Post on 06-May-2015
Control Charts
1. Introduction
Introduction
Quality control charts, are graphs on which the quality of the product is plotted as the manufacturing is actually proceeding.
By enabling corrective actions to be taken at the earliest possible moment and avoiding unnecessary corrections, the charts help to ensure the manufacture of uniform products.
History of Control Chart
Mr. Shewart, an American, has been credited with the invention of control charts for variable and attribute data in the 1920s, at the Bell Telephone Industries.
The term ‘Shewart Control Charts’ is in common use.
Dynamic Picture of Process
Plotting graph, charting and presenting the data as a picture is common to process control method, used throughout the manufacturing and service industries.
Converting data into a picture is a vital step towards greater and quicker understanding of the process.
Confidence While Control Charting
Control charting enables everyone to make
decision and to know the degree of
confidence with which the decisions are
made. There may be some margin of error.
No technique, even 100% automated
inspection, can guarantee the validity of the
result; there is always some room to doubt.
Control Charts
Statistically based control chart is a device intended to be used
- at the point of operation- by the operator of that process- to asses the current situation- by taking sample and plotting
sample result
To enable the operator to decide about the process.
What Control Chart Does?
It graphically, represents the output of
the process.
And
Uses statistical limits and patterns of
plot, for decision making
Analogy to Traffic Signal
A control chart is like a traffic signal, the operation of which is based on evidence from samples taken at random intervals.
A control chart is like a traffic signal, the operation of which is based on evidence from samples taken at random intervals.
Analogy to Traffic Signal
GoNo action on Process
Wait and Watch
StopInvestigate/Adjust
Decision About The Process
Go
To let the process continue to run without any adjustment.
This means only common causes are present.
Decision About the Process
Wait and watch
Be careful and seek for more information
This is the case where presence of trouble is possible
Decision About the Process
Stop
Take action ( Investigate/Adjust )
This means that there is practically no doubt a special cause has crept in the system. Process has wandered and corrective actions must be taken, otherwise defective items will be produced.
2. Why control charts
Why Control Chart?
To ensure that the output of the process is ‘Normal’
Whether Output is Normal?
Both histogram and control chart can tell us whether
the output is normal? However,
Histogram views the process as history ,
as the entire output together.
Control chart views the process in real time,
at different time intervals as the process
progresses.
0
2
4
8
10
12
14
16
6Fre
quen
cy
47 48 49 50 51 52 53 54
kg
Histogram: a History of Process Output
Control Chart Views Process in Real Time
UCLx
Target
UCLr
Time Intervals
Ran
ge
Mea
n
LCLx
Target
Output of the process in real time
Why Control Chart?
It helps in finding
Is there any change in location of process
mean in real time?
Change in Location of Process Mean
43 48 49 50 51 52 5344 45 46 47
Process with mean at Target
Process with mean at more
than target
Process with mean at less than target
Why Control Chart?
It helps in finding
Is there any change in the
spread of the process in real
time?
Change in Spread of Process
43 48 49 50 51 52 5344 45 46 47
Larger spread dueto special causes
Spread dueto common causes
Why Control Chart?
To keep the cost of production minimum
Since the control chart is maintained in real time, and gives us a signal that some special cause has crept into the system, we can take timely action. Timely action enables us to prevent manufacturing of defective. Manufacturing defective items is non value added activity; it adds to the cost of manufacturing, therefore must be avoided.
By maintaining control chart we avoid 100% inspection, and thus save cost of verification.
Why Control Chart?
Pre-requisite for process capability studies
Process capability studies, are based on premises that the process during the study was stable i.e. only common causes were present. This ensures that output has normal distribution. The stability of the process can only be demonstrated by maintaining control chart during the study.
Why Control Chart?
Decision in regards to production process
Control chart helps in determining whether we should :
- let the process to continue without adjustment
- seek more information
- stop the process for investigation/adjustment.
3. Basic steps for control charting
Basic Steps for Control Charts
Step No. 1
Identify quality characteristics of product or process that affects “fitness for use”.
Maintaining control chart is an expensive activity. Control charts should be maintained only for critical quality characteristics. Design of Experiments is one of the good source to find the critical quality characteristics of the process.
Basic Steps for Control Charts
Step No . 2
Design the sampling plan and decide method of its measurement.
At this step we decide, how many units will be in a sample and how frequently the samples will be taken by the operator.
Basic Steps for Control Charts
Step No. 3
Take samples at different intervals and plot statistics of the sample measurements on control chart.
Mean, range, standard deviation etc are the statistics of measurements of a sample. On a mean control chart, we plot the mean of sample and on a range control chart, we plot the range of the sample.
