lesson 6technical component

8/12/2019 Lesson 6Technical Component

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Dr. Pham Huynh TramDepartment of ISE

[email protected]


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Review of basic probability & statistics- Probability- Types of data-

Describing dataStabilizing and improving a process with controlcharts

- Needs of control chart

- Structure of control chart- Rules of identifying out-of-control point- Possible mistakes un using control chart


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Example: a bin contains 4000 screws; 2000 are good and2000 are defective

What is the probability of drawing a defective screw?- Classical probability- Relative frequency probability- Difference?


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Sub-group

No. ofdefective

Fraction ofdefective

Cummulativeno. ofdefective

Cummulativeno. of screw

Cummulativeof fraction

1234567

Subgroup size :50


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Pupose of collecting data? Attribute data

- Classificaion of items into categories. Eg.: grade A, B, C- Counts of the number of items in a given category or a

proportion in a given category- Counts of the number of occurrences per unit . Eg.: no. ofdefects per batch, no. of sales per month Variables (measurment) data

- Measurement of a characteristic. Eg.: length of time toresolve customer complaint, weights of boxes of detergent

- Computation of Numerical Value from two or moremeasurements of variables data. Eg.: computation of arectangular containe, km per litre for each truck


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For frequency distributionTabular displaysGraphical displays

- Histogram (variable data)- Bar chart (attribute data)- Ogive- Run chart


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The number of intervalsinfluences the pattern, shape, or spreadof your Histogram.


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Run chart


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Mode = 16

The mode is the most frequently occurring value. It is the value with the highest frequency .

Given a data set:9, 10, 6, 12, 16, 14, 19, 20, 14, 15, 22, 24, 13, 16, 17, 5, 17, 18,19, 18, 16, 22


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The mean of a set of observations is theiraverage - the sum of the observed values dividedby the number of observations.

Population Mean Sample Mean

m = = x

N i

N

1 x

x

n i

n

= =

1


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Range Difference between maximum and minimum values

VarianceMean * squared deviation from the meanStandard Deviation

Square root of the variance

Definitions of population variance and sample variance differ slightly .


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Find the sample mean and sample variance forthe following series of data:

Value

21

12

34

22

17

18

43

28

56

34

12

Practice with Calculator !!


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Skewness Measure of asymmetry of a frequency distribution

Skewed to leftSymmetric or unskewedSkewed to right

KurtosisMeasure of flatness or peakedness of a frequencydistribution

Platykurtic (relatively flat)Mesokurtic (normal)Leptokurtic (relatively peaked)


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Skewed to left

6 0 0 5 0 0 4 0 0 3 0 0 2 0 0 1 0 0

3 0

2 0

1 0

0

x

F r e

q u e n c y

Mean < median < mode


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Mean = median = mode

6 0 0 5 0 0 4 0 0 3 0 0 2 0 0 1 0 0

x

3 0

2 0

1 0

0

F r e

q

u e n c y

Symmetric


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3 . 7 2 . 9 2 . 1 1 . 3 0 . 5 - 0 . 3 - 1 . 1 - 1 . 9 - 2 . 7 - 3 . 5

7 0 0

6 0 0

5 0 0

4 0 0

3 0 0

2 0 0

1 0 0

0

X

F r e

q u e n c y

Platykurtic - flat distribution


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4 3 2 1 0 - 1 - 2 - 3 - 4

5 0 0

4 0 0

3 0 0

2 0 0

1 0 0

0

X

F r e

q u e n c y

Mesokurtic - not too flat and not too peaked


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Leptokurtic - peaked distribution

1 0 0 - 1 0

2 0 0 0

1 0 0 0

0

Y

F r e

q u e n c y


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Normal distributionCalculate probabilitySkewed distribution

Unknown distribution


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1 1

21

14

34

75%

1 1

31

1

9

8

9 89%

1 1

41

116

1516

94%

2

2

2

= = =

= = =

= = =

At least of the elements of any distribution lie within k standard deviations of the mean

2

11

k

Atleast

Lie within

Standarddeviations

of the mean

2

3

4


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Control charts are constructed by drawing samples andtaking measurements of a process characteristics. Each setof measurements is called a subgroupControl charts help to

- identify and differentiate between common causes andspecial causes of variation- determine a processs capability

Process is stable if it only exhibits common cause variation

When a process is stable, continuous improvement helps tobring the centerline of the process closer to a desired level(nominal) by reducing the magnitude of common cause variations


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-Centerline: drawn at the average value of all the plotted data.

-Control Limits (UCL, LCL): set at a distance of 3 sigma above and 3sigma below the centerline. They indicate variation from the centerline

* Difference between control limits and specification limits ?27


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31


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32


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Rule 5: 8 or more successive values continually increase

or decrease


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Rule 6: unusual small number of runs above and below

center line are present ( a sawtooth pattern)


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Rule 7: 13 consecutive points fall in zone C


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Over adjustmentProcess should be adjusted not on the basis of time-to-

time observations, but on the basis of informationprovided by a statistical control chart

Funnel experimentUnder adjustment

Lack of attention when the process is out of control and

no effort is made to provide neccesary regulation

*Also, becareful on false out-of control signal


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Defect prevention: atribute chartP chart, mp chart, c chart, u chart

Continuous improvement: variable control chart

X bar chart, R chart, MR chart, s chart

lesson 6technical component

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