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STATISTICAL    QUALITY   CONTROL   (S.Q.C.)   PRESENTED BY-:   NIKHIL GARG   ROLL NO- 0129626
Contents-: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Control chart for attributes-:   p-chart…………   np-chart…......   C-Chart…………  Product Control/Acceptance Sampling-:   Meaning…………..   Definition………….   Risks in Acceptance Sampling-:   Producer’s Risk……….   Consumer’s Risk……….   Types of Sampling Inspection plans-:   Single Sampling plan………   Double Sampling Plan……..   Multiple Sampling Plan…….  Advantages of S.Q.C…………… Limitations of S.Q.C…………….
Acknowledgement-: ,[object Object]
MEANING-: ,[object Object],[object Object]
DEFINATION-: ,[object Object],[object Object],[object Object]
Definition-: ,[object Object],[object Object],[object Object]
CHARACTERISTICS OF S.Q.C.-: ,[object Object],[object Object],[object Object],[object Object]
CAUSES OF VARIATIONS IN QUALITY-: ,[object Object],[object Object]
METHODS OF S.Q.C.-: ,[object Object],[object Object]
Control Chart A  control chart   is a time plot of a statistic, such as a sample mean, range, standard deviation, or proportion, with a center line and  upper and lower   control limits .  The limits give the desired range of values for the statistic.  When the statistic is outside the bounds, or when its time plot reveals certain patterns, the process may be out of control. A process is considered in  statistical control  if it has no assignable causes, only natural variation. UCL LCL Center Line Time Value This point is out of the control limits 3  3 
PURPOSE & USES OF CONTROL CHARTS ,[object Object],[object Object],[object Object],[object Object],[object Object]
Types-: Types of Control Charts Control Charts for Variables    Chart Control Charts for Attributes R-Chart σ -Chart p-Chart np-Chart C-Chart
CONTROL CHATS FOR VARIABLES ,[object Object],[object Object]
EXAMPLE-: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],1 2 3 4 5 Weights Sample  No.
Solution-: 10 14 11 8 14 Σ R=57 14 14 16 16 20 Σ     =80 70 70 80 80 100 ,[object Object],[object Object],[object Object],[object Object],[object Object],1 2 3 4 5 K=5 Range R=(L-S)    =( Σ X/5) Total Weights ( Σ X) Weights (X) Sample no.
Grand   =  Σ  /K = 80/5=16   Grand   Chart  Grand   = 16 (Central line)   Control limits-:  UCL =  Grand + A 2    = 16 + 0.577 x 11.4  = 22.577  LCL  =  Grand -  A 2     = 16 – 0.577 x 11.4   = 9.423  UCL=22.57 CL=16 LCL=9.423 0  1  2  3  4  5  6 25 20 15 10 5 MEAN CHART . . . . . SAMPLE MEANS SAMPLE NOS.
  =  Σ R/K = 57/5 = 11.4 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],UCL=24.09 CL=11.4 LCL=0 0  1  2  3  4  5  6 25 20 15 10 5 RANGE CHART . . . . . SAMPLE RANGE SAMPLE NOS.
[object Object],Example-:  Quality control is maintained in a factory with the help of standard deviation chart. Ten items are chosen in every sample. 18 samples in all were chosen whose  Σ S was 8.28. Determine the three sigma limits of  σ - chart.  You may use the following-:  n = 10, B 3  = 0.28, B 4  = 1.72, K = 18. Solution-:    =  Σ S/K = 8.28/18 = 0.46 UCL = B 4 .   LCL = B 3 .  = 1.72 x 0.46  = 0.28 x 0.46 = 0.7912  = 0.1288
Control Charts for Attributes-: ,[object Object],[object Object]
Example-: Σ d = 60 K = 10 0.05 0.03 0.03 0.06 0.05 0.06 0.08 0.1 0.1 0.04 5 3 3 6 5 6 8 10 10 4 100 100 100 100 100 100 100 100 100 100 1 2 3 4 5 6 7 8 9 10 Fraction defectives (d/n) No. of defectives (d) Size of sample (n) Sample No.
  =  Total no. of defectives/Total no. of units = 60/1000 = 0.06 »q ̅   = 1-    = 1- 0.06 = 0.94     = 0.06 (central line) UCL =   + 3 √  . q ̅ /n   = 0.06 + 3√0.06x0.94/100   = 0.1311 LCL =    - 3   √  . q ̅/n   = 0.06 - 3   √  0.06x0.94/100   = -0.0111 = 0
UCL=0.1311 CL=0.06 LCL=0 0 1 2 3 4 5 6 7 8 9 10 .16 .12 .08 .04 p-CHART . . . . . FRACTION DEFECTIVE SAMPLE NOS. . . . . .
Example-: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
UCL=25.025 CL=14 LCL=2.975 0 1 2 3 4 5 6 7 8 9 10 25 20 15 10 5 np-CHART . . . . . FRACTION DEFECTIVE SAMPLE NOS. . . . . .
