Jpm Tqm Course Mat-3 T-3 Imba 2013

7/30/2019 Jpm Tqm Course Mat-3 T-3 Imba 2013

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CONTROL

CHARTS

&CONTROL

LIMITS


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# CAUSES OF VARITION OF MEASUREMENTSVariation in measurement (quality) can be caused in two ways,

i) Assignable Causes (causes for variation which can be identified)

ii) Natural (not under control) or Chance or Random Causes.

ASSIGNABLE CAUSES OF VARITIONBasic Nature :1) For Assignable Causes the variations are generally greaterin

magnitude (in comparison to Natural Causes)

2) The variations do not follow Normal Statistics.

3) Assignable Causes of variation are generally easily traceable &identifiable

4) The Assignable causes & variations are not inevitable.

5) Assignable Causes of variation normally can be removed/

rectified/ eliminated.6) If Assignable Causes are not rectified, the process becomes

Out of Control.


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CAUSES OF VARITIONBasic Assignable Causes :1. Faulty process

2. Quality of raw materials and/orcomponents,

3. Wear & Tear of the machine and equipment4. Operating Condition ofmachine and equipment, like vibration,

leveling defect, defective centering, non-alignment, etc

5. Wrong setting up of machine(cutting speed, depth of cut, etc)

6. Improper Maintenance

7. Wrong tools8. Improper fixing / fitting of tools

9. Faultyjigs and fixtures

10. Use of uncalibrated or poorly calibrated instrument, gauges, etc.

11. Operating Condition of Instrumentation & Control

12. Faulty Environmental Condition of working place (improperlighting & ventilation, dust, smoke, temperature variation, toxicor corrosive atmosphere, humidity, etc),

13. Inadequate Skillof operators,

14. Mental condition / Mood of operators,

15. Carelessness and mistake on the part of operators,


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Natural or Chance or Random CausesOF VARITION

Basic Nature :

1. Such causes are inherent in the process and thus areINEVITABLE,

2. The variations in measurement are generally smaller inmagnitude

3. Such causes are non-rectifiable in nature (very difficult to

rectify even under best care & conditions)4. The causes are unpredictable and very difficult to identify &

trace

5. Variations due to such causes follow Statistical Rules andNormal Curve (chance factorie Probability is involved).

6. With this type of variations, the process is said to be UNDER-CONTROL.

# [If the variations do not follow Normal Curve, there must besome Assignable Causes which can be detected and rectified.]


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Control Chart for VARIABLES (Quality Characteristics)Let, Variables (individual measurements/observations) = Xi ,(where i = 1 to n),

Sample Size for each sub-group (sample) = n,No. of Samples / Sub-group (lot) = N.

_Sample Average (Sample Mean), Xmean, X = ( Xi) n where i = 1 to n

= Process Average (Process Mean), X = ( Xk) N where k = 1 to N

Range (in each sample), Rk = ( X max Xmin) where k = 1 to N

Mean Range (of the Process), R = ( Rk) N where k = 1 to N

Standard Deviation(in each Sample), Sk = [( Xi Xmean)2 (n-1) ]

_Mean Standard Deviation for process, S = ( Sk) N where k = 1 to N

Standard DeviationofPOPULATION,

_ = R d2

_

= S C2

[Since, R > S always, d2

> C2 ]


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_

X

N

LCL

UCL

=X

N

R

_

R

UCL

LCL

_

X - Chart R - Chart

X Chart R-Chart

Central Line (CL)=X

R

Upper Control Limit (UCL)= X + A2.R

_

D4 . R

Lower Control Limit (LCL)= X A2.R

_D3 . R


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_

X

N

LCL

UCL

=X

N

S

_

S

UCL

LCL

_

X - Chart S - Chart

X Chart S-Chart

Central Line (CL)=X

S

Upper Control Limit (UCL)= X + A3.S

_

B4 . S

Lower Control Limit (LCL) = X A3.S _B3 . S


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_X Chart and R-Chart

_

X Chart

R-Chart

Central Line (CL)=X

_R

Upper Control Limit (UCL)=

X + A2.R

_

D4 . R

Lower Control Limit (LCL)=

X A2.R_

D3 . R

_X Chart and S-Chart

_

X Chart

S-Chart

Central Line (CL) =X_S

Upper Control Limit (UCL)=

X + A3.S_

B4 . S

Lower Control Limit (LCL)=

X A3.S_

B3 . S

# X S charts are preferably applicable over X R chart, when

(1) Sample size, n > 10,

(2) Tight control of Process Variability is needed, and

(3) Sample size nvaries.


