ME 445 INTEGRATED MANUFACTURING TECHNOLOGIES
EXPERIMENT 4
“STATISTICAL PROCESS CONTROL: THEORY AND LABORATORY
DEMONSTRATION”
INTRODUCTION
Quality is an important task to be considered in any manufacturing system. It is a cost
issue, with an obvious impact on company sales and profitability and an important factor in
marketability of manufactured parts. Previously quality was only determined by a basic
detection and sorting system. In recent years, the emphasis has shifted toward a preventive
approach in which in-process or automated inspection eliminates or minimizes the faults and
errors even at the processing stage.
Coordinate Measuring Machines (CMM) are powerful tools for geometric dimension
and tolerance inspection and are being used in manufacturing industry as effective
instruments for quality control. A CMM is typically built with :
-
a highly accurate and stable base structure, having simple yet accurate
transmission mechanism to support X-Y-Z motion
a highly reliable probe sensing system to make measurements and collect
dimensional data
a software system including data fitting algorithms for 3D geometry analysis
a computer hardware and control system
These machines normally possess high accuracy and reliability for achieving accurate
inspection results. As the name indicates, the inspection principle underlying these machines
is the use of a coordinate system for inspection. Dimensions and tolerances of part features
are measured in the chosen coordinate system in the spatial coordinate locations of the
selected contact points between the probe and part features. These coordinate points are then
registered in computer memory and processed with the built in geometry analysis software to
determine features’ dimensions and tolerances.
Coordinate Measuring machine inspection has many advantages over conventional
inspection methods. Some of these advantages are summarized below:
- Flexibility: CMMs are universal machines and can in principle measure any
dimensional characteristic of any part configuration. In reality, some limitations may be
imposed on unsophisticated machines. In most cases, no special fixtures are required for the
holding of a part during inspection as probe contact is very light.
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- Reduction of setup time: In conventional geometry inspection, part alignment and
establishment of appropriate reference points are difficult tasks and consequently, these
inspection processes are labor intensive and time consuming. With CMMs, an inspector can
set up a part in a convenient orientation for the inspection and, because it uses a coordinate
system and a set of data fitting algorithms, all coordinate data measured is subsequently
corrected according to the calibration of the part and the probe. Thus, the time for setup is
minimized for part inspection and inspection efficiency is improved.
- Improved Accuracy: All measurements are carried out using a common measuring
system, so the accumulation of errors that would have resulted from hand-gauge inspection
methods is avoided. Also, the operator’s influence is kept at a minimum level, and hence the
inspection quality is consistent.
- Automation: CMMs are fully equipped with a computer system and use high-level
control languages for their programming and, therefore, they have potential for automated
inspection and integration with CAD systems.
STATISTICAL PROCESS CONTROL
Although accuracy is of great importance to engineers, absolute accuracy is
unattainable. Even gage blocks of the highest order of accuracy have manufacturing
tolerances which are as small as a few hundred thousands of a millimeter. These tolerances,
whose magnitude depends on the function of a component, are necessary to allow for the
inherent variability of the production processes.
When the quantity involved is large, the pattern of variation can be studied on a
statistical basis. Then it becomes possible to assess the quality achieved by the process
without testing every piece produced. Various applications for statistics in quality control
were achieved following the introduction of statistical control method, but among all of the
SPC techniques, control charts proved the most efficient.
Control charts are used to determine the inherent variation in a process. As long as the
data related to the process are within constructed control limits and presents a normal
distribution, the process is considered stable and the resulting variation in the process
acceptable. However if any data lies outside the limit or show abnormal variations, assignable
sources of error in the process can be suggested thus ensuring a path of quality production.
The benefits of control charts are simply as follows:
-
Products have minimum variation among themselves.
With stable processes, inspection can be reduced or eliminated altogether.
The width of control limits is a measure of the process capability. This information is
used to enhance product quality through design by matching the process capability with
design tolerances.
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SPC is the whole technical and managerial effort to control the manufacturing
processes for improving and maintaining quality and the technique proves fulfill these tasks
simultaneously. SPC cannot be limited to the control charts only. It is also a diagnostic tool
such that it provides the hints on where the problem exists and what the probable causes are.
Implementing SPC begins with the task of knowing the process in terms of what is called
process capability. Process capability refers to the extent of variation in the product data
when the process is stable. It is established by tracking the process spread for specific
combinations of tooling, workpiece material and even the operator. The benefits of SPC
briefly are:
-
The process planner knows what the shop can do.
The operator knows immediately when the process begins to behave abnormally.
Rejected products decrease.
Obviously the burden of analyzing the process data is quite much. To relieve this
burden various analyzers and software packages are developed. These commercial packages
and tools helps operator in quickly interpreting measurement data thus provide an ease in
quickly detecting abnormal process variations.