[object Object]
USES-: ,[object Object],[object Object],[object Object]
ACCEPTANCE SAMPLING ,[object Object],[object Object]
DEFINATION-: ,[object Object],[object Object],[object Object]
Risks in Acceptance sampling ,[object Object],[object Object]
Types of Sampling Inspection Plan ,[object Object]
Single Sampling Plan Count the no. of defectives,  ‘ d’ in the sample of size ‘n’ Is ‘d’ ≤ ‘c’ If yes, than accept the lot If no, then reject the lot
Double Sampling Plan-: ,[object Object]
Double Sampling Plan-: Count the no. of defectives, d 1 in the first sample of size n 1 Is d 1  ≤ c 1  ? Draw another sample of size n 2 If No, then check  If c 1  ≤ d 1  ≥ c 2  ? Count the no. of defectives d 2  in this sample Is d 1  + d 2  ≤ c 2 If No, reject the lot If yes, accept the lot If yes, then accept the lot.
Multiple Sampling Plan-: ,[object Object]
ADVANTAGES OF S.Q.C.-: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
LIMITATIONS-: ,[object Object],[object Object],[object Object],[object Object]
THE   END

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Ppt On S.Q.C.

  • 1. STATISTICAL QUALITY CONTROL (S.Q.C.) PRESENTED BY-: NIKHIL GARG ROLL NO- 0129626
  • 2.
  • 3. Control chart for attributes-: p-chart………… np-chart…...... C-Chart………… Product Control/Acceptance Sampling-: Meaning………….. Definition…………. Risks in Acceptance Sampling-: Producer’s Risk………. Consumer’s Risk………. Types of Sampling Inspection plans-: Single Sampling plan……… Double Sampling Plan…….. Multiple Sampling Plan……. Advantages of S.Q.C…………… Limitations of S.Q.C…………….
  • 4.
  • 5.
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 11. Control Chart A control chart is a time plot of a statistic, such as a sample mean, range, standard deviation, or proportion, with a center line and upper and lower control limits . The limits give the desired range of values for the statistic. When the statistic is outside the bounds, or when its time plot reveals certain patterns, the process may be out of control. A process is considered in statistical control if it has no assignable causes, only natural variation. UCL LCL Center Line Time Value This point is out of the control limits 3  3 
  • 12.
  • 13. Types-: Types of Control Charts Control Charts for Variables  Chart Control Charts for Attributes R-Chart σ -Chart p-Chart np-Chart C-Chart
  • 14.
  • 15.
  • 16.
  • 17. Grand = Σ  /K = 80/5=16 Grand Chart Grand = 16 (Central line) Control limits-: UCL = Grand + A 2  = 16 + 0.577 x 11.4 = 22.577 LCL = Grand - A 2  = 16 – 0.577 x 11.4 = 9.423 UCL=22.57 CL=16 LCL=9.423 0 1 2 3 4 5 6 25 20 15 10 5 MEAN CHART . . . . . SAMPLE MEANS SAMPLE NOS.
  • 18.
  • 19.
  • 20.
  • 21. Example-: Σ d = 60 K = 10 0.05 0.03 0.03 0.06 0.05 0.06 0.08 0.1 0.1 0.04 5 3 3 6 5 6 8 10 10 4 100 100 100 100 100 100 100 100 100 100 1 2 3 4 5 6 7 8 9 10 Fraction defectives (d/n) No. of defectives (d) Size of sample (n) Sample No.
  • 22.  = Total no. of defectives/Total no. of units = 60/1000 = 0.06 »q ̅ = 1-  = 1- 0.06 = 0.94  = 0.06 (central line) UCL =  + 3 √ . q ̅ /n = 0.06 + 3√0.06x0.94/100 = 0.1311 LCL =  - 3 √ . q ̅/n = 0.06 - 3 √ 0.06x0.94/100 = -0.0111 = 0
  • 23. UCL=0.1311 CL=0.06 LCL=0 0 1 2 3 4 5 6 7 8 9 10 .16 .12 .08 .04 p-CHART . . . . . FRACTION DEFECTIVE SAMPLE NOS. . . . . .
  • 24.
  • 25. UCL=25.025 CL=14 LCL=2.975 0 1 2 3 4 5 6 7 8 9 10 25 20 15 10 5 np-CHART . . . . . FRACTION DEFECTIVE SAMPLE NOS. . . . . .
  • 26.
  • 27.
  • 28.
  • 29.
  • 30.
  • 31.
  • 32. Single Sampling Plan Count the no. of defectives, ‘ d’ in the sample of size ‘n’ Is ‘d’ ≤ ‘c’ If yes, than accept the lot If no, then reject the lot
  • 33.
  • 34. Double Sampling Plan-: Count the no. of defectives, d 1 in the first sample of size n 1 Is d 1 ≤ c 1 ? Draw another sample of size n 2 If No, then check If c 1 ≤ d 1 ≥ c 2 ? Count the no. of defectives d 2 in this sample Is d 1 + d 2 ≤ c 2 If No, reject the lot If yes, accept the lot If yes, then accept the lot.
  • 35.
  • 36.
  • 37.
  • 38. THE END