【正文】 as reviewed. Example 4 Stat ? Quality Tools ? Capability Analysis (Weibull) Example 4 2 52 01 51 050U S LP r o c e s s C a p a b i l i t y f o r C o m p l a i n t C l o s u r eC a l c u l a t i o n s B a s e d o n E x p o n e n t i a l D i s t r i b u t i o n M o d e lP P M T o t a lP P M U S LP P M L S LP P M T o t a lP P M U S LP P M L S LP p kP P LP P UP pS c a l eS h a p eS a m p l e NM e a nL S LT a r g e tU S L1 2 2 9 7 0 . 8 01 2 2 9 7 0 . 8 0 * 7 5 0 0 0 . 0 0 7 5 0 0 0 . 0 0 *0 . 3 9 *0 . 3 9 *3 . 3 41 . 0 04 0 03 . 3 4 * *7 . 0 0E x p e c t e d L T P e r f o r m a n c eO b s e r v e d L T P e r f o r m a n c eO v e r a l l ( L T ) C a p a b i l i t yP r o c e s s D a t aExample 4A Stat ? Quality Tools ? Capability Sixpack (Weibull) Example 4A 4 0 03 0 02 0 01 0 002 41 680I n d i v i d u a l a n d M R C h a r tO b s e r .Individual ValueM e a n = 3 . 3 4U C L = 1 0 . 4 6L C L = 3 . 7 7 92 41 680Mov.RangeR = 2 . 6 7 7U C L = 8 . 7 4 6L C L = 04 0 03 9 03 8 0L a s t 2 5 O b s e r v a t i o n s9630O b s e r v a t i o n N u m b e rValues7O v e r a l l ( L T )S h a p e : 1 . 0 0S c a l e : 3 . 3 4P p : *P p k : 0 . 3 9C a p a b i l i t y P l o tP r o c e s s T o l e r a n c eS p e c i f i c a t i o n sIIII1 0 . 0 01 . 0 00 . 1 00 . 0 1W e i b u l l P r o b P l o t2 01 00C a p a b i l i t y H i s t o g r a mP r o c e s s C a p a b i l i t y f o r C o m p l a i n t C l o s u r eProcess Capability for Reject Rate For a Normal Distribution, the proportion of parts produced beyond a specification limit is ? ? ?)Z(F1USLZPr1USLZPrUSLXPr???????????????????????????Reject Rate Process Capability for Reject Rate Thus, for every reject rate there is an acpanying ZScore, where Recall that Hence ????3NSLPpk ????? LimitSpecScoreZ3ScoreZpk?Process Capability for Reject Rate Estimation of Ppk for Reject Rate ? Determine the longterm reject rate (p) ? Determine the inverse cumulative probability for p, using Calc ? Probability Distribution ? Normal ? ZScore is the magnitude of the returned value ? Ppk is onethird of the ZScore Example 5 A sales manager plans to assess the process capability of his telephone sales department’s handling of ining calls. The following data was collected over a period of 20 days: ? number of ining calls per day ? number of unanswered calls per days Example 5 Stat ? Quality Tools ? Capability Analysis (Binomial) Example 5 2 01 000 . 2 60 . 2 50 . 2 40 . 2 30 . 2 20 . 2 10 . 2 00 . 1 9S a m p l e N u m b e rProportionP = 0 . 2 2 6 4U C L = 0 . 2 5 5 5L C L = 0 . 1 9 7 32 01 02 3 . 52 2 . 52 1 . 5S a m p l e N u m b e r%Defective2 62 42 22 02 0 5 01 9 5 01 8 5 02 62 52 42 32 22 12 0%DefectiveS a m p l e S i z eP r o c e s s C a p a b i l i t y f o r T e l e p h o n e S a l e sS u m m a r y S t a t sC u m u l a t i v e % D e f e c t i v e D i s t o f % D e f e c t i v eP C h a r t R a t e o f D e f e c t i v e s( d e n o t e s 9 5 % C . I . )A v e r a g e P :% D e f e c t i v e :T a r g e t :P P M D e f . :P r o c e s s Z :0 . 2 2 6 4 2 72 2 . 6 4 302 2 6 4 2 70 . 7 5 1( 0 . 2 2 2 2 , 0 . 2 3 0 7 )( 2 2 . 2 2 , 2 3 . 0 7 )( 2 2 2 2 4 1 , 2 3 0 6 5 4 )( 0 . 7 3 7 , 0 . 7 6 5 )Ppk = Process Capability for Defect Rate Other applications, approximating a Poisson Distribution : ? error rates ? particle count ? chemical concentration Process Capability for Defect Rate Estimation of Ytp for Defect Rate ? Define size of an inspection unit ? Determine the longterm defects per unit (DPU) DPU = Total Defects ? Total Units ? Determine the throughput yield (Ytp) Ytp = exp{–DPU} Process Capability for Defect Rate Estimation of SigmaCapability for Defect Rate ? Determine the opportunities per unit ? Determine the longterm defects per opportunity (d) d = defects per unit ? opportunities per unit ? Determine the inverse cumulative probability for d, using Calc ? Probability Distribution ? Normal ? ZScore is the magnitude of the returned value ? SigmaCapability = ZScore + Example 6 The process manager for a wire manufacturer is concerned about the effectiveness of the wire insulation process. Random lengths of electrical wiring are taken and tested for weak spots in their insulation by means of a test voltage. The number of weak spots and the length of each piece of wire are recorded. Example 6 Stat ? Quality Tools ? Capability Analysis (Poisson) Example 6 1 0 09 08 07 06 05 04 03 02 01 000 . 0 80 . 0 70 . 0 60 . 0 50 . 0 40 . 0 30 . 0 20 . 0 10 . 0 0S a m p l e N u m b e rSample CountU = 0 . 0 2 6 5 2U C L = 0 . 0 6 9 0 4L C L = 01 0 09 08 07 06 0