【正文】 CL (X) = X = () = ? R Chart UCL (R) = D4R = () = CL (R) = R = LCL (R) = D3R = 0 Example of Computing Control Limits for X R Chart n = 5, D3 = 0, D4 = O bser va t ion s Me an Movi ng Ra ng e RangeS ub grou p 1 2 3 4 5 ( X b ar ) ( MR ) ( R)1 8. 0 7. 7 8. 1 8. 0 7. 8 7. 92 0. 402 7. 1 6. 9 7. 4 7. 3 7. 2 7. 18 0. 74 0. 503 8. 0 7. 5 7. 6 7. 8 7. 9 7. 76 0. 58 0. 50::30 7. 5 7. 8 7. 9 7. 8 7. 6 7. 72 0. 70 0. 40Ave r age 7. 64 0. 68 0. 5520 1) Calculate the control limits for X R chart based on data collected from . 2) Plot the control limits on the charts monitor for and . Exercise O b ser v at i o n s M ea n M o v i n g R an g e R an g eW W / D ay S h i f t 1 2 3 4 5 ( X b ar) ( M R ) ( R )3 5 . 1 A 1 0 1 . 3 1 0 0 . 7 1 0 2 . 3 9 9 . 5 1 0 0 . 5 1 0 0 . 9 2 . 83 5 . 1 B 1 0 6 . 9 1 0 2 . 7 1 0 6 . 9 1 0 2 . 9 1 0 3 . 2 1 0 4 . 5 3 . 7 4 . 23 5 . 2 C 9 2 . 9 9 4 . 8 9 4 . 6 9 1 . 9 9 4 . 8 9 3 . 8 1 0 . 7 2 . 93 5 . 2 D 9 3 . 8 9 2 . 3 9 1 . 7 8 9 . 7 9 3 . 5 9 2 . 2 1 . 6 4 . 03 5 . 3 A 1 1 5 . 5 1 0 6 . 8 1 0 9 . 4 1 1 1 . 3 1 1 3 . 4 1 1 1 . 3 1 9 . 1 8 . 73 5 . 3 B 9 8 . 3 1 0 0 . 8 9 6 . 9 9 9 . 9 9 9 . 9 9 9 . 1 1 2 . 1 4 . 03 5 . 4 C 1 0 4 . 9 1 0 2 . 9 1 0 4 . 4 1 0 3 . 1 1 0 6 . 3 1 0 4 . 3 5 . 2 3 . 43 5 . 4 D 9 2 . 9 9 3 . 2 9 2 . 4 9 1 . 9 9 0 . 6 9 2 . 2 1 2 . 1 2 . 63 5 . 5 A 9 6 . 1 9 7 . 3 9 9 . 5 9 8 . 6 1 0 1 . 1 9 8 . 5 6 . 3 5 . 13 5 . 5 B 1 0 2 . 5 1 0 6 . 4 1 0 8 . 4 1 0 5 . 9 1 0 1 . 9 1 0 5 . 0 6 . 5 6 . 53 5 . 6 C 8 9 . 3 9 0 . 0 8 8 . 9 9 0 . 3 8 7 . 2 8 9 . 1 1 5 . 9 3 . 03 5 . 6 D 1 0 6 . 2 1 0 6 . 2 1 0 6 . 8 1 0 5 . 7 1 0 2 . 6 1 0 5 . 5 1 6 . 4 4 . 23 5 . 7 A 9 0 . 4 9 0 . 5 9 1 . 2 9 1 . 0 8 7 . 2 9 0 . 1 1 5 . 4 4 . 03 5 . 7 B 1 0 2 . 8 1 0 2 . 1 1 0 1 . 6 1 0 2 . 8 1 0 6 . 5 1 0 3 . 2 1 3 . 1 4 . 93 6 . 1 C 9 8 . 4 1 0 2 . 1 9 9 . 5 9 8 . 8 1 0 0 . 3 9 9 . 8 3 . 3 3 . 73 6 . 1 D 9 7 . 1 9 7 . 7 1 0 0 . 2 9 5 . 5 9 7 . 6 9 7 . 6 2 . 2 4 . 73 6 . 2 A 9 1 . 2 9 3 . 3 9 3 . 2 9 7 . 7 9 4 . 2 9 3 . 9 3 . 7 6 . 53 6 . 2 B 9 9 . 0 9 8 . 2 9 7 . 4 9 8 . 4 9 8 . 4 9 8 . 3 4 . 4 1 . 63 6 . 3 C 1 0 3 . 3 9 8 . 5 1 0 5 . 5 1 0 1 . 6 1 0 5 . 4 1 0 2 . 9 4 . 6 7 . 13 6 . 3 D 9 8 . 6 9 7 . 5 9 5 . 5 9 7 . 0 9 6 . 5 9 7 . 0 5 . 9 3 . 13 6 . 4 A 9 7 . 0 1 0 2 . 9 9 3 . 8 9 5 . 8 9 7 . 5 9 7 . 4 0 . 4 9 . 13 6 . 4 B 1 1 0 . 6 1 1 1 . 3 1 0 9 . 6 1 0 9 . 2 1 1 0 . 2 1 1 0 . 2 1 2 . 8 2 . 23 6 . 5 C 1 0 7 . 3 1 0 6 . 