, ,85 0, , ,50 0, , ,17 0, ,65. col1 = id (1, 2,, 662) row id ,41
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1 1 Source : From: Bernard Clément, PhD, Montréal, CANADA genistat@sympatico.ca or bernard.clement@polymtl.ca DATA: MY-PROJECT-WORK.xlsx has been reorganized. The new EXCEL file is MY_PROJECT-WORK-reorganized.xlsx and is available form Bernard Clément. Partial view of MY_PROJECT-WORK-reorganized.xlsx 1 id 2 group 3 X 4 error 5 new 6 sub group 7 N Xbar 9 S , ,49 0, , ,4 0, , ,41 0, , ,49 0, , ,77 0, , ,71 0, , ,71 0, , ,47 0, , ,72 1, , ,64 0, , ,5 0, , ,97 0, , ,57 0, , ,46 0, , ,44 0, , ,34 0, , ,31 0, , ,46 0, , ,5 0, , ,50 0, , ,17 0, , ,54 original data was reorganized as: 662 obs. (rows) ,41 col1 = id (1, 2,, 662) row id ,41 col2 = group (1, 2,, 74) group id... col3 = X (measurements) 651 col4 = error case id=530 group=5 X=2, ,36 col5 = new empty column , summary statistics ,44 col6 = subgroup ,44 col7 = N (sample size) ,02 col = Xbar (mean of subgroup) 656 col9 = S (standard deviation of subgroup) 74 21, , , , , , ,31
2 2 COMMENTS Histogram of sample sizes N = 3 to Histogram of N 10 No of obs Pareto chart of sample sizes N N 12 Pareto chart of sample sizes 10 No of obs N An observation (X=2,21) was a typo error; it is not used in the forthcoming computations. Two subgroups (56, 57) are identical and we think suspicious but they are used in the computations. Given the data structure, the control chart chosen is an Xbar &S chart with varying sample sizes. The data collecting strategy is unusual with large varying sampling sizes; It need to be revised in the future. Control charts do not make sense without a knowledge of the context; A time life information about the collecting process should have been included; this is a missed opportunity. Xbar & S control chart with varying sample sizes were produced with STATISTICA, NCSS and JMP. Xbar & S control chart with varying sample sizes is not available with MINITAB. Control charts are presented in the following pages with identification of out of control cases.
3 3 Solution with STATISTICA: Xbar & S control chart Histogram of Means 22,5 22,0 21,5 21,0 20,5 X-bar and S Chart; variable: X X-bar: 21,026 (21,026); Sigma: 0,67959 (0,67959); n:, ,671 21,026 20,32 20,0 19, Histogram of Std.Devs 2,2 2,0 1, 1,6 1,4 1,2 1,0 0, 0,6 0,4 0,2 0,0-0, Std.Dv.: 0,6556 (0,6556); Sigma: 0,16456 (0,16775); n:,9324 1,1345 0, ,
4 4 Sub group in color: out of control case for Xbar and/or S (in red) sub group N Xbar S Center Xbar LCL Xbar UCL Xbar Center S ,4 0,570 21,026 20,517 21,536 0,66 0,299 1, ,40 0,760 21,026 20,347 21,706 0,659 0,15 1, ,410 0,52 21,026 20,43 21,615 0,664 0,235 1, ,492 0,505 21,026 20,532 21,521 0,669 0,312 1, ,771 0,542 21,026 20,559 21,494 0,670 0,333 1, ,714 0,636 21,026 20,559 21,494 0,670 0,333 1, ,714 0,636 21,026 20,559 21,494 0,670 0,333 1, ,470 0,33 21,026 20,592 21,461 0,672 0,359 0, ,723 1,570 21,026 20,007 22,046 0,626 0,000 1, ,643 0,235 21,026 20,256 21,797 