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NOKIA 2020 Confidence of Cpk ? Cpk values are not definite numbers as they are based on relatively small samples of a population. ? The 95% confidence interval determines the interval which includes the true Cpk value with a probability of 95%, . there is a probability of 5% that Cpk is either lower or higher than this confidence interval. 95% confidence interval Actual cpk Cpk upper confidence limit Cpk lower confidence limit 54 169。 NOKIA 2020 Graphical Presentation: Xbar and RChart XBar Chart RChart 50 169。 NOKIA 2020 Example of how to Collect Data 1. Run in and stabilise process 2. Note the main parameters for reference 3. When the process is stable run the tool for 10 hours 3. Take 5 parts out from each cavity every half hour and mark them with time, date and cavity. Total 20 sets of 5 parts from each cavity must be made, or according to agreement. 4. After the last sample lot note the main process parameters for reference 5. Measure and record the main functional characteristics (white diamonds) 6. Fill data into the NMP data collection spreadsheet 7. Analyse! Time Dimension Subgroup size n = 5 Number of subgroups N = 20 0,5 hours between samples taken Note: For clarity, only 6 subgroups are shown 46 169。 NOKIA 2020 Estimate Cp and Cpk? B) LSL USL B) Nominal Mean USL LSL 6*s USL Mean Mean LSL 3*s 42 169。 NOKIA 2020 Exercise 2: Cp and Cpk ? Calculate Cp and Cpk for the 100 measurements in the file Data exercise ? Determine the approximate Cp and Cpk for the 4 sample populations on the following page ? Should actions be made to improve these processes. If yes, which? 39 169。 NOKIA 2020 What Do These Indexes Tell Us ?? ?If Cp = Cpk, ?If Pp = Ppk, ?If Cpk Cp, ?If Ppk Pp, ?If Cp = Pp, ?If Cpk = Ppk, ?If Pp Cp, ?If Ppk Cpk, … then process is affected by special causes. Investigate Xbar/Rchart for outofcontrol conditions. SPC may be effective … then process is not affected by special causes during the study run. SPC would not be effective in this case … then process perfectly centred … then process not centred (check process mean against design nominal) 36 169。 NOKIA 2020 What Do These Indexes Tell Us ?? ? Simple numerical values to describe the quality of the process The higher the number the better ?Requirement for Cp and Cpk is min. ?Remendation for Pp and Ppk is min. ? This leaves us some space for the variation, . a safety margin ? Are we able to improve our process by using SPC? ? If index is low, following things should be given a thought: ? Is the product design OK? ? Are tolerance limits set correctly? ? Too tight? ? Is the process capable of producing good quality products? Process variation? DOE required? ? Is the measuring system capable? (See Gage Ramp。 NOKIA 2020 Section 3. Cp and Cpk Concept 29 169。 NOKIA 2020 The Difference Between SST and sLT !! mean Time Dimension Short term Standard Deviation Long term Standard Deviation Subgroup size n = 5 Number of subgroups N = 7 Subgroup No. 1 25 169。 NOKIA 2020 ? sST often notated as ??or sigma, is another measure of dispersion or variability and stands for “shortterm standard deviation”, which measures the variability of a process or system using “rational” subgrouping. s R N d R dST jjN????? ???? ???12 2* *where is the range of subgroup j, N the number of subgroups, and d2* depends on the number N of subgroups and the size n of a subgroup (see next slide) R X Xj j j? ?m a x m i nWhat Measurements Can Be Used to Describe Process variation? 22 169。 NOKIA 2020 What Measurements Can Be Used to Describe a Process or System ? x x x xN N? ? ? ?1 2 . . .Example: x1 = 5 x2 = 7 x3 = 4 x4 = 2 x5 = 6 62475 ???????x? mean (average) or describes the location of the distribution x? 181。 NOKIA 2020