CONTROL CHARTS FOR VARIABLES DATA
The key task in improving quality is to reduce the variability of the quality
characteristic of product, e.g. the diameter of cylinder bore. Obviously the variation of a
characteristic depends on some reason which is further classified as common causes and
special causes. A process is said to be in statistical control if only common causes are present.
However special or assignable causes may shift the process state to out-of-control and lead to
production of non-conforming products. In order to detect and eliminate such causes in a
process, control charts are utilized.
Quality characteristic
Control charts are graphical presentation of quality characteristic measured on a
sample versus the sample number or time. Three essential elements of a control chart are the
center line, an upper control limit and a lower control limit line. The figure below illustrates a
sample control chart. The control charts are classified into two general categories: variable
control chart and attribute control chart.
UC
L
CL
LCL
3
Order of sampling
Variables data, that is used to construct the variables control charts, is data that is
acquired through measurements, such as length, time, diameter, strength, height, temperature,
density, thickness, pressure, and height. Variables data is normally analyzed in pairs of charts
which present data in terms of location or central tendency and spread. Location, usually the
top chart, shows data in relation to the process average. It is presented in X , individuals, or
median charts. Spread, usually the bottom chart, looks at piece-by-piece variation. Range, ,
and moving range charts are used to illustrate process spread. Another aspect of these
variables control charts is that the subgroup size is generally constant.
The two most frequently used control charts are the X and R charts. These charts are
used to monitor and control the process mean and range of variability. The sample size for
these charts is larger than two, i.e. at least two specimen are measured to create a subgroup.
Analyzing variables charts for special cause variation depends on the assessing of the
patterns arise in the constructed chart. Some of the typical patterns indicating lack of control
can be presented as follows:
-
any point lying outside the control limits
seven or more points in a row above or below the centerline
seven or more points in a row going in one direction, up or down
systematic, non-random fluctuations, such as cycles, sawtooth patterns
When these patterns develop and the process state is declared to be out-of-control, the
diagnosis stage will start. Patterns on X charts are affected by causes which are capable of
affecting all units produced at once or in the same general way. Examples of some of these
changes that may affect the X chart are:
- material defects
- inspector error
- supplier changes
- operator error
- machine setting
- unusual tool wear
The range chart measures the uniformity or consistency of the process. Assignable
causes for changes in R charts are due to some units receiving different treatment from
others, thus reflecting variability. Ideally, values and level of the R chart should be as low as
possible. Causes which affect only part of the units being produced will cause variations and
out-of-control readings on the range chart. Some of the assignable causes of R-chart
variability may be:
-
poorly trained operator or inspector
non-uniform materials
machine out of adjustment or repair
non-standard parts at beginning or end of run
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X – R CHARTS
An X and R (range) chart is a pair of control charts used with processes that have a
subgroup size of two or more. X and R charts are used to determine if a process is stable and
predictable. The X chart shows how the mean or average changes over time and the R chart
shows how the range of the subgroups changes over time. It is also used to monitor the
effects of process improvement studies. X and R charts can be used for any process with a
subgroup size greater than one. Typically, it is used when the subgroup size falls between two
and nine.
X and R charts are used when the answer to the following questions is yes:
- Do you need to assess system stability?
- Is the data in variables form?
- Is the data collected in subgroups larger than one but less than eleven?
- Is the time order of subgroups preserved?
Before calculating control limits as many subgroups as possible should be collected.
With smaller amounts of data, the X and R chart may not represent variability of the entire
system. The more subgroups used in control limit calculations, the more reliable the analysis.
Typically, twenty to twenty-five subgroups will be used in control limit calculations.
X and R charts have several applications. When a system is to be improved, these
charts are used to assess the system’s stability. After the stability has been assessed, the need
to stratifying the data should be determined. Entirely different results may occur between
shifts, among workers, among different machines, among lots of materials, etc. To see if
variability on the X and R chart is caused by these factors, data should be collected and
entered in a way that lets stratifying by time, location, operator, and lots.
X and R charts can also be used to analyze the results of process improvements. It
would be considered how the process is running and compared to how it ran in the past and if
process changes produce the desired improvement.
The most common (and recommended) method of computing control limits for X
chart with range and range chart based on three standard deviations is:
Upper Control Limits:
UCLX  X  A2  R
UCLR  D4  R
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Lower Control Limits:
LCLX  X  A2  R
LCLR  D3  R
where X is the average of the mean of values in group of observations and R is the average
of the range values. A2, D3 and D4 are read from table of control limits. D3 does not exist for
subgroup sizes less than seven, so the lower control limit for range charts with subgroup size
less than seven is zero.
