7 QC ToolsCheck-sheetCause and EffectParetoHistogramControl ChartScatter PlotStratification

Check-sheetFor problem solving data is to be captured.Check-sheet is a tool to capture data as per check listCheck list is a tool to capture the parameter

4. Additional causes can be branched off the tertiary causes.

Pareto ChartFind the few important reasons !the vital few and the trivial many80 20 ruleClass dataCollect data in a tableCalculate the cumulative valuesPlot pareto diagram

Example

Chart1

0.0050.0204-0.0099

0.0050.0204-0.0099

0.0050.0204-0.0099

0.0050.0204-0.0099

0.0050.0204-0.0099

0.0050.0204-0.0099

0.0050.0204-0.0099

0.010.0204-0.0099

0.0050.0204-0.0099

0.0050.0204-0.0099

0.0050.0204-0.0099

0.0050.0204-0.0099

0.0050.0204-0.0099

0.0050.0204-0.0099

0.0050.0204-0.0099

0.0050.0204-0.0099

0.0050.0204-0.0099

0.010.0204-0.0099

0.0050.0204-0.0099

0.0050.0204-0.0099

0.0050.0204-0.0099

0.0050.0204-0.0099

00.0204-0.0099

U.C.L. =0.0204

L.C.L. = -0.0099

DATE

FRACTION DEFECTIVE

FRACTION DEFECTIVE CHART(PRESS SHOP)JAN-05

Chart2

44.144.1

38.282.3

11.894.1

5.9100

DEFECTS

% AGE

CUMULATIVE % AGE

PARETO CHART FOR PRESS SHOP(JAN-05)

Sheet1

Type of DefectNo. of defective pc.%Cum. %

3-Jan0.0050.0204-0.0099Sheet Hard5644.144.1

4-Jan0.0050.0204-0.0099Draw & Die Setting4938.282.3

5-Jan0.0050.0204-0.0099Sheet Line1511.894.1

6-Jan0.0050.0204-0.0099Operator Defect75.9100

7-Jan0.0050.0204-0.0099Total127

9-Jan0.0050.0204-0.0099

10-Jan0.0050.0204-0.0099

11-Jan0.010.0204-0.0099

12-Jan0.0050.0204-0.0099

13-Jan0.0050.0204-0.0099

15-Jan0.0050.0204-0.0099

17-Jan0.0050.0204-0.0099

18-Jan0.0050.0204-0.0099

19-Jan0.0050.0204-0.0099

20-Jan0.0050.0204-0.0099

21-Jan0.0050.0204-0.0099

22-Jan0.0050.0204-0.0099

24-Jan0.010.0204-0.0099

25-Jan0.0050.0204-0.0099

27-Jan0.0050.0204-0.0099

28-Jan0.0050.0204-0.0099

29-Jan0.0050.0204-0.0099

31-Jan00.0204-0.0099

Sheet2

Sheet3

Chart1

Chart3

0.0050.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.010.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.010.0224-0.0104

0.0050.0224-0.0104

0.010.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.010.0224-0.0104

0.010.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

U.C.L. = 0.0224

L.C.L. = -0.0104

DATE

FRACTION DEFECTIVE

FRACTION DEFECTIVE CHART(PRESS SHOP)DEC-04

Sheet1

3-Dec0.0050.0224-0.0104

4-Dec0.0050.0224-0.0104

6-Dec0.0050.0224-0.0104

7-Dec0.0050.0224-0.0104

8-Dec0.010.0224-0.0104

9-Dec0.0050.0224-0.0104

10-Dec0.0050.0224-0.0104

11-Dec0.0050.0224-0.0104

13-Dec0.0050.0224-0.0104

14-Dec0.0050.0224-0.0104

15-Dec0.0050.0224-0.0104

16-Dec0.0050.0224-0.0104

17-Dec0.0050.0224-0.0104

18-Dec0.0050.0224-0.0104

20-Dec0.010.0224-0.0104

21-Dec0.0050.0224-0.0104

22-Dec0.010.0224-0.0104

23-Dec0.0050.0224-0.0104

24-Dec0.0050.0224-0.0104

25-Dec0.0050.0224-0.0104

27-Dec0.010.0224-0.0104

28-Dec0.010.0224-0.0104

29-Dec0.0050.0224-0.0104

30-Dec0.0050.0224-0.0104

31-Dec0.0050.0224-0.0104

Sheet1

46.146.1

38.584.6

10.394.9

5.1100

&A

Page &P

DEFECTS

% AGE

CUMULATIVE %AGE

PARETO CHART FOR PRESS SHOP (DEC-04)

Sheet2

Sheet3

Chart5

46.146.1

38.584.6

10.394.9

5.1100

DEFECTS

% AGE

CUMULATIVE %AGE

PARETO CHART FOR PRESS SHOP (DEC-04)