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Values of Statistical Constants

Sample

Size (n)A2 D3 D4 A3 B3 B4 d2 c2

2 1.88 0 3.27 2.66 0 3.27 1.128 0.7979

3 1.02 0 2.57 1.95 0 2.57 1.693 0.8862

40.73 0 2.28 1.63 0 2.27 2.059 0.9213

5 0.58 0 2.11 1.43 0 2.09 2.326 0.9400

6 0.48 0 2.00 1.29 0.03 1.97 2.534 0.9515

7 0.42 0.08 1.92 1.18 0.12 1.88 2.704 0.9594

8 0.37 0.14 1.86 1.10 0.19 1.81 2.847 0.9650

9 0.34 0.18 1.82 1.03 0.24 1.76 2.970 0.9693

10 0.31 0.22 1.78 0.98 0.28 1.72 3.078 0.9727

[Since R >S, A3> A2, d2 > c2; and always D4 & B4> 1 but D3 & B3 < 1 ]

A M d l f D t Sh t f X R h t


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A Model of Data Sheet for X R chart

----------------------------------------------------------------------------------------------------------Department : Specification :

Drawing No. : USL = LSL =

Part Name. : Sample Size, n =

Part No. : Total No. of Sample, N =

Machine ID :Operator ID: Inspector :

-----------------------------------------------------------------------------------------------------------------------------------

Sample No. X1 X2 X3 X4 Xn Xmean Range R

(= Xi n) (Xmax Xmin)1.

2.

3.

4.

:

:

N (normally 20 -25)

--------------------------------------------------------------------------------======--------------------=======

Xmean R= _X = ( Xmean) N = R = R N =

CL = CL =UCL = UCL =LCL = LCL =

_

= R / d2 PCR = (USL LSL) 6

A M d l f D t Sh t f X S h t


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A Model of Data Sheet for X S chart

----------------------------------------------------------------------------------------------------------Department : Specification :

Drawing No. : USL = LSL =

Part Name. : Sample Size, n =

Part No. : Total No. of Sample, N =

Machine ID :Operator ID: Inspector :

---------------------------------------------------------------------------------------------------------------------------

Sample No. X1 X2 X3 Xn Xi Xmean ( Xi n) (Xi Xmean)2 S

1.

2.

3.

4.

:

:

N (normally 20 -25)

----------------------------------------------------------------==========---------------------------=====

Xmean s=X = ( Xmean) N = [S = [(Xi Xmean)2] (n-1) S = S N]CL = CL =UCL = UCL =LCL = LCL =

_

= S / C2 6 = PCR = (USL LSL) 6


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Normal Distribution CurveFrequency of

occurrence

Deviation

Limits

2 3-3 -2 - =X ()

68.28%

95.46%

99.73%

Area under the Curve

indicates Population

6

TO ERANCE


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TOLERANCETolerance is the acceptable / allowed limits of variations of the measurements

(dimensions, strength, properties, finish, etc) of the items of the lot.

Tolerance Limits are the maximum variations of the measurement those can

be acceptable / allowed, above (Upper Control Limit) or below (Lower Control

Limit) the corresponding specified measurement. Example :

+ 0.2 + 0.8 +10Diameter 455 mm, Cr content 14 %, Strength 540 kg/cm2

0.3 0. 5 0

Tolerance may be : (i) Natural Tolerance and/or (ii) Specified Tolerance

Natural Tolerance :If the process is Under Control (ie the variations aresmall and follow statistical laws), the Upper Control Level (UCL) and the

Lower Control Limit (LCL) together indicate the Natural Tolerance.

Gap between Natural Tolerance Limits UNTL & LNTL (ie 6 ) is BAND.

Specified Tolerance :The tolerance limits (U & L) predefined orspecified by the designer or the user of the product (depending on the

quality needed to fit it in its use) is termed as Specified Tolerance.

Specified Tolerance is not directly related to or dependent on Natural

Tolerance ie Natural Control Limits. Specified Tolerance is important and

considered in QC of industrial Products.

The gap between Specified Tolerance Limits USL & LSL is SPREAD.

SPECIFIED TOLERANCE


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SPECIFIED TOLERANCE : (example : 250 +3 4 )

Process Control Limits :

USL = Upper specified Limit (here 253) LSL = Lower specified Limit (here 246)

(USL LSL) = SPECIFIED SPREADor simply SPREAD (S) (here 253 246 = 7)CENTER LINE of Specified Spread = (USL + LSL) / 2 (here 249.5)

NATURAL TOLERANCE: =Process Central Line = X =

Upper Natural Tolerance Limit = UNTL=+ 3

Lower Natural Tolerance Limit = LNTL = 3

NATURAL /PROCESS SPREADor simply BAND (B) = (UNTL LNTL) = 6

PROCESS CAPABILITY RATIO (PCR) = Specified Spread.

Process Spread

PCR = Specified spread = (USL LSL) = Spread (S) = S

Process Spread (UNTL LNTL) Band (B) 6

P C bilit b d SPREAD d BAND


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Process - Capability based on SPREAD and BAND1) If 6 < SThe processisCapablecan be easily

be kept under control by adjusting=

the position of X very near to Centre

Line of the Spread (S).Position2 is shifted and keptat position 1.

2) If 6 = SStrict Centering care to be taken

=to keep the Control (Centre) Line X

perfectly at the Centre Line of Spread.It is also better to relax the SpecifiedTolerance to make S> 6 . Position2is shifted and kept at position 1.TheProcess is marginally Capable.3) If6 > SEven with Extreme care & control and

Perfect Centering, the process is not Capable.The Process is said to beOut of Control. Quality non-conformance willbe there and there by Quality RejectionWill take place.Care to be taken : (1) Fundamental change in process,(2) Revision of Specified Tolerance, (3) Perfect Centering,

(4) 100% inspection

21

SC

USL

LSL

6

6S

USL

LSL

SC S2

1

6

6

=X

=X

Jpm Tqm Course Mat-3 T-3 Imba 2013

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