0,652 0,077 1, ,53 0,659 21,026 19,49 22,203 0,602 0,000 1, ,967 0,714 21,026 20,43 21,615 0,664 0,235 1, ,567 0,440 21,026 20,194 21,59 0,647 0,020 1, ,456 0,570 21,026 20,517 21,536 0,66 0,299 1, ,43 0,625 21,026 20,559 21,494 0,670 0,333 1, ,335 0,591 21,026 20,32 21,671 0,661 0,1 1, ,309 0,642 21,026 20,461 21,592 0,666 0,254 1, ,462 0,69 21,026 20,461 21,592 0,666 0,254 1, ,592 0,659 21,026 20,500 21,553 0,66 0,26 1, ,375 0,531 21,026 20,412 21,641 0,663 0,213 1, ,167 0,653 21,026 20,43 21,615 0,664 0,235 1, ,471 0,645 21,026 20,43 21,615 0,664 0,235 1, ,411 0,756 21,026 20,412 21,641 0,663 0,213 1, ,411 0,907 21,026 20,517 21,536 0,66 0,299 1, ,643 0,774 21,026 20,256 21,797 0,652 0,077 1, ,972 0,722 21,026 20,461 21,592 0,666 0,254 1, ,972 0,592 21,026 20,347 21,706 0,659 0,15 1, ,614 0,373 21,026 20,256 21,797 0,652 0,077 1, ,92 0,35 21,026 20,115 21,93 0,639 0,000 1, ,701 0,51 21,026 20,306 21,747 0,656 0,121 1, ,27 1,36 21,026 19,49 22,203 0,602 0,000 1, ,733 0,53 21,026 20,007 22,046 0,626 0,000 1, ,562 1,754 21,026 20,194 21,59 0,647 0,020 1, ,593 0,276 21,026 20,256 21,797 0,652 0,077 1, ,643 0,235 21,026 20,256 21,797 0,652 0,077 1, ,913 1,947 21,026 19,49 22,203 0,602 0,000 1, ,593 0,276 21,026 20,256 21,797 0,652 0,077 1, ,766 0,652 21,026 20,32 21,671 0,661 0,1 1, ,452 1,073 21,026 20,194 21,59 0,647 0,020 1, ,0 0,675 21,026 20,115 21,93 0,639 0,000 1, ,567 0,440 21,026 20,194 21,59 0,647 0,020 1, ,22 0,03 21,026 20,194 21,59 0,647 0,020 1, ,992 0,641 21,026 20,115 21,93 0,639 0,000 1, ,30 0,49 21,026 20,194 21,59 0,647 0,020 1, ,026 0,493 21,026 20,115 21,93 0,639 0,000 1, ,020 0,615 21,026 20,256 21,797 0,652 0,077 1, ,725 0,455 21,026 20,194 21,59 0,647 0,020 1, ,171 0,61 21,026 20,32 21,671 0,661 0,1 1, ,97 0,45 21,026 19,49 22,203 0,602 0,000 1, ,495 0,534 21,026 20,461 21,592 0,666 0,254 1, ,734 0,536 21,026 20,256 21,797 0,652 0,077 1, ,729 0,476 21,026 20,347 21,706 0,659 0,15 1, ,533 0,409 21,026 20,007 22,046 0,626 0,000 1, ,92 0,35 21,026 20,115 21,93 0,639 0,000 1,334 LCL S UCL S
5 ,63 0,652 21,026 19,49 22,203 0,602 0,000 1, ,340 0,20 21,026 20,115 21,93 0,639 0,000 1, ,340 0,20 21,026 20,115 21,93 0,639 0,000 1, ,754 0,505 21,026 20,115 21,93 0,639 0,000 1, ,026 0,493 21,026 20,115 21,93 0,639 0,000 1, ,171 0,61 21,026 20,32 21,671 0,661 0,1 1, ,63 0,652 21,026 19,49 22,203 0,602 0,000 1, ,542 0,557 21,026 20,43 21,615 0,664 0,235 1, ,734 0,536 21,026 20,256 21,797 0,652 0,077 1, ,994 0,367 21,026 20,115 21,93 0,639 0,000 1, ,642 0,475 21,026 20,194 21,59 0,647 0,020 1, ,97 0,45 21,026 19,49 22,203 0,602 0,000 1, ,171 0,61 21,026 20,32 21,671 0,661 0,1 1, ,375 0,531 21,026 20,412 21,641 0,663 0,213 1, ,375 0,531 21,026 20,412 21,641 0,663 0,213 1, ,01 0,755 21,026 20,461 21,592 0,666 0,254 1, ,614 0,373 21,026 20,256 21,797 0,652 0,077 1, ,52 0,539 21,026 20,115 21,93 0,639 0,000 1, ,501 0,553 21,026 20,461 21,592 0,666 0,254 1, ,171 0,61 21,026 20,32 21,671 0,661 0,1 1,134 Zones A/B/C: 3,000/2,000/1,000 * Sigma Tests for special causes (runs rules) (Western rules) X ; Runs Tests X-bar Chart Center line: 21,026 Sigma: 0,227 from sample to sample 9 samples on same side of center samples in row in/decreasing OK OK 14 samples alternating up & down OK OK 2 of 3 samples in Zone A or beyond of 5 samples in Zone B or beyond samples in Zone C OK OK samples beyond Zone C
