tailieunhanh - A textbook of Computer Based Numerical and Statiscal Techniques part 50

A textbook of Computer Based Numerical and Statiscal Techniques part 50. By joining statistical analysis with computer-based numerical methods, this book bridges the gap between theory and practice with software-based examples, flow charts, and applications. Designed for engineering students as well as practicing engineers and scientists, the book has numerous examples with in-text solutions. | 476 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Sol. Mean Chart Mean of 10 sample mean X XL 442 10 10 Mean Range of 10 sample ranges R X R 58 10 10 As we have for n 5 A2 D3 0 D4 3-c control limits for x chart are UCL- X A2 R x 2 x LCL- X - AR x2 - x CLx X Range Chart 3-0 Control Limits for R chart are UCLr D4 R LCLr D3 R 0 x 0 CLr R FIG. From mean chart we see that 2nd 3rd 6th and 7th samples lies outside the control limits. Hence the process is out of control. This shows that some assignable causes of variation are operating which should be detected and removed. STATISTICAL QUALITY CONTROL 477 FIG. Since all the points with in the control limits. Hence the process is in statistical control. Example 2. The following are the mean lengths and ranges of lengths of a finished product from 10 samples each of size 5. The specification limits for length are 200 5 cm. Construct x and R-chart and examine whether the process is under control and state your recommendation. Sample No. 1 2 3 4 5 6 7 8 9 10 x 201 198 202 200 203 204 199 196 199 201 R 5 0 7 3 4 7 2 8 5 6 Assume for n 5 A2 D3 0 D4 . Sol. In given problem specification limits for length are given 200 5 cm. Hence standard deviation is unknown. 1 Control Limits for x-chart are Central limit CLx p 200 UCLx p A2 R 200 X R 47 R - LCLx p-A2 R 200 - x R 2 Control limits for R-Chart are UCLr D4 R x CLr R LCLr 0 D3 R 0 x from control charts for mean and range the process is in statistical control in R-Chart because all points lies with in the control limits where as in -chart process is out of control because sample 5 6 and 8 lies outside the control limits. The process therefore should be halted to check 478 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES whether there are any assignable causes. If assignable causes found the process

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