X chart and R chart.pptx

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1. X Chart and R Chart Dr. Kumar Abhishek Assistant Professor Department of Mechanical Engineering IITRAM Quality Design & Control

2. It shows changes in process average and is affected by changes in process variability. It is a chart for the measure of central tendency. It shows cyclic shifts in the process. It detects study progress changes, light tool wear. It is the most commonly used variables chart. and R charts when used together form a powerful instrument for diagnosing quality problems.   Chart  

3. R Chart It controls general variability of the process and is affected by changes in process variability. It is a chart for measure of spread. It is generally used along with an chart.  

4. A good number of samples of items coming out of the machine are collected at random at different intervals of times and their quality characteristics are measured. For each sample, the mean value and range is found out. For example, if a sample contains 5 items, whose diameters are D1, D2, D3, D4 and D5     Sample average And Range, Plotting of and R Charts  

5. Sample No. (Sample Size: 5) R 1 7.0 2 2 7.5 3 3 8.0 2 4 10.0 2 5 9.5 3   Sample No. (Sample Size: 5) R 1 7.0 2 2 7.5 3 3 8.0 2 4 10.0 2 5 9.5 3     4   Plotting of and R Charts  

6. UCL=   LCL=       Upper Control Limit L ower Control Limit For R Chart For Chart   Upper Control Limit L ower Control Limit Plotting of and R Charts  

7. Sample Size (No. of items in a Sample) A 2 (Limit Average) D 3 (Range Lower Limit) D 4 (Range Upper Limit) 2 1.88 3.27 3 1.02 2.57 4 0.73 2.28 5 0.58 2.11 6 0.48 2.00 8 0.37 0.14 1.86 10 0.31 0.22 1.78 12 0.27 0.28 1.72 The value of various factors (like A 2, D4 , D3) based on normal distribution can be found from the following table: For Sample Size 5 A2 = 0.58 D3 = 0 D4 = 2.11 Plotting of and R Charts  

8. Plotting of and R Charts   UCL = = 8.5 + (0.58 * 2.4) = 9.892   LCL = = 8.5 - (0.58 * 2.4) = 7.108   UCL = = 2.11 * 2.4 = 5.064   LCL = = 0 * 2.4 = 0   Upper Control Limit L ower Control Limit For R Chart For Chart   Upper Control Limit L ower Control Limit

9. Chart       7.108      

10. R Charts R          

11. THANK YOU!