Chart3

0.0050.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.010.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.010.0224-0.0104

0.0050.0224-0.0104

0.010.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.010.0224-0.0104

0.010.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

0.0050.0224-0.0104

U.C.L. = 0.0224

L.C.L. = -0.0104

DATE

FRACTION DEFECTIVE

FRACTION DEFECTIVE CHART(PRESS SHOP)DEC-04

Sheet1

3-Dec0.0050.0224-0.0104

4-Dec0.0050.0224-0.0104

6-Dec0.0050.0224-0.0104

7-Dec0.0050.0224-0.0104

8-Dec0.010.0224-0.0104

9-Dec0.0050.0224-0.0104

10-Dec0.0050.0224-0.0104

11-Dec0.0050.0224-0.0104

13-Dec0.0050.0224-0.0104

14-Dec0.0050.0224-0.0104

15-Dec0.0050.0224-0.0104

16-Dec0.0050.0224-0.0104

17-Dec0.0050.0224-0.0104

18-Dec0.0050.0224-0.0104

20-Dec0.010.0224-0.0104

21-Dec0.0050.0224-0.0104

22-Dec0.010.0224-0.0104

23-Dec0.0050.0224-0.0104

24-Dec0.0050.0224-0.0104

25-Dec0.0050.0224-0.0104

27-Dec0.010.0224-0.0104

28-Dec0.010.0224-0.0104

29-Dec0.0050.0224-0.0104

30-Dec0.0050.0224-0.0104

31-Dec0.0050.0224-0.0104

Sheet1

46.146.1

38.584.6

10.394.9

5.1100

&A

Page &P

DEFECTS

% AGE

CUMULATIVE %AGE

PARETO CHART FOR PRESS SHOP (DEC-04)

Sheet2

Sheet3

What is a Histogram?Histogram is a visual tool for presenting variable data. It organises data to describe the process performance.

Additionally histogram shows the amount and pattern of the variation from the process.

Histogram offers a snapshot in time of the process performance.

Definition of HistogramA histogram is a graphical summary of variation in a set of data.

The pictorial nature of the histogram enables us to see patterns that are difficult to see in a table of numbers.

Key Concept of HistogramData always have variationVariation have patternPatterns can be seen easily when summarized pictorially

Location of mean of the process Spread of the process Shape of the process

While studying histogram look for its

Calculations for Histogram

Calculations for HistogramSmallest Value, S= 47Largest Value, L = 55Range= L-S= R= 8No. of cells= 1+3.22log10(50)= 7Calculated cell width (CW)= R/no. of cell=1.14Rounded off Cell width= 1 (multiple of 1,2,5 of least count

Calculations for HistogramStarting value, A= 47LCB(1)= A-cw/2= 47-1/2= 46.5UCB (1)= LCB(1)+CW= 46.5+1= 47.5

Plotting Histogram

Histogram

Skewness Is the histogram symmetrical? If so, Skewness is zero. If the left hand tail is longer, skewness will be negative. If the right hand tail is longer, skewness will be positive. Where skewness exists, process capability indices are suspect. For process improvement, a good rule of thumb is to look at the long tail of your distribution; that is usually where quality problems lie

Kurtosis Kurtosis is a measure of the pointiness of a distribution. The standard normal curve has a kurtosis of zero. The Matter horn, has negative kurtosis, while a flatter curve would have positive kurtosis. Positive kurtosis is usually more of a problem for quality control, since, with "big" tails, the process may well be wider than the spec limits.

Distributions you may encounter

The standard normal distribution, with its zero skewness and zero kurtosisA skewed distribution, with one tail longer than the other.

A double-peaked curve often means that the data actually reflects two distinct processes with different centers. You will need to distinguish between the two processes to get a clear view of what is really happening in either individual process

Why Control Chart ?To findIs there any change in location of process average ?Is there any change in the spread of the process ?Is there any change in shape?

Control ChartsVariablesAttributesp Chartnp ChartC Chartu Chart

defect prevention and process improvementmore expensive to construct and maintaincan tell reason for process behaviorsmaller n (1-10) neededdefect detection a screening device to initiate variables control chartingcheaper to construct and maintaincannot tell cause of defectneed large n (>100)Variable Control ChartsAttribute Control Charts

Attribute Control Chartsp ChartMeasures % defectiveCharts number of defects in varying sized samplesnp ChartMeasures number of defective piecesCharts the numbers of defective pieces in fixed size samplesC ChartMeasures number of defectsLooks at a single product or pieceu ChartMeasures number of defects per unit area, time, length, etc.Charts number of defects in a product of varying size

StartSelecting a Control Chart

Control Limits1234567Sample NumberUpper Control LimitLower Control LimitTarget3 x sd of means

Control Chart Technique - 1 Select a quality characteristicsWeightLengthViscosityTensile StrengthCapacitance

Control Chart Technique - 2 Choose sub group size Sensitivity increases with the sub group size Cost of sampling increases with size In case of destructive testing - 2 or 3 Normally sub group size can be 4 or 5Choose Interval of data collection (frequency) of sample sizeCollect the data

If mean of the process shifts by 1 times sd ( Impact of sample size)

Sample Size

Chances of Detecting a shift (%)

2

5

4

10

10

55

15

82

20

95

Typical Data Table

Part

Operation

Other Details

SN

Date

Time

Measurement

Mean

Range

X1

X2

X3

X4

1

12/12

10.25

35

40

32

33

35.0

8

2

12/12

13.45

46

42

40

38

41.5

8

3

12/12

15.34

34

40

34

36

36.0

6

..

