Integrated Process Capability Analysis Model (IPCAM) for a Product with Multiple Quality Characteristics 報告人 : 游崑慈

1.Supply chain management 2.Process capability indices 3.Taguchi loss function 4.Process yield & Six-sigma 5.IPCAM 6.Future applications Outlines

Supply chain management Manufacturing Distribution Supplier INFORMATION FLOW Retail OutletConsumer CASH FLOW Transfer

LSL USL Process distribution m d LSL USL Process distribution m d 製造業通常透過統計製程管制 (SPC) 來監控與改善產品品質，使製程變異降 低進而達到穩定狀態，當製程穩定後，品管工程師想進一步了解產品符合規 格的能力，或出現不良品的比率有多少？

Nominal-the-best Process Capability Index 製程能力指標 (PCI) 便是用來衡量製程符合規格的能力，與結合製 程參數與製程規格 (LSL ， T ， USL) 的函數，能夠表示製程中心偏移 與製程變異程度，因此常被用來評估供應商是否有能力製作出符合 產品規格的一種量數，並作為購買契約上買賣雙方對品質要求的依 據以及工廠內部持續改善品質的參考。 LSL USL Process distribution m d T Yield%  2Φ(3C pm ) - 1

Taguchi loss function LSL USL T U.S.A Japan Loss function

Smaller-the-better Process Capability Index C pu = Quality characteristics : roughness, noise, waiting time, thickness. Yield% =  (3 C pu )  2  (3 C pu ) - 1 μBμB

Larger -the-better Process Capability Index C pl = Quality characteristics : Life-span 、 hardness 、 pulling force 、 resolution. Yield% =  (3C pl ) 2  (3C pl ) – 1

Process Yield %Yield = 2Φ(3C pu ) – 1 %Yield = 2Φ(3C pl ) – 1 %Yield  2Φ(3C pm ) - 1 PCI ↗  process yield ↗ process loss ↘

假設品質特性符合 Normal distribution T=100U=112L=88 若 則稱此製程具有 6-sigma quality level 。 Six Sigma

Six-sigma process concept Normal distribution centered Spec. Limit Percent Defective PPM % 8

Integrated Process Capability Analysis Model (IPCAM)

Estimations One -side capability indices (UMVUE) i  {u, l } is distributed as, where

C pl : represent axes X (larger-the-better) C pu : represent axes Y (smaller-the-better) C pm : represent XY plane (nominal-the-best)

Two-side capability index Estimations It is a more complicated distribution, we often used the mathematical software to do numerical Analysis.

Hypothesis test for one-side quality specification where i  {u, l}. The critical regions are C S = { |  S 0 } and the critical value S 0 is determined by Pr (  s 0 | C pi  ) = H 0 : C pi  H 1 : C pi .

Hypothesis test for two-side quality specification H 0 : C pm  H 1 : C pm  Pr (  m 0 | C pm  ) =

IPCAM (sampling inspection)

Item  LSLTUSL S 0 m 0 A B C D E F G H I

S 0 =1.899 m 0 =1.911

Future Applications Technical education quality management model Medical service quality control Human resources management