Factors for X and R Charts Control Limits
Subgroup Size
A2
d2
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
1.880
1.023
0.729
0.577
0.483
0.419
0.373
0.337
0.308
0.285
0.266
0.249
0.235
0.223
0.212
0.203
0.194
0.187
0.180
0.173
0.167
0.162
0.157
0.153
1.128
1.693
2.059
2.326
2.534
2.704
2.847
2.970
3.078
3.173
3.258
3.336
3.407
3.472
3.532
3.588
3.640
3.689
3.735
3.778
3.819
3.858
3.859
3.931
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D3 D4
-------------------------0.076
0.136
0.184
0.223
0.256
0.283
0.307
0.328
0.347
0.363
0.378
0.391
0.403
0.415
0.425
0.434
0.443
0.451
0.459
3.276
2.574
2.282
2.114
2.004
1.924
1.864
1.816
1.777
1.276
1.717
1.693
1.672
1.653
1.637
1.622
1.608
1.597
1.585
1.276
1.566
1.557
1.548
1.541
PROCESS CAPABILITY
Control chart is an effective way in controlling assignable process variations, but it is
powerless for normal variations. Normal process variations are measured by the process
capability index Cp and Cpk. Process capability study relates the needs of the design with the
capabilities of the process. Cp implies the process capability index which is defined as:
Cp 
USL  LSL
6
where  denotes the process standard deviation and USL-LSL is the difference between the
upper and lower specification limits set during design stage, i.e. tolerance.
The process capability index Cp by itself is unable to measure process performance in
terms of target or nominal value fixed by the designer. This performance is measured by the
other parameter Cpk and defined as
C pk 
Z
3
where Z is the smaller of USL- X or X -LSL and X is is the average of the mean of values in
group of observations
Analysis of process capability is a vital part of a quality improvement system. The
followings are among the major uses of a process capability study:
- Predicting how well the process will hold the tolerances.
- Assisting in design stage in selecting or modifying a process.
- Assisting in establishing an interval between sampling for process control.
- Specifying performance requirements for new equipment.
- Planning the sequence of production processes when there is an interactive effect of
processes on tolerances.
- Reducing the variability in a manufacturing process.
The figure below presents an example analysis method for process capability interpretation.
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LABORATORY WORK
The primary aim of this demonstration is to present quality control capabilities of the
METUCIM system. The Coordinate Measuring Machine (CMM) that exists in the system is
utilized for the dimensional inspection and analysis of manufactured parts. The machine has
certain measurement capabilities which are to be presented during the demonstration. The
automatic measurement programming feature of the CMM allows efficient use of such
machines in automated manufacturing systems.
During the laboratory demonstration, a sample measurement operation will be carried
out. Measurement of different features and automatic measurement exercises will be done.
The collected data for a number of measured workpieces will be recorded. As an output for
the study a process control chart for a given subgroup size will be prepared and necessary
comments on the control chart and process capability figures will be presented.
Below figure shows the dimensions and tolerances on the sample workpiece that is
going to be measured.
8.00.1
12 0.1
20 0.1
6.0  0.1
0.2
C
C
9
14.5 0.1
PROCESS CONTROL CHART
Lot No: 1
Operation : Turning
M/C Tool : CNC Lathe
Control Point: A
Work Limits :
50.00 +0.24 mm
50.00 mm
Production rate : 200 parts/hr
Sampling rate : 10% (20 parts/hr)
Sample size : 5
Sampling period : 15 min
x : 50.130
UCL = x +A2 * R = 50.177
LCL = x -A2 * R = 50.083
Measured

R =
d2
R : 0.081
UCL = D4 * R = 0.171
LCL = D3 * R = 0.0
Measured
0.035 Cp = 1.143
Cpk = 1.048
SAMPLE PROCESS CONTROL CHART
x1
x2
x3
x4
x5
x6
x
R
Sample No
Time
Date
50.080
50.100
50.110
50.100
50.080
50.120
50.110
50.090
50.120
50.080
50.150
50.090
50.110
50.150
50.090
50.160
50.150
50.090
50.150
50.100
50.100
50.160
50.080
50.130
50.140
50.150
50.090
50.170
50.090
50.170
50.160
50.170
50.110
50.170
50.100
50.090
50.150
50.160
50.210
50.140
50.100
50.100
50.230
50.160
50.170
50.110
50.240
50.110
50.140
50.170
50.094
0.030
1
8:15
50.104
0.040
2
8:30
50.118
0.060
3
8:45
50.130
0.070
4
9:00
50.122
0.080
5
9:15
50.134
0.080
6
9:30
50.142
0.070
7
9:45
50.150
0.120
8
10:00
50.152
0.130
9
10:15
50.154
0.130
10
10:30
Average Chart
50.250
USL
50.200
UCL
50.150
mean
50.100
LCL
50.050
50.000
LSL
49.950
1
2
3
4
5
6
7
8
9
10
Sample No
Range Chart
0.200
UCL
0.150
0.100
0.050
10
0.000
1
2
3
4
5
6
Sample No
7
8
9
10
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