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IE 673 LIVE - Assignment 3

KAMIL DZWONKOWSKI

ELeARNING ID: IE 673-Fall 2008-70-38

Pack-It-Solutions Collaborating with:

   Noax Technologies

  GE Healthcare

Rockwell Automation

BioPharma Solutions

Table of Contents:

Introduction and Project Objective

Methodologies Applied

The main body of the project

Statistical Quality Control Applied

Summary

 

Introduction and Project Objective:

 The main character of this project is to apply Total Quality Management strategies, focused around the control chart modeling for a number of different variables and attributes and their convention to better a process and its quality.

 There is a verity of methods, and a number of solutions to develop any method. One of these types of methods is represented statistically, however this is not the only strategy available that will result in a process improvement.

 

Methodologies applied:

 The quality tools that we focus on are called statistical Process Control Charts. There are used for variation controlling, and obtaining a process associated data with inputs/outputs. It becomes very importuned fo the predicted changes in the future to better the processing system. It’s used as an additional tool to back up the quality factors introduced as CORA analysis.

The data measurements required for a Process Control Charts are collected thru measurements from a verity of sensors and A/D meters. When the data is collected, it is transformed into frequency distribution algorithms. Such frequency distribution is described as a number of times when a particular quality characteristic occurs within it sample of the products to be tested.

It is significant to understand, that the testing of a progression, including the collected data involves comparing it with a set of defined specifications sheets. This is also called as Key Characteristics. The statistical process control charts make it easier to identify bad processes and design upstream production techniques, therefore resulting in continues process control and seamless production.

 

The Main Body of the project:

Control charts deal with characteristics that can be measured and assigned a numerical value. These values are plugged into equations that the control charts uses. Below is a list of mathematical data or formula used in control charts.

·         Xi: value -The actual value of each measurement.

·         fi: frequency -The frequency of each measurement - The number of times each measurement occurs in the sample.

·         n: sample size - The sample size - the number of products measured or investigated.

·         ∑: Sigma - the sum of all values taken.

·         X bar -The average of a sample - is the sum of all values divided by the sample size. (formula given below)

·         R - Range - the difference between the highest and the smallest value encountered in the sample.

·         S - Standard Deviation - The standard deviation measures the variability in a sample data set. The higher the standard deviation, the larger the scatter about the average is.

 

There are two different types of data that can be used in control charts. Grouped and ungrouped data

 Grouped data:

           In this case, data is classified by increasing order (Xi) and frequencies (fi) of occurrence next to their values.

Ungrouped data:

          Data (Xi) is gathered in a bunch of values, without any classification.

The table on the left represents ungrouped data as can be seen by the random values for X. The table on the right is that of grouped data as can be seen by the    increasing values of X and by the frequency column.

Many different types of control charts are available for use. Some control charts and their respective uses are listed below. For the context of this assignment however, we will be using X -Bar and R type control charts.

bullet The X-bar chart: it is a control chart for the variation of the mean value of a characteristic.
bullet The R-chart: it is a control chart for the range of values in a sample.
bullet The p-chart: it is a control chart for fraction nonconforming.
bullet The c-chart: it is a control chart for number of defects or nonconformities.
bullet The u-chart: it is a control chart for number of nonconformities per unit.

Formulas for X-Bar and R-Charts are given below. The coefficients A2, D3, and D4 in the formula below depend on the sample size and are usually found in mass media.

                    Steps in Constructing an R Chart:

1.      Select k successive subgroups where k is at least 20, in which there are n measurements in each subgroup. Typically n is between 1 and 9. 3, 4, or 5 measurements per subgroup is quite common.

2.      Find the range of each subgroup R(i) where R(i)=biggest value - smallest value for each subgroup i.

3.      Find the centerline for the R chart, denoted by

4.      Find the UCL and LCL with the following formulas:  

UCL= D(4)RBAR and LCL=D(3)RBAR

 

Statistical Quality Control Applied:

After collecting the required data and plotting it into the control charts, we output analysis that will oversee the future of our processing line.

The first step is deriving the coefficients A2, D4 and D3.

We simply fallow the table form the specification sheet.

