STATISTICAL PROCESS CONTROL
Mr J.C Kabala
kabalaj@cput.ac.za
Lecture Outline
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Basics of Statistical Process Control
Control Charts
Control Charts for Variables
Control Charts for Attributes
Control Chart Patterns
SPC with Excel
Process Capability
Objectives
After studying this chapter, you should
• Understand the purpose of statistical process
control;
• Be able to set up and use charts for means, ranges,
standard deviations and proportion nonconforming;
• Be able to use an appropriate method to estimate
short-term standard deviation;
• Be able to interpret the variability of a process in
relation to the required tolerances
Introduction
• SPC methods extend the use of descriptive statistics to monitor the
quality of the product and process
• There are common and assignable causes of variation in the
production of every product.
• Using SPC, we want to determine the amount of variation that is
common.
• Then we monitor the production process to make sure production
stays within this normal range. That is, we want to make sure the
process is in a state of control.
• The most commonly used tool for monitoring the production
process is a control chart.
• Different types of control charts are used to monitor different
aspects of the production process.
• In this section we will learn how to develop and use control charts.
Control Charts
• Control Charts are used to distinguishes between special-cause
or common-cause of variation that is present in a process.
• Common cause variation is introduced by the variation present
in People, Information systems, Machines/Equipment,
Measurement, Materials and Environment. So, this type of
variation can typically only be reduced through management
intervention.
• In the spirit of improvement, the idea is to bring the process in
a state of control by removing the sources of special-cause
variation from the process. Then the process should be further
improved by reducing common-causes of variation. This can
be accomplished by reducing variation in the elements that
make up the process.
Control Charts
Common Causes of Variations
Special Causes of Variations
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1.
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Inappropriate procedures
Poor design
Poor maintenance of machines
Lack of clearly defined standard
operating procedures
Poor working conditions, e.g.,
lighting, noise, dirt, temperature,
Substandard raw materials
Quality control error
Vibration in industrial processes
Variability in settings
Computer response time
Poor adjustment of equipment
Operator falls asleep
Faulty controllers
Machine malfunction
Computer crashes
Poor batch of raw material
Power surges
High healthcare demand from
elderly people
• Broken part
• Abnormal traffic (click-fraud) on
web ads
• Operator absent
Control Charts
Developing Control Charts
• A control chart has upper and lower control limits
• We say that a process is out of control when a plot of data
reveals that one or more samples fall outside the control limits.
• The upper and lower control limits on a control chart are
usually set at ±3 standard deviations from the mean. If we
assume that the data exhibit a normal distribution, these
control limits will capture 99.74 percent of the normal
variation.
• Control limits can be set at ±2 standard deviations from the
mean. In that case, control limits would capture 95.44 percent
of the values.
Control Charts
Developing Control Charts
• Looking at this figure, we can conclude that
observations that fall outside the set range represent
assignable causes of variation.
Control Charts
Types of Control Charts
• Control charts are one of the most commonly used
tools in statistical process control.
• They can be used to measure any characteristic of a
product, such as the weight of a cereal box, the
number of chocolates in a box, or the volume of
bottled water.
• The different characteristics that can be measured by
control charts can be divided into two groups:
1. Variables -Quantitative data (Measured)
2. Attributes-Qualitative data (Counted)
Control chart for variables
• A control chart for variables is used to monitor
characteristics that can be measured and have a
continuous values,
• such as
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height,
volume.
the weight of a bag of sugar,
the temperature of a baking oven,
the diameter of plastic tubing.
Control chart for variables
Types of Variable Control Charts
• Use actual measurements for charting
– Average & Range charts
– Median & Range charts
– Average & Standard deviation charts
– Individual & Moving Range charts
– Run Charts
Control chart for variables
OBJECTIVES OF VARIABLE CONTROL
CHARTS
• For quality improvement.
• To determine the process capability.
• For decisions in regard to product specifications.
• For current decisions in regard to the production
process.
• For current decisions in regard to recently produced
items.
Control chart for variables
Formulae for calculating -Chart and R-Chart CL
• Average Chart ( -Chart ): uses average of a sample
• Range chart ( R-Chart ): uses amount of dispersion in
a sample
• Where:
Control chart for variables
Formulae for calculating -Chart and S-Chart CL
• Average Chart ( -Chart ): uses average of a sample
• Standard Deviation chart ( S-Chart ): uses amount of
dispersion in a sample
• Where:
Control chart for variables
Formulas for: X-double bar; R-bar and S-bar
• 𝑋=
• 𝑅=
• 𝑆=
𝑁
𝑖=1 𝑥𝑖
𝑁
𝑁
𝑖=1 𝑅𝑖
𝑁
𝑁
𝑖=1 𝑆𝑖
𝑁
Process Capability and Tolerance
• Process capability is referred to as the process spread and
is equal to 6 .
• The difference between specifications is called the
tolerance (USL-LSL).
– USL- upper specification limit
– LSL-lower specification limit
• When tolerance are established, 3 situations are possible:
1.
2.
3.
When the Process Capability is less than the tolerance
When the Process Capability is equal to the tolerance
When the Process Capability is greater than the tolerance
Process Capability and Tolerance
• Case 1:
6  USL LSL
– The tolerance is appreciably greater than the process capability.
– Any shift resulted in an out-of-control condition, will produce no waste
– Corrective action is required to bring the process into control.
• Case 2:
6  USL LSL
– When the process is in control, no nonconforming products
– When the process is out of control, nonconforming product is produced
– Assignable causes of variation must be corrected
• Case 3:
6  USL LSL
– Process in control but nonconforming product is produced
– Process is not capable of manufacturing a product that will meet
specifications
– When the process changes, the problem is much waste
– 100% inspection is necessary to eliminate the nonconforming product.
Process Capability and Tolerance
The process capability can be obtained by using two different methods:
Method 1: using the Range
• Take N subgroups of size n
• Calculate the range, R for each subgroup.
• Calculate the average range.
• Calculate the estimate of the population standard deviation
𝑅
𝜎=
𝑑2
• Process capability will be equal to 6.
Process Capability and Tolerance
Method 2: using the standard deviation
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Take N subgroups of size n
Calculate the sample standard deviation, S for each subgroup.
Calculate the average sample standard deviation, .
Calculate the estimate of the population standard deviation
𝑆
𝜎=
𝐶4
• Process capability will be equal to 6.
Capability Index
Process capability and tolerance are combined to form a
capability index which is the potential capability, and
defined as
𝑈𝑆𝐿 − 𝐿𝑆𝐿
𝐶𝑝 =
6𝜎
Where:
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C p = capability index
USL = upper specification limit
LSL = lower specification limit
6 = Process capability
Capability Index
The capability index does not measure process
performance in terms of the target value. This measure
is accomplished using Cpk , which is defined as
C pk
Z (USL) 
USL  X