Basic Steps for Control Charts
Step No. 4
Take corrective action - when a signal for significant change in process characteristic is received.
Here we use OCAP (Out of Control Action Plan) to investigate, as why a significant change in the process has occurred and then take corrective action as suggested in OCAP, to bring the process under control.
Summary of Control Chart Techniques
Quality characteristics
Sampling procedure
Plotting of statistics
Corrective action
In ‘Control Chart Technique’ we have:
4. Typical control charts
Elements of Typical Control Chart
1. Horizontal axis for sample number
2. Vertical axis for sample statistics e.g.
mean, range, standard deviation of sample.
3. Target Line
4. Upper control line
5. Upper warning line
6. Lower control line
7. Lower warning line
8. Plotting of sample statistics
9. Line connecting the plotted statistics
Elements of Typical Control Chart
1 2 3 4 5Sample Number
Upper control line
Target
Lower control line
Upper warning line
Lower warning line
Sam
ple
Sta
tistic
s
5. Types of control chart
Types of Control Chart
We have two main types of control charts. One for variable data and the other for attribute data.
Since now world-wide, the current operating level is ‘number of parts defective per million parts produced’, aptly described as ‘PPM’; control charts for ‘attribute data’ has no meaning. The reason being that the sample size for maintaining control chart at the ‘PPM’ level, is very large, perhaps equal to lot size, that means 100% inspection.
Most Commonly Used Variable Control Charts
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
Most Common Type of Control Chart for Variable Data
VariableControlChart
VariableControlChart
For tracking Accuracy
For tracking Accuracy
For tracking Precision
For tracking Precision
Mean control chart
Mean control chart
Rangecontrol chart
Rangecontrol chart
6. Concepts behind control charts
Understanding effect of shift of process mean
Case When Process Mean is at Target
43 48 49 50 51 52 5344 45 46 47
Target ProcessMean
Chances of getting a reading beyond U & L is almost nil
42
UL
- 3 s +3 s
U - L = 6 s
Case - Small Shift of the Process Mean
43 48 49 50 51 52 5344 45 46 47
Target
ProcessMean
Chances of getting a reading outside U is small
Small shift in process
42
Shaded area shows the
probability of getting
a reading beyond U
UL
U-L = 6 s
ProcessMean
Case - Large Shift of the Process Mean
43 48 49 50 51 52 5344 45 46 47
Target
Chances of getting a reading outside U is large
Large shift in process
42
Shaded area shows the
probability of getting
a reading beyond U
UL
U-L = 6 s
Summary of Effect of Process Shift
When there is no shift in the process nearly all the
observations fall within -3 s and + 3 s.
When there is small shift in the mean of process some
observations fall outside original -3 s and +3 s zone.
Chances of an observation falling outside original -3 s and +
3 s zone increases with the increase in the shift of process
mean.
Conclusion from Normal Distribution
When an observation falls within original +3 s and -3 s zone of mean of a process, we conclude that there is no shift in the mean of process. This is so because falling of an observation between these limits is a chance.
When an observation falls beyond original +3 s and -3 s zone of process mean, we conclude that there is shift in location of the process
7. Distribution of population vs
Distribution of mean
Distribution of Mean of Samples
Since on the control charts for accuracy we plot and watch
the trend of the means and ranges of the samples, it is
necessary that we should understand the behaviour of
distribution of mean of samples.
Distribution of Averages of Samples
Suppose we have a lot of 1000 tablets, and let us say, weight of the tablets follows a normal distribution having a standard deviation, s.
Let us take a sample of n tablets. Calculate mean of the sample and record it. Continue this exercise of taking samples, calculating the mean of samples and recording, 1000 times.
The mean of samples shall have normal distribution with standard deviation, Sm = (s÷ n). Distribution of population and ‘means of sample’ shall have same means.
Distribution - Population Vs Sample Means
43 48 49 50 51 52 5344 45 46 47
Quality Characteristics
Distribution of population(standard deviation = s
Distribution of means of samples
[standard deviation = (s÷ n)]
Control and Warning Limits for Mean Control Chart
If we know the standard deviation of the population, say sand the number of units in a sample, say n; then the control and warning limits are calculated as follows:
If desired target of the process is T, then
Upper control limit, UCL = T + 3 (s÷ n)
Upper warning limit. UWL = T + 2 (s÷ n)
Lower control limit, LCL = T - 3 (s÷ n)
Lower warning limit, LWL = T - 2 (s÷ n)
Control Limits for Mean Control Chart
1 2 3 4 5 6 7
Sample Number
UCL
Target
LCL
Distribution of mean of samples
3 (s ÷ n)UWL
LWL
2 (s ÷ n)
2 (s ÷ n)3 (s÷ n)
8. Flow Chart for Establishing Control Chart
Decide subgroup size
Record observations
Find mean and range of each subgroup
Calculate mean range, R
Start
Flow Chart for Establishing Control Chart
Is any sub-group mean or range
out side the controllimit ?