 

n

D (3)

D (4)

3

0

2.574

4

0

2.574

5

0

2.114

6

0

1.998

7

0.076

1.924

8

0.136

1.864

9

0.184

1.816

Therefore:

A2

1.023

D4

2.574

D3

0

 We apply the collected data to construct the Control Chart:

 

Subgroup

X1

X2

X3

X-bar

UCL-X-bar

X-Dbar

LCL-X-bar

R

UCLR

R-bar

LCLR

1

6.31

6.16

6.91

6.46

6.79

6.44

6.09

0.75

0.89

0.34

0.00

2

6.81

6.69

6.23

6.58

6.79

6.44

6.09

0.58

0.89

0.34

0.00

3

6.36

6.79

6.64

6.60

6.79

6.44

6.09

0.43

0.89

0.34

0.00

4

6.11

6.58

6.6

6.43

6.79

6.44

6.09

0.49

0.89

0.34

0.00

5

6.42

6.52

6.51

6.48

6.79

6.44

6.09

0.10

0.89

0.34

0.00

6

6.36

6.29

6.42

6.36

6.79

6.44

6.09

0.13

0.89

0.34

0.00

7

6.82

6.24

6.48

6.51

6.79

6.44

6.09

0.58

0.89

0.34

0.00

8

6.12

6.19

6.43

6.25

6.79

6.44

6.09

0.31

0.89

0.34

0.00

9

6.59

6.27

6.92

6.59

6.79

6.44

6.09

0.65

0.89

0.34

0.00

10

6.85

6.5

6.56

6.64

6.79

6.44

6.09

0.35

0.89

0.34

0.00

11

6.94

6.59

6.62

6.72

6.79

6.44

6.09

0.35

0.89

0.34

0.00

12

6.23

6.14

6.42

6.26

6.79

6.44

6.09

0.28

0.89

0.34

0.00

13

6.28

6.62

6.35

6.42

6.79

6.44

6.09

0.34

0.89

0.34

0.00

14

6.36

6.2

6.24

6.27

6.79

6.44

6.09

0.16

0.89

0.34

0.00

15

6.74

6.24

6.36

6.45

6.79

6.44

6.09

0.50

0.89

0.34

0.00

16

6.44

6.62

6.59

6.55

6.79

6.44

6.09

0.18

0.89

0.34

0.00

17

6.37

6.4

6.43

6.40

6.79

6.44

6.09

0.06

0.89

0.34

0.00

18

6.26

6.31

6.51

6.36

6.79

6.44

6.09

0.25

0.89

0.34

0.00

19

6.6

6.59

6.5

6.56

6.79

6.44

6.09

0.10

0.89

0.34

0.00

20

6.24

6.3

6.63

6.39

6.79

6.44

6.09

0.39

0.89

0.34

0.00

21

6.46

6.29

6.24

6.33

6.79

6.44

6.09

0.22

0.89

0.34

0.00

22

6.64

6.37

6.25

6.42

6.79

6.44

6.09

0.39

0.89

0.34

0.00

23

6.21

6.15

6.53

6.30

6.79

6.44

6.09

0.38

0.89

0.34

0.00

24

6.18

6.18

6.47

6.28

6.79

6.44

6.09

0.29

0.89

0.34

0.00

Sum

 

 

 

154.59

 

 

 

8.26

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Next we plotting the subgroup data and assuring that the process is in statistical control. In a case that the test is not successful, we need to eliminate the cause and repeat the testing procedure.

 

We never eliminate subgroups that have points out of the range.

PLEASE CLICK HERE TO SEE THE EXCEL ANALYSIS SHEET.

Next step is the application of standard deviation that could be executed by applying the following formula:

 , where D(2) @ try 3 is 1.693.

Therefore we conclude that:

·        We see no points out of control limits and no seven consecutive points above the CL.

·        Neither have we seen any points below the central line or decreasing, nor increasing.

 

 

 

·        Therefore the R-Chart process is in control.

 

 

 

 

 

 

While we have identified the R-BAR, we need to find also the X-BAR. As noted from the methodologies applied, we used the following formulas:

 , and

While we assume A(2) to be at 1.023, we result the following findings after plotting in to a X-chart:

Therefore we conclude that:

·        We find no points out of control limits and non seven consecutive points above or   below the CL.

 

·        Nor decreasing or increasing points.

 

 

 

 

 

 

 

·        This is the X-chart process is in control.

 

 

 

 

 

 

 

Summary:

1.      The Control charts are excellent tool to determine mistake processes, and deriving an upstream process control, which results in continuous monitoring of the system.

2.      While there might exist an out-of-control action, it has to be immediately corrected.

3.      As the system is capable of self-correction, if it undergoes a malfunction, it has to be reconfigured by the administrator.

4.      As a result of sub-processes, an out-of-limit variation might be produced. These variations have a very strong effect on the quality of the product and seamless production line. When the statistical methodologies of PCC are applied, this variation can be easily identified and eliminated.

5.      A greater costumer satisfaction, lower waste of production, and highest possible quality could be achieved when implementing process control charts in a particular process.

6.      While the highest satisfaction of the costumer is important, the lowest waste assures being environmental friendly, and continuously GREEN.

 

References and Bibliography

"Paul G. Ranky, IE673 Total Quality Management, Fall 2008, e-Learning Pack ID # IE673-FALL2008-70-38" "Paul G. Ranky"


http://www.cimwareukandusa.com/All_IE673/IE673Fall2008.html

Ranky, P.G.: http://www.cimwareukandusa.com

 

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