track the precision of the process
Range control chart
29

 The quality can be expressed in multiple basic units or
derived units of a particular product.
 It relates to performance of a particular product & multiple
functions are involved in it such raw material, components or
finished goods etc.
 There is need to prioritize the selection criteria in relation to
the product.
 Sometimes the decision for cost saving opportunities reduce
the cost but it spoil rework cost.
 Pareto Analysis would be effective tool for testing & product
inspection.
 Its really a tough ask to display X and R but there is need to
select some quality measurement.
30

 As discussed control chart are present to show multiple
subgroup in random manner, it need to limits within the group as
well. It would help to ensure the stability within the group. The
decision on particular sample size are considered as empirical
judgment.
1. As subgroup size increased it gets closer to central tendency.
2. When the size of subgroup increased it would increase
inspection cost.
3. It increase the cost of testing & item become expensive.
4. Due to computation the sample size with common features
within the industry are selected.
5. By using statistical distribution of subgroup averages taken
from non-normal population already proven by central limit
theorem.
31

32
Control limits, also known as natural process limits, are
horizontal lines drawn on a statistical process control chart,
usually at a distance of ±3 standard deviations of the plotted
statistic from the statistic's mean.

Jamil 33

 There is need to have amendments in regards when some points
out-of-control that needs to recalculate central lines & control
limits.
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 A process is considered to be in a state of control, or under
control, when the performance of the process falls within the
statistically calculated control limits and exhibits only chance, or
common, causes.
 When special causes have been eliminated from the process to the
extent that the points plotted on the control chart remain within
the control limits, the process is in a state of control cause a
natural pattern of variation.
 Type I, occurs when looking for a special cause of variation when
in reality a common cause is present
 Type II, occurs when assuming that a common cause of variation
is present when in reality there is a special cause
Jamil 37

1. Individual units of the product or service will be more uniform
2. Since the product is more uniform, fewer samples are needed
to judge the quality
3. The process capability or spread of the process is easily
attained from 6ơ
4. Trouble can be anticipated before it occurs
5. The % of product that falls within any pair of values is more
predictable
6. It allows the consumer to use the producer’s data
7. It is an indication that the operator is performing satisfactorily
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39
Natural pattern of variation
Common Cause
Special Cause

The term out of control is
considered when condition
arises for undesirable. It
considered when data lies
between 3∂. Below are some
conditions arises for out of
control processes.
1. Change or jump in level.
2. Trend or steady change in
level
3. Recurring cycles
4. Two populations
5. Mistakes
40

 The process spread will be referred to as the process capability and is
equal to 6σ i.e. +3σ & -3σ. The difference between specifications is
termed as tolerance
 When the tolerance is established by the design engineer without regard
to the spread of the process, undesirable situations can result
 Case I: When the process capability is less than the tolerance
6σ<USL-LSL
 Case II: When the process capability is equal to the tolerance
6σ=USL-LSL
 Case III: When the process capability is greater than the tolerance
6σ >USL-LSL
41

 The range over which the natural variation of a process occurs as
determined by the system of common causes measured by the
proportion of output that can be produced within design specifications.
 Following method of calculating the process capability assumes that
the process is stable or in statistical control:
 Take 25 (g) subgroups of size 4 for total of 100 measurements
 Calculate the range, R, for each subgroup
 Calculate the average range, RBar= ΣR/g
 Calculate the estimate of the population standard deviation
 Process capability will equal 6σ0
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43
Case I: 6σ<USL-LSL
Case II: 6σ = USL-LSL
Case III : 6σ > USL-LSL

 Process capability and tolerance are combined to form the capability
index.
 The capability index does not measure process performance in terms
of the nominal or target value. This measure is accomplished by Cpk
44
 The Capability Index does not measure process performance in terms
of the nominal or target

1. The Cp value does not change as the process center changes
2. Cp= Cpk when the process is centered
3. Cpk is always equal to or less than Cp
4. A Cpk = 1 indicates that the process is producing product that
conforms to specifications
5. A Cpk < 1 indicates that the process is producing product that does
not conform to specifications
6. A Cp < 1 indicates that the process is not capable
7. A Cp =0 indicates the average is equal to one of the specification
limits
8. A negative Cpk value indicates that the average is outside the
specifications
45

46
Cpk = negative number
Cpk = zero
Cpk = between 0 and 1
Cpk = 1
Cpk > 1

Used when the sample size is not the same
 Different control limits for each
subgroup
 As n increases, limits become narrower
 As n decreases, limits become wider
apart
 Difficult to interpret and explain
 To be avoided
Chart for Trends:
Used when the plotted points have an upward or
downward trend that can be attributed to an
unnatural pattern of variation or a natural pattern
such as tool wear. The central line is on a slope,
therefore its equation must be determined.
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 Used when we cannot have multiple observations per time
period. Extreme readings have a greater effect than in
conventional charts. An extreme value is used several times in
the calculations, the number of times depends on the averaging
period.
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This is a simplified variable control chart.
 Minimizes calculations
 Easier to understand
 Can be easily maintained by operators
 Recommended to use a subgroup of 3, then all data is used.

49
Formulae for Median & Range
Chart for Individual values (Moving)
Used when only one measurement
 Too expensive
 Time consuming
 Destructive
 Very few items

Chapter 18

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Chapter 18