Drop thatGroup
UCLx = T + A2 x RLCLx = T - A2 x R
UCLr = D4 x RLCLr = D3 x R
Yes
No
Flow Chart for Control Chart
Select suitable scale formean control chart and
range control chart
Draw Lines forTarget, UCL, UWL, LCL & LWL for mean
Mean range, UCL , UWL, LCL & LWL for range
Stop
9. Interpreting control charts
Interpreting Control Chart
The control chart gets divided in three zones.
Zone - 1 If the plotted point falls in this zone, do not make any adjustment, continue with the process.
Zone - 2 If the plotted point falls in this zone then special cause may be present. Be careful watch for plotting of another sample(s).
Zone - 3 If the plotted point falls in this zone then special cause has crept into the system, and corrective action is required.
Zones for Mean Control Chart
1 2 3 4 5 6 7
Sample Number
UCL
Target
LCL
UWL
LWL
Zone - 3
Sa
mp
le M
ean
Zone - 2
Zone - 3
Zone - 2
Zone - 1
Action
Action
Warning
Warning
Continue
ContinueZone - 1
Interpreting Control Charts
Since the basis for control chart theory follows the normal distribution, the same rules that governs the normal distribution are used to interpret the control charts. These rules include:
- Randomness.- Symmetry about the centre of the distribution.- 99.73% of the population lies between - 3 s of and + 3 s the centre line.- 95.4% population lies between -2 s and + 2 s of the centre line.
Interpreting Control Chart
If the process output follows these rules, the process is
said to be stable or in control with only common causes of
variation present. If it fails to follow these rules, it may be
out of control with special causes of variation present.
These special causes must be found and corrected.
Interpreting Control Chart
A single point above or below the control limits.
Probability of a point falling outside the control limit is less than 0.14%. This pattern may indicate:
- a special cause of variation from a material, equipment, method, operator etc.- mismeasurement of a part or parts.- miscalculated or misplotted data point.
Interpreting Control Chart
UCL
1 2 3 4 5 6 7 8
Sample Number
Sta
tis
tic
s
UWL
LCL
Target
LWL
One point outsidecontrol limit
Interpreting Control Chart
Seven consecutive points are falling on one side of the centre line.
Probability of a point falling above or below the centre line is 50-50. The probability of seven consecutive points falling on one side of the centre line is 0.78% ( 1 in 128)
This pattern indicates a shift in the process output from changes in the equipment, methods, or material or shift in the measurement system.
Interpreting Control Chart
UCL
1 2 3 4 5 6 7 8
Sample Number
Sta
tis
tic
s
UWL
LCL
Target
LWL
Seven consecutive points on one side of the centre line
Interpreting Control Chart
Two consecutive points fall between warning limit and corresponding control limit.
In a normal distribution, the probability of two consecutive points falling between warning limit and corresponding control limit is 0.05% (1 in 2000).
This could be due to large shift in the process, equipment, material, method or measurement system.
Interpreting Control Chart
UCL
1 2 3 4 5 6 7 8
Sample Number
Sta
tis
tic
s
UWL
LCL
Target
LWL
Two consecutive points between warning limit and corresponding control limit
Interpreting Control Chart
Two points out of three consecutive points fall between warning limit and corresponding control limit.
This could be due to large shift in the process, equipment, material, method or measurement system.
Interpreting Control Chart
UCL
1 2 3 4 5 6 7 8
Sample Number
Sta
tis
tic
s
UWL
LCL
Target
LWL
Two points out of three consecutive points between warning limit and corresponding control limit
Interpreting Control Chart
A trend of seven points in a row upward or downward demonstrates non-randomness.
This happens in the following cases:
- Gradual deterioration or wear in equipment.- Improvement or deterioration in technique.- Operator fatigue.
Interpreting Control Chart
UCL
1 2 3 4 5 6 7 8
Sample Number
Sta
tis
tic
s
UWL
LCL
Target
LWL
Seven consecutive points having upward trend
Interpreting Control Chart
UCL
1 2 3 4 5 6 7 8
Sample Number
Sta
tis
tic
s
UWL
LCLLCL
Target
LWL
Seven consecutive points having downward trend