0 1 0 6 . 7 1 0 9 . 0 1 1 0 . 4 1 0 7 . 9 2 . 3 4 . 53 6 . 5 D 8 7 . 3 8 9 . 7 9 2 . 3 8 5 . 7 8 9 . 1 8 8 . 8 1 9 . 1 6 . 63 6 . 6 A 9 4 . 3 9 4 . 3 9 1 . 1 9 3 . 9 9 6 . 7 9 4 . 1 5 . 2 5 . 63 6 . 6 B 1 0 1 . 6 9 3 . 3 9 9 . 5 1 0 3 . 2 9 8 . 8 9 9 . 3 5 . 2 9 . 93 6 . 7 C 9 9 . 4 9 5 . 2 9 6 . 3 9 5 . 6 9 9 . 9 9 7 . 3 2 . 0 4 . 63 6 . 7 D 1 0 4 . 0 1 0 5 . 5 1 0 1 . 5 1 0 2 . 0 1 0 4 . 2 1 0 3 . 4 6 . 2 4 . 03 7 . 1 A 9 8 . 1 9 8 . 0 9 5 . 2 9 8 . 9 9 8 . 5 9 7 . 7 5 . 7 3 . 73 7 . 1 B 9 4 . 7 9 5 . 7 9 9 . 7 9 8 . 0 9 5 . 1 9 6 . 7 1 . 1 4 . 9A v erag e 9 9 . 1 7 . 7 4 . 7O n l i n e mo n i t o r i n g3 7 . 2 C 1 0 2 . 5 1 0 7 . 5 1 0 5 . 0 1 0 4 . 0 1 0 6 . 03 7 . 2 D 1 1 0 . 0 1 0 8 . 0 1 1 2 . 0 1 1 5 . 0 1 1 0 . 03 7 . 3 A 1 0 5 . 5 9 5 . 5 9 8 . 0 1 0 0 . 5 1 0 0 . 53 7 . 3 B 1 2 0 . 0 1 2 5 . 0 1 3 5 . 0 1 3 0 . 0 1 1 5 . 0 Interpretation of X R Chart Some special causes of outofcontrol for ? X Chart – Changes in machine setting or adjustment – MStoMS technique inconsistent – Changes in material ? R Chart – Machine in need of repair or adjustment – New MSes – Materials are not uniform 22 Attributes Control Charts ? Attribute control charts are useful when it is difficult or impractical to monitor a process numerically (on a continuous scale) ? A defect is an individual failure to meet a single requirement ? A defective unit is a unit that contains one or more defects 23 Control Charts For Attributes C o n t ro l C h a rt Sym b o l D e s cri p t i o n Sa m p l e Si zep C h a rt p Pro p o rt i o n o f D e f e ct i v e sMa y Be U n e q u a ln p C h a rt np o f D e f e ct i v e sMu s t Be Eq u a lc C h a rt c o f D e f e ct sMu s t Be Eq u a lu C h a rt u D e f e ct s Pe r U n i t sMa y Be U n e q u a lC u m u l a t i v e C o u n t CCCC u m u l a t i v e G o o d U n i t s U n t i l T h e N e x t R e j e ct 24 Control Limits for Attribute Control Charts C on v e nt i on a l Fo r m ul a sC on t r ol C ha r t UCL CL LC LpnpcuCCC*p p p n? ?3 1( ) p p p p n? ?3 1( ) n pn p n p p? ?3 1( ) n p n p p? ?3 1( )c c? 3 c c c? 3uu u n? 3 u u n? 3 3 00. p 0 70. p 0 . 0 5 pNotes: 1. * The formulas are based on a = . 25 ? The 3 Standard Deviation Method is highly remended in HVM environment for p, np, c or u Chart. To be discussed later. ? Methods based on the Binomial or Poisson distribution are also used depending on the application. Consult yo