【正文】 Example: 41 174。 Materials Quality PCS Training Rev 2 Feb 23 2023 SPC Trend Rules Rule 2: 9 consecutive points on the same side of the centerline Uses: Detects small shifts or trends False alarm rate: % Example: UCL CL LCL 39 174。 Materials Quality PCS Training Rev 2 Feb 23 2023 How to Interpret a Control Chart? It is based on the Normal Distribution. 0 . 1 3 5 % 2 . 1 4 5 % 1 3 . 5 9 0 % 3 4 . 1 3 0 % 3 4 . 1 3 0 % 1 3 . 5 9 0 % 2 . 1 4 5 % 0 . 1 3 5 %4 3 2 1 0 1 2 3 46 8 . 2 6 %9 5 . 4 4 %9 9 . 7 3 %37 174。 Materials Quality PCS Training Rev 2 Feb 23 2023 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, use Sigma (Std Dev) Method for control limits putation (Refer to Appendix B) 35 174。 Materials Quality PCS Training Rev 2 Feb 23 2023 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。 Materials Quality PCS Training Rev 2 Feb 23 2023 Exercise 2 The dataset contains defect levels for undissolved flux. The number of units inspected the number of units containing undissolved flux were recorded over several lots. Make a p Chart for Undissolved Flux Interpret the control chart 32 174。 Materials Quality PCS Training Rev 2 Feb 23 2023 Notes : ? The MRMethod describes how the control limits are calculated assuming equal (or nearequal) sample sizes. If the sample sizes vary by more than 50 % of each other, you should consult a statistician. ? np Chart is applicable when all subgroups have constant sample sizes. In terms of practicality, p Chart can/should be used when sample sizes are equal as p carry more meaning than of rejected units (np) Computing Control Limits for p Chart 30 174。CL (p) = p 187。 Materials Quality PCS Training Rev 2 Feb 23 2023 Computing Control Limits for p Chart with MRMethod ? Obtain at least k = 30 subgroups or lots. Data collected in of units inspected of units rejected. ? Compute the defective rate from the ith lot (i =1,2,...,k), pi = of units rejected / of units inspected ? Compute the control limits using: 187。 Materials Quality PCS Training Rev 2 Feb 23 2023 Control Charts For Attributes C on trol C ha rt Sy m bo l D es criptionp C ha rt p % De fectivenp cha rt np de fective27 174。 Materials Quality PCS Training Rev 2 Feb 23 2023 Interpretation of X S Chart Some special causes of outofcontrol for ? X Chart – Changes in machine setting or adjustment – MStoMS technique inconsistent – Changes in material ? S Chart – Machine in need of repair or adjustment – New MSes – Materials are not uniform 25 174。 Materials Quality PCS Training Rev 2 Feb 23 2023 WARNINGS: Group / Summary will sort the new table in alphabetical order of the grouping variable. Control charts must always be plotted in time order. Therefore, if the summary table is not in time order, you will have to sort the table in correct time order before making the control chart. Example of Computing Control Limits for X S Chart using JMP LCL (S) = 0 23 174。 Materials Quality PCS Training Rev 2 Feb 23 2023 Observations Mean Moving Range S. D. Moving Range Subgroup 1 2 3 4 5 (X bar) (MRX ) (S) (MR S ) 1 2 3 : : 30 Average ? X Chart UCL (X) = X + = + () = CL (X) = X = LCL (X) = X = () = Example of Computing Control Limits for X S Chart ? S Chart UCL (S) = S + = + () = CL (S) = S = LCL (S) = S = () = 21 174。CL (S) = S 187。LCL (X) = X = = = Computing Control limits for X R Chart S Chart 187。UCL (X) = X + 187。 Materials Quality PCS Training Rev 2 Feb 23 2023 Computing Control limits for X R Chart ? Compute the Overall Mean, X = (X1 + X2 + X3 ... + Xk) / k ? Compute the Average of Range, S = (S1 + S2 + S3 ... + Sk) / k ? Compute the Average of Moving Range for the mean, MRX = (MRX2 + MRX3 + MRX4 ... + MRXk) / (k 1) ? Compute the Average of Moving Range for the range, MRS = (MRS2 + MRS3 + MRS4 ... + MRSk) / (k 1) = 19 174。 Shows the changes in dispersion or process variability of one sample to another 17 174。 Shows the changes of the mean of one sample to another – S Chart 187。 Materials Quality PCS Training Rev 2 Feb 23 2023 X S Chart Concept Consists of Two Portions: – X Chart 187。 Materials Quality PCS Training Rev 2 Feb 23 2023 Why MR Method is used to determine Control Limits for Mean Variability (Range Standard Deviation) Chart? ? Most batch 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 15 174。 Materials Quality PCS Training Rev 2 Feb 23 2023 Control Chart When to Use (Guidelines only)? XR when subgrouping of samples or (MeanRange) Chart measurements is applicable n 10 X when subgrouping is not applicable (Individual) due to single unit reading may take Chart a long time, unit reading is extremely expensive, etc. when it39。 Materials Quality PCS Training Rev 2 Feb 23 2023 ? Validate the puted control limits against data collected by replotting the control chart with data new control limits – Do the limits dete