Z min

3
Z ( LSL) 
X  LSL

Capability Ratio
Another measure of the capability is called capability
ratio which is the percentage of specifications’ width
used by the process, and is defined as
6𝜎
𝐶𝑟 =
× 100
𝑈𝑆𝐿 − 𝐿𝑆𝐿
The relationships between Cp and Cr
Cp - VALUE
Larger than 1,33
Between 1,0 & 1,33
Less than 1,00
Cr - VALUE
Less than 75%
DECISION
Process conforms very
good. No possibility of
defectiveness.
Process conforms
marginally, but should be
monitored closely for
Between 75% & 100% defectives, particularly
when small changes in
averages occur.
Larger than 100%
Process do not conform.
The relationships between Cp and Cpk
1.
The Cp value does not change as the process center changes.
2.
Cp = Cpk when the process is centered.
3.
Cpk is always less than or equal Cp.
4.
When Cpk has value of 1.00, it indicates the process is producing product
that conforms to specifications.
5.
When Cpk has a value less than 1.00, it indicates the process is producing
product that does not conform to specifications.
6.
A Cp value of less than1.00 indicates that the process is not capable.
7.
A Cpk value of zero indicates the process average is equal to one of the
specification limits.
8.
A negative Cpk value indicates that the average is outside the
specification limits.
The relationships between Cp and Cpk
Cp
Cpk
Process
Case
1,33
1.33
Centered
1
1.00
0.67
1.33
1.00
0.67
1.00
0.67
1.00
0.67
0.33
Centered
Centered
Off Center
Off Center
Off Center
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1
2
3