6 Solution with NCSS: Xbar & S control chart 6 X-bar and s Charts Report Variables X Center Line Section for All Subgroups Number of Subgroups 74 Center Line Estimate Estimated Grand Average (X-bar-bar) 21,02634 s-bar 0, Primary Control Limit Section for All Subgroups These limits are based on a subgroup of size 22. Primary Control Limits Chart Type Lower Upper X-bar 20,602 21,4444 s 0, , Sigma Estimation Section for All Subgroups Estimation Estimated Estimated Type Value Sigma Ranges (R-bar) 1, , Standard Deviations (s-bar)* 0, , Weighted Approach (s-bar) 0, ,65346 * Indicates the estimation type used in this report. X-bar and s Charts Report Chart Section for All Subgroups Sample Mean (X-bar) Chart 22, ,6 21,65 21,0 21, ,4 20,41 19, Subgroup
7 7 X-bar and s Charts Report Sample Standard Deviation (s) Chart 36 2, ,5 1,10 1,0 0,65 0,5 0,19 0, Subgroup X-bar and s Charts Report: Out-of-Control List for Subgroups 1 to 74 Subgroup Reason Subgroup Mean s Label beyond limits or Western rules 2 21,4 0, X-bar: 2 of 3 in zone A 3 21,41 0, X-bar: 2 of 3 in zone A 4 20, , X-bar: beyond control limits 6 20, , X-bar: 2 of 3 in zone A 7 20, , X-bar: 2 of 3 in zone A 20, , X-bar: beyond control limits 20, , s: beyond control limits 9 21,7225 1, s: beyond control limits 10 20,6426 0, X-bar: 4 of 5 in zone B or beyond 10 20,6426 0, s: beyond control limits 15 21,4342 0, X-bar: 2 of 3 in zone A 17 21, , X-bar: 4 of 5 in zone B or beyond 1 21, , X-bar: 4 of 5 in zone B or beyond 19 21,592 0, X-bar: beyond control limits 20 21, , X-bar: 2 of 3 in zone A 21 21, , X-bar: 4 of 5 in zone B or beyond 22 21,4703 0, X-bar: 4 of 5 in zone B or beyond 23 21, , X-bar: 4 of 5 in zone B or beyond 24 21, , X-bar: 2 of 3 in zone A 25 21,6426 0, X-bar: 4 of 5 in zone B or beyond 26 20, , X-bar: 2 of 3 in zone A 29 20,92 0, s: 2 of 3 in zone A 30 20, , s: 2 of 3 in zone A 31 21,2667 1, s: beyond control limits 33 21, , X-bar: 2 of 3 in zone A 33 21, , s: beyond control limits 34 20,5926 0, s: beyond control limits 35 20,6426 0, s: beyond control limits 36 21, , s: beyond control limits 37 20,5926 0, X-bar: with none in zone C 37 20,5926 0, s: beyond control limits 3 20,766 0, X-bar: 4 of 5 in zone B or beyond 39 21, , s: beyond control limits 53 20,5325 0, s: 4 of 5 in zone B or beyond 54 20,92 0, s: 2 of 3 in zone A 55 20,6333 0, s: 2 of 3 in zone A 72 20,52 0, s: 4 of 5 in zone B or beyond 73 20, , X-bar: 2 of 3 in zone A
8 Solution with JMP : Xbar & S control chart Carte de contrôle des variables X-bar de X group S écart-type de X 2,0 1,5 1,0 0,5 0,0 group
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