average and range charts

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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