average and range charts
TRANSCRIPT
Presentation topic. Average and Range chart
Group Member1)Kashif Mazhar (Introduction )2)Ahmed Raza(Define Average and Range Chart)3)Rehan Saeed (Explain and Interpret With
Example)4)Ali Imran (Conclusion)
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Types of control charts.
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Types of measurement
Measure where the metric is composed of classification in one of two (or more) categories is called attribute data.
• Good / Bad• Yes / No. Measure where the metric consists of a number
which indicates a prices value is called variable data.
• time / hours• Miles / Temperature
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Average charts In this chart the sample means are plotted in order to
control the mean value of a variable (e.g., size of
piston rings, strength of materials, etc.)
the X-bar chart is a type of control chart that is used to monitor the arithmetic means of successive samples of constant size, n. This type of control chart is used for characteristics that can be measured on a continuous scale, such as weight, temperature, thickness etc.
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RANGE charts
In this chart, the sample ranges are plotted in order to control the variability of a variable.
Range chart shows how the range of the subgroups changes over time.
Simply, Range measures the variability of the process.
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• There is no two natural items in any category are the same.
• Variation may be quite large or very small.
• If variation very small, it may appear that items are identical, but precision instruments will show differences.
Variation
SOURCES OF Variation• Equipment
– Tool wear, machine vibration, …
• Material– Raw material quality
• Environment– Temperature, pressure, humadity
• Operator– Operator performs- physical & emotional 6
The management of West Allis Industries is concerned
about the production of a special metal screw used by
several of the company’s largest customers. The diameter
of the screw is critical to the customers. Data from five
samples appear in the table below. The sample size is 4. Is
the process in statistical control?
Average and Range-Charts Example
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RANGE Chart
SOLUTION
Step 1: For simplicity, we collect only 5 samples. In practice, more than 20 samples would be desirable. The data are shown in the following table.
Sample
Number Obs.1 Obs.2 Obs.3 Obs.4
1 0.5014 0.5022 0.5009 0.5027
2 0.5021 0.5041 0.5024 0.5020
3 0.5018 0.5026 0.5035 0.5023
4 0.5008 0.5034 0.5024 0.5015
5 0.5041 0.5056 0.5034 0.5047
Special Metal Screw
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Step 2: Compute the range for each sample by subtracting the lowest value from the highest value. For example, in sample 1 the range is 0.5027 – 0.5009 = 0.0018 in. Similarly, the ranges for samples 2, 3, 4, and 5 are 0.0021, 0.0017, 0.0026, and 0.0022 in., respectively. As shown in the table, R = 0.0021.
Sample Samples
Number Obs.1 Obs.2 Obs.3 Obs.4 R
1 0.5014 0.5022 0.5009 0.5027 0.0018
2 0.5021 0.5041 0.5024 0.5020 0.0021
3 0.5018 0.5026 0.5035 0.5023 0.0017
4 0.5008 0.5034 0.5024 0.5015 0.0026
5 0.5041 0.5056 0.5034 0.5039 0.0022
Special Metal Screw
0.5027 – 0.5009 = 0.0018
R = 0.0021
RANGE Chart
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Step 3: To construct the R-chart, select the appropriate constants from Table for a sample size of 4. The control limits are
Factor for FactorSize of LCL for UCL forSample R-Charts R-Charts
(n) (D3) (D4)
2 0 3.2673 0 2.5754 0 2.2825 0 2.1156 0 2.0047 0.076 1.9248 0.136 1.8649 0.184 1.81610 0.223 1.777
UCLR = D4R = 2.282 (0.0021) = 0.00479 in.LCLR = D3R = 0 (0.0021) = 0 in.
R = 0.0021
D4 = 2.282
D3 = 0
RANGE Chart
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Step 4: Plot the ranges on the R-chart, as shown in Figure 5.10. None of the sample ranges falls outside the control limits so the process variability is in statistical control. If any of the sample ranges fall outside of the limits, or an unusual pattern appears, we would search for the causes of the excessive variability, correct them, and repeat step 1.
RANGE Chart
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Step 1: Compute the mean for each sample. For example, the mean for sample 1 is
Average Chart
Sample Samples
Number Obs.1 Obs.2 Obs.3 Obs.4 X
1 0.5014 0.5022 0.5009 0.5027 0.5018
2 0.5021 0.5041 0.5024 0.5020 0.5027
3 0.5018 0.50260.5035 0.5023 0.5026
4 0.5008 0.5034 0.5024 0.5015 0.5020
5 0.5041 0.5056 0.5034 0.5039 0.5045
Special Metal Screw
(0.5014 + 0.5022 + 0.5009 + 0.5027)/4 =0.5018
X = 0.502712
Step 2: Now construct the x-chart for the process average. The average screw diameter is 0.5027 in., and the average range is 0.0021 in., so use x = 0.5027, R = 0.0021, and A2 from Table 5.1 for a sample size of 4 to construct the control limits:
Average and Range-Charts Example
Factor for UCL and LCL for X charts
(n) (A2)
2 1.8803 1.023 4 0.729 5 0.577 6 0.483
R = 0.0021 A2 = 0.729 x = 0.5027=
UCLx = x + A2R = 0.5027 + 0.729 (0.0021) = 0.5042 in.LCLx = x - A2R = 0.5027 – 0.729 (0.0021) = 0.5012 in.
==
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Average and Range-Charts ExampleStep 3: Plot the sample means on the control chart, as shown in Figure
5.11.
The mean of sample 5 falls above the UCL, indicating that the process average is out of statistical control and that assignable causes must be explored, perhaps using a cause-and-effect diagram.
Sample the process Find the assignable cause
Eliminate the problem Repeat the cycle
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9A-15
Common criteria for concluding process is
out of control or in danger of being so
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Average and range chart not applied
When ?• data is collected once per period• single value measurement• few units of each product• individual Values Chart
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Benefits of Average and Range Charts
• Focuses attention on detecting and monitoring process variation over time.
• Distinguishes “special” from “common” causes.
• Helps predict performance of a process.
• Helps improve a process to perform consistently.
• Provides a common language to discuss process behavior.
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•Help you recognize and understand variability and
how to control it
•. Identify .special causes. of variation and changes in
performance
•. Determine if process improvement effects are
having the desired affects
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Questions?
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