【正文】 LCL (X) = X – R Chart 187。 s m on to hav e si ng le me as ure ment s pace d t ime apar t X S w hen s ub grou pin g o f s amples or (Me an S t and ar d me as ure ment s is a pp lic able De vi atio n) Char t n 1 0Control Charts For Variables Note: S Chart can also be used for any subgroup sample size (n) especially for automated SPC system as standard deviation (s) is a better estimator for within lot variation. 10 Traditio nal Shew hart Fo rmulasC on t rol Ch ar t UCL CL LC LX X + A 2 R X X A 2 RXRR D 4 R R D 3 RX X + A 3 S X X A 3 SXSS B 4 S S B 3 SX X + 2 .6 6MR X X 2 .6 6MRXM RMR 3. 26 7MR MR 0Control Limits for Variable Control Charts Notes: 1. Constants A2, A3, D3, D4, B3 B4 are given in Appendix A. 2. The Moving Range (MR) Method is used to determine the control limits for Mean Chart at Intel A/T sites. 11 Why MR Method is used to determine Control Limits for Mean Chart? ? Most Intel A/T production processes have a larger runtorun variation than withinrun variation ? Traditional control chart formulas developed in the 20’s by Walter Shewhart considerably underestimate control limits, . too narrow 12 Traditional vs. MR Method Traditional control chart formulas are used. Moving Range (MR) Method is used. Xbar Control Chart Xbar Control Chart 13 Caution When Using MR Method ? If there is autocorrelation, MR(Summary Stat) will underestimate the true process variation the control limits will be too narrow ? If autocorrelation is evident, see your site statistician for better control limits putation method ? Methods for calculating control limits: – Std Dev Method – Moving Range (MR) Method – Percentile Method (Normal Probability Plot) – Traditional Shewhart Method 14 Ti m eDataC o ns e c u t iv e l ot sa re v e ry s imi l a rLo t s far a par t ma ybe v e ry dif f e re nt? Timerelated condition where consecutive data values are correlated (. dependent) ? Data values collected nearby in time are very similar ? Data values collected far apart in time may be very different ? Tend to drift over time。 Shows the changes in dispersion or process variability of one sample to another 16 Computing Control Limits for X R Chart ? Obtain at least k = 30 subgroups with n = 3, 4 or 5 on a data sheet ? Compute the Mean for each subgroup, X= (X1 + X2+ X3 ... + Xn) / n ? Compute the Range for each subgroup, R = Xmax Xmin ? Compute the Moving Range for each subgroup, MRi = | Xi Xi1 | 17 Computing Control limits for X R Chart ? Compute the Overall Mean, X = (X1 + X2 + X3 ... + Xk) / k ? Compute the Average of Range, R = (R1 + R2 + R3 ... + Rk) / k ? Compute the Average of Moving Range, MR = (MR2 + MR3 + MR4 ... + MRk) / (k 1) = 18 ? Compute the Control Limits: ? Constant D3 D4 are given in Appendix A ? Draw the control limits on both the X R chart respectively – X Chart 187。LCL (R) = D3R = = = Computing Control limits for X R Chart 19 ? X Chart UCL (X) = X + = + () = CL (X) = X = LCL (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