8/7/2019 control chart p,np,c,u
1/64
8/7/2019 control chart p,np,c,u
2/64
8/7/2019 control chart p,np,c,u
3/64
8-1 Quality Improvement and Statistics
Definitions of Quality
Quality means fitness for use
- quality of design
- quality of conformance
Quality is inversely proportional to
variability.
8/7/2019 control chart p,np,c,u
4/64
8-1 Quality Improvement and Statistics
Quality Improvement
Quality improvementis the reduction of
variability in processes and products.
Alternatively, quality improvementis also
seen as waste reduction.
8/7/2019 control chart p,np,c,u
5/64
8-1 Quality Improvement and Statistics
Statistical process control is a
collection of tools that when usedtogether can result in process stability
and variance reduction.
8/7/2019 control chart p,np,c,u
6/64
8-2 Statistical Process Control
The seven major tools are
1) Histogram
2) Pareto Chart4) Cause and Effect Diagram
5) Defect Concentration Diagram
6) Control Chart
7) Scatter Diagram8) Check Sheet
8/7/2019 control chart p,np,c,u
7/64
8-3 Introduction to Control Charts
8-3.1 Basic Principles
A process that is operating with onlychance causes of variation present is saidto be in statistical control.
A process that is operating in the presenceofassignable causes is said to be out of
control. The eventual goal of SPC is the elimination
of variability in the process.
8/7/2019 control chart p,np,c,u
8/64
8-3 Introduction to Control Charts
8-3.1 Basic PrinciplesA typical control chart has control limits set at valuessuch that if the process is in control, nearly all points
will lie within the upper control limit (UCL) and the
lower control limit (LCL).
8/7/2019 control chart p,np,c,u
9/64
8-3 Introduction to Control Charts
8-3.1 Basic Principles
8/7/2019 control chart p,np,c,u
10/64
8-3 Introduction to Control Charts
8-3.1 Basic Principles
8/7/2019 control chart p,np,c,u
11/64
8-3 Introduction to Control Charts
8-3.1 Basic PrinciplesImportant uses of the control chart
1. Most processes do not operate in a state of statistical
control2. Consequently, the routine and attentive use of control
charts will identify assignable causes. If these causes
can be eliminated from the process, variability will be
reduced and the process will be improved3. The control chart only detects assignable causes.
Management, operator, and engineering action will be
necessary to eliminate the assignable causes.
8/7/2019 control chart p,np,c,u
12/64
8-3 Introduction to Control Charts
8-3.1 Basic PrinciplesTypes the control chart
Variables Control Charts
These charts are applied to data that follow acontinuous distribution.
Attributes Control Charts
T
hese charts are applied to data that follow adiscrete distribution.
8/7/2019 control chart p,np,c,u
13/64
8-3 Introduction to Control Charts
8-3.1 Basic PrinciplesPopularity of control charts
1) Control charts are a proven technique for improving
productivity.2) Control charts are effective in defect prevention.
3) Control charts prevent unnecessary process adjustment.
4) Control charts provide diagnostic information.5) Control charts provide information about process
capability.
8/7/2019 control chart p,np,c,u
14/64
8-3 Introduction to Control Charts
8-3.2 Design of a Control Chart
Suppose we have a process that we assume the
true process mean is Q = 74 and the process
standard deviation is W = 0.01. Samples of size 5are taken giving a standard deviation of the sample
average, is
0045.05
01.0
nx !!
W!W
8/7/2019 control chart p,np,c,u
15/64
8-3 Introduction to Control Charts
8-3.2 Design of a Control Chart Control limits can be set at 3 standard
deviations from the mean in both directions.
3-Sigma Control LimitsUCL = 74 + 3(0.0045) = 74.0135
CL= 74
LCL=
74 - 3(0.0045)=
73.9865
8/7/2019 control chart p,np,c,u
16/64
8-3 Introduction to Control Charts
8-3.2 Design of a Control Chart
8/7/2019 control chart p,np,c,u
17/64
8-3 Introduction to Control Charts
8-3.2 Design of a Control Chart
Choosing the control limits is equivalent to
setting up the critical region for hypothesistesting
H0: Q = 74
H1: Q { 74
8/7/2019 control chart p,np,c,u
18/64
8-3 Introduction to Control Charts
8-3.3 Rational Subgroups
Subgroups or samples should be selected
so that if assignable causes are present, thechance for differences between subgroups
will be maximized, while the chance for
differences due to these assignable causeswithin a subgroup will be minimized.
8/7/2019 control chart p,np,c,u
19/64
8-3 Introduction to Control Charts
8-3.3 Rational Subgroups
Constructing Rational Subgroups
Select consecutive units of production.
Provides a snapshot of the process. Good at detecting process shifts.
Select a random sample over the entire sampling
interval.
Good at detecting if a mean has shifted
out-of-control and then back in-control.
8/7/2019 control chart p,np,c,u
20/64
8-3 Introduction to Control Charts
8-3.4 Analysis of Patterns on Control Charts
Look for runs - this is a sequence of
observations of the same type (all above the
center line, or all below the center line) Runs of say 8 observations or more could
indicate an out-of-control situation.