25

15/12

10.30

38

34

44

40

39

10

Determine trial control limits

Constants for Trial Control Limits

group Size

A2

D4

D3

2

1.880

3.267

0

3

1.023

2.527

0

4

0.729

2.282

0

5

0.577

2.115

0

6

0.483

2.004

0

7

0.419

1.924

0.076

Formula for Control LimitsFor mean control chartUpper Control Limit, UCLx = T + A2 x R Lower Control Limit, LCLx = T - A2 x RFor range control chartUpper Control Limit, UCLr = D4 x RLower Control Limit, LCLr = D3 x R

Sample CalculationIn our caseTarget, T = 50Mean range, R = 9Sub Group size, n = 4Values obtained from the table of constantsA2 = 0.729D4 = 2.282D3 = 0

Sample CalculationsUCLX = 50 + 0.729 X 9 = 56.56LCLX = 50 - 1.079 X 9 = 43.44UCLr = 2.282 X 9 = 20.54LCLr = 0 X 9 = 0

OutliersOutliers are those observations which do not belong to normal population.If Outliers are included in the calculation, then the information is distorted. Not more than 20% subgroups are omitted

OutliersScan column for meansIf any mean is more than UCLx or mean is less than LCLx then drop that sub-group

Checking for range outliersScan column for ranges, if any range is more than UCLr then drop that sub-group

If any sub-group(s) is dropped then recalculate the trial control limits using remaining sub-group(s)Continue this exercise till there is no further droppings ( max 20%)

Control Chart12345678Sample Number MeanUCLx LCLxUCLrT=50Range555040456020100

Control Chart with Action Limit12345678Sample Number MeanUCLx LCLxT=5050404030603010020UWLx LWLx 2/3 A2 x R2/3 A2 x R

One Point Falling Out side Control Limit12345678Sample NumberSample MeanUCLxLCLx

12345678Sample NumberSample MeanTwo out of 3 points falling between Control Limit and Warning LimitsUCLxLCLx

12345678Sample NumberSample Mean7 Consecutive points falling on one side of the center line ( A run of seven )UCLxLCLx

Over Adjustment Over adjustment is fiddling with the controls of stable process.

It is often a well intention move of the process owner, but bad attempt to improve the process.

It actually adds a further source of variation to the process, and hence will increase total variation.

Problem of Over Adjustment3848505254565840424446Resultant distributionwith flat top

Scatter Plot

Scatter diagram Exhibits RelationshipA scatter diagram shows the relationship between independent variable (cause) and dependent variable (effect).

The independent variable is plotted on x-axis and dependent variable on y-axis.

Characteristics of Independent VariableIt should be measurable on a continuous scale.

It should have a logical relationship with the dependent variable.

Changes in level of independent variable should cause changes in level of dependent variable.

Typical Relationship We Normally Like to StudyIndependent VariableDependent VariableMoisture contents Elongation of threadWax purity Hardness of lipstickRoller PressurePaper thicknessCharge weight Range of bulletNumber of users Response time

Pull SpeedLength of barTypical RelationshipYX

Shelf LifePotencyTypical RelationshipYX

Table - Humidity Vs Voltage

Humidity %

Voltage

V1

V2

V3

V4

V5

10

20

30

40

50

60

70

80

90

100

40

46

45

49

51

54

54

57

59

60

43

43

43

45

47

51

52

55

57

58

41

46

43

48

50

51

51

54

56

57

42

46

44

49

51

52

55

58

59

58

40

44

43

46

49

53

53

58

57

58

Scatter Plot1050204060307080901004045505560HumidityVoltage35

StratificationStratification is simply the creation of a set of pareto charts for the same data, using different possible causative factors

Following figures plot defects against three possible sets of potential causes. The figure shows that there is no significant difference in defects between production lines or shifts. But product type three has significantly more defects than do the others. Finding the reason for this difference in number of defects could be worthwhile

A problem is solved according to the following SEVEN STEPS of Q.I.Story.

SEVEN STEPS OF Q.I.STORY :

1. Reason For Improvement

2. Current Situation

3. Analysis

4. Counter Measure

5. Result

6. Standardization

7. Future Plan

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