tcb_roadmap_to__qualitiy_vol1

r control charts average and range x these are used

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Unformatted text preview: is set at 2 to 6. The sub-group size should be made uniform. The letter “k” represents the number of sub-groups made by data classification. Normally, 20 to 25 sub-groups are supplied. A Roadmap to Quality 23 Unit 9 - Problem solving 05-87581_unit 9.qxd 09/09/2005 11:55 Page 24 In this example, numbers are set as follows: Sub-group size n=3 Number of data items in a sub-group k = 30 Number of all data items N = n x k = 90 Step 3. Calculate the average for sub-groups Calculate the average (represented by –) for respective sub-groups. The value – is calculated x x using the following formula: – = (X + X + ... + X )/n x 1 2 n – The value “x” should be calculated to three decimal places after the measured values, then rounded off. For example, the value for sub-group 1 is calculated as follows. – = (0.42 + 0.40 + 0.41)/3 = 0.410 x – The average “x ” for all sub-groups should be calculated in the same manner. Calculated averages should be arranged as shown in Figure 9.8b. Figure 9.8b Calculation table for –-R control charts: Amount of steam consumed in drying x synthetic rubber B over a period of one month. An –-R control chart is prepared based on x this data (page 25). Step 4. Calculate Calculate “R”, range per sub-group, where R = [maximal value within the sub-group] – [minimal value within the sub-group] For example, the value for sub-group 1 is calculated as follows: R = 0.42 - 0.40 = 0.02 Range “R” for all sub-groups should be calculated in the same manner. Calculated values should be arranged as shown in Figure 9.8b. Step 5. Calculate = x – Add up the value “x“ for all sub-groups and divide this total by “k”, the number of data items in a sub-group. – = = (– + – + ... +x )/k x x1 x2 k – Value “x” should be calculated to four decimal places after the measured value. For example, the value for data presented in Figure 9.8b is calculated as follows: = = 13.165/30 = 0.4388 x – Step 6. Calculate R Add up the value “R” for all sub-groups and divide this total by “k”, the number of – data items in a sub-group. The resulting figure is value “R” – R= (R1+ R2 + ... + Rk)/k – Value “R“ should be calculated to four decimal places after the measured values. For example, the value for data presented in Figure 9.8b is calculated as follows: – R = 4.27/30 = 0.1423 Figure 9.8c Coefficient table for calculating the control lines of control charts (page 26) Unit 9 - Problem solving 24 A Roadmap to Quality 05-87581_unit 9.qxd 09/09/2005 11:55 Page 25 Figure 9.8b Calculation table for –-R control charts x Sub-group number (date) Morning shift Mid-day shift Night shift Average Range R 1 0.42 0.40 0.41 0.410 0.02 2 0.48 0.53 0.47 0.493 0.06 3 0.46 0.88 0.66 0.667 0.42 4 0.50 0.44 0.46 0.467 0.06 5 0.33 0.23 0.30 0.287 0.10 6 0.60 0.40 0.36 0.453 0.24 7 0.41 0.35 0.51 0.423 0.16 8 0.41 0.40 0.45 0.420 0.05 9 0.55 0.59 0.42 0.520 0.17 10 0.28 0.50 0.45 0.410 0.22 11 0.56 0.43 0.50 0.497 0.13 12 0.43 0.40 0.45 0.427 0.05 13 0.45 0.36 0.41 0.407 0.09 14 0.44 0.53 0.48 0.483 0.09 15 0.45 0.51 0.29 0.417 0.22 16 0.14 0.30 0.62 0.353 0.48 17 0.47 0.62 0.46 0.517 0.16 18 0.45 0.32 0.57 0.447 0.25 19 0.49 0.43 0.48 0.467 0.06 20 0.49 0.65 0.50 0.547 0.16 21 0.52 0.49 0.48 0.497 0.04 22 0.44 0.68 1.19 0.770 0.75 23 0.48 0.36 0.36 0.400 0.12 24 0.39 0.35 0.34 0.360 0.05 25 0.32 0.30 0.30 0.307 0.02 26 0.35 0.36 0.35 0.353 0.01 27 0.40 0.40 0.38 0.393 0.02 28 0.36 0.35 0.37 0.360 0.02 29 0.31 0.30 0.33 0.313 0.03 30 0.29 0.30 0.31 0.300 0.02 Total 13.165 4.27 A Roadmap to Quality 25 Unit 9 - Problem solving 05-87581_unit 9.qxd 09/09/2005 11:55 Page 26 Figure 9.8c Coefficient table for calculating the control lines of control charts Control chart types – x ~ x Sub-group size (n) A2 m3A2 D3 D4 2 1.880 1.880 - 3.267 3 1.023 1.187 - 2.575 4 0.729 0.796 - 2.282 5 0.577 0.691 - 2.115 6 0.483 0.549 - 2.004 7 0.419 0.509 0.076 1.924 8 0.373 0.432 0.136 1.864 9 0.337 0.412 0.184 1.816 10 0.308 0.363 0.223 1.777 R Note: Columns denoted by “-” are disregarded. – Step 7. Calculate control lines of x-R control charts – Control Charts x CL: Central Line CL = = x UCL: Upper Control Limit – UCL = = + A2 R x LCL: Lower Control Limit – LCL = = - A2 R x R Control Charts – CL; R – UCL = D4 R – LCL = D3 R (When n<=6, there is no need to consider LCL) Values A2, D3 and D4 are numbers fixed by “n”, the sub-group size (see Figure 9.8c). For example, control lines for the control charts presented in Figure 9.8c are calculated as follows: – Control Chart x CL = = = 0.4388 x – UCL = = + A2R (when n = 3, A2 = 1.023) x = 0.4388 + 0.145573 = 0.584373 Rounded off to 0.5844 (two more decimal places after the measured values) – LCL = = - A2R x = 0.4388 - 0.145573 = 0.293227 Rounded off to 0.2932 Unit 9 - Problem solving 26 A Roadmap to Quality 05-87581_unit 9.qxd 09/09/2005 11:55 Page 27 R Control Chart – 1. CL = R= 0.1423 – 2. UCL = D4R (when n = 3...
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This note was uploaded on 10/07/2013 for the course MKT marketing taught by Professor Anamika during the Spring '12 term at Punjab Engineering College.

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