Run up: a series of observations are increasing
Run down: a series of observations are decreasing
8/7/2019 control chart p,np,c,u
21/64
8-3 Introduction to Control Charts
8-3.4 Analysis of Patterns on Control Charts
8/7/2019 control chart p,np,c,u
22/64
8-3 Introduction to Control Charts
8-3.4 Analysis of Patterns on Control Charts
8/7/2019 control chart p,np,c,u
23/64
8-3 Introduction to Control Charts
8-3.4 Analysis of Patterns on Control Charts
8/7/2019 control chart p,np,c,u
24/64
8-3 Introduction to Control Charts
8-3.4 Analysis of Patterns on Control Charts
8/7/2019 control chart p,np,c,u
25/64
8-3 Introduction to Control Charts
8-3.4 Analysis of Patterns on Control Charts
8/7/2019 control chart p,np,c,u
26/64
8-4 X-bar and R Control Charts
8/7/2019 control chart p,np,c,u
27/64
8-4 X-bar and R Control Charts
8/7/2019 control chart p,np,c,u
28/64
8/7/2019 control chart p,np,c,u
29/64
8-4 X-bar and R Control Charts
8/7/2019 control chart p,np,c,u
30/64
8-4 X-bar and R Control Charts
8/7/2019 control chart p,np,c,u
31/64
8-4 X-bar and R Control Charts
8/7/2019 control chart p,np,c,u
32/64
8-4 X-bar and R Control Charts
Computer Construction
8/7/2019 control chart p,np,c,u
33/64
8-5 Control Charts for Individual
Measurements
What if you could not get a sample size greater than 1(n =1)? Examples include
Automated inspection and measurement technology
is used, and every unit manufactured is analyzed.The production rate is very slow, and it is
inconvenient to allow samples sizes of N > 1 toaccumulate before analysis
Repeat measurements on the process differ onlybecause of laboratory or analysis error, as in manychemical processes.
The individual control charts are useful for samples ofsizes n = 1.
8/7/2019 control chart p,np,c,u
34/64
8-5 Control Charts for Individual
Measurements
The moving range (MR) is defined as theabsolute difference between two successive
observations:MRi = |xi - xi-1|
which will indicate possible shifts or
changes in the process from one observationto the next.
8/7/2019 control chart p,np,c,u
35/64
8-5 Control Charts for Individual
Measurements
8/7/2019 control chart p,np,c,u
36/64
8-5 Control Charts for Individual
Measurements
8/7/2019 control chart p,np,c,u
37/64
8-5 Control Charts for Individual
Measurements
X Charts can be interpreted similar to charts. MR charts
cannot be interpreted the same as or R charts.
Since the MR chart plots data that are correlated with
one another, then looking for patterns on the chart does not
make sense.
MR chart cannot really supply useful information about
process variability. More emphasis should be placed on interpretation of the X
chart.
Interpretation of the Charts
x
x
8/7/2019 control chart p,np,c,u
38/64
8-6 Process Capability
Process capability refers to the performance of
the process when it is operating in control.
Two graphical tools are helpful in assessingprocess capability:
Tolerance chart (or tier chart)
Histogram
8/7/2019 control chart p,np,c,u
39/64
8-6 Process Capability
8/7/2019 control chart p,np,c,u
40/64
8-6 Process Capability
8/7/2019 control chart p,np,c,u
41/64
8-6 Process Capability
8/7/2019 control chart p,np,c,u
42/64
8-6 Process Capability
8/7/2019 control chart p,np,c,u
43/64
8-6 Process Capability
8/7/2019 control chart p,np,c,u
44/64
8-7 Attribute Control Charts
8-7.1 PChart (Control Chart for Proportions)
and nPChart
8/7/2019 control chart p,np,c,u
45/64
8-7 Attribute Control Charts
8-7.1 PChart (Control Chart for Proportions)
and nPChart
8/7/2019 control chart p,np,c,u
46/64
8-7 Attribute Control Charts
8-7.1 PChart (Control Chart for Proportions)
and nPChart
8/7/2019 control chart p,np,c,u
47/64
8-7 Attribute Control Charts
8-7.1 PChart (Control Chart for Proportions)
and nPChart
8/7/2019 control chart p,np,c,u
48/64
8-7 Attribute Control Charts
8-7.2 UChart (Control Chart for Average
Number of Defects per Unit) and C
Chart
8/7/2019 control chart p,np,c,u
49/64
8-7 Attribute Control Charts
8-7.2 UChart (Control Chart for Average
Number of Defects per Unit) and C
Chart
8/7/2019 control chart p,np,c,u
50/64
8-7 Attribute Control Charts
8-7.2 UChart (Control Chart for Average
Number of Defects per Unit) and C
Chart
8/7/2019 control chart p,np,c,u
51/64
8-7 Attribute Control Charts
8-7.2 UChart (Control Chart for Average
Number of Defects per Unit) and C
Chart
8/7/2019 control chart p,np,c,u
52/64
8-8 Control Chart Performance
Average Run Length
The average run length (ARL) is a very
important way of determining the appropriate
sample size and sampling frequency.
Let p = probability that any point exceeds the
control limits. Then,
8/7/2019 control chart p,np,c,u
53/64
8-8 Control Chart Performance
8/7/2019 control chart p,np,c,u
54/64
8-8 Control Chart Performance
8/7/2019 control chart p,np,c,u
55/64
8-8 Control Chart Performance
8/7/2019 control chart p,np,c,u
56/64
8-9 Measurement Systems Capability
8/7/2019 control chart p,np,c,u
57/64
8-9 Measurement Systems Capability
8/7/2019 control chart p,np,c,u
58/64
8-9 Measurement Systems Capability
8/7/2019 control chart p,np,c,u
59/64
8-9 Measurement Systems Capability
8/7/2019 control chart p,np,c,u
60/64
8-9 Measurement Systems Capability
8/7/2019 control chart p,np,c,u
61/64
8-9 Measurement Systems Capability
8 9 S C i i
8/7/2019 control chart p,np,c,u
62/64
8-9 Measurement Systems Capability
8 9 M S C bili
8/7/2019 control chart p,np,c,u
63/64
8-9 Measurement Systems Capability
8/7/2019 control chart p,np,c,u
64/64