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- Chart R - Chart S - Chart VARIABLE CONTROL CHART : Mean and Dispersion 1. To understand the Quality Characteristics 2. To understand the benefit of control chart Targ et 3. Able to develop the control chart 4. To know the control chart types 5. Able to evaluate the process using the control chart 2 Introduction The control chart can help to detect the change of process parameters. Generally, there are two types of the control chart : 1. Variable control chart 2. Attribute control chart 3 The Change of Process Parameter (Mean) LSL USL m0 m1 4 The Change of Process Parameter (Standard Deviation) LSL m0 USL s0 s1 5 Quality Characteristics Variable Something that can be measured and expressed by the numerical scale. Attribute Something that can be classified into conforming or non conforming. 6 To choose the quality characteristics Develop ing and the applicat ion of control charts Pareto analysis Developing the control chart : Preparation Making the control chart Implementation : Process evaluation using the control chart. 7 To Choose the Quality Characteristic Product has many the quality characteristics. Choose the quality characteristics using the Pareto analysis. 8 Pareto Analysis (1) Defect Code 1 2 3 4 5 6 7 8 Defect Outside diameter of hub Depth of keyway Hub length Inside diameter of hub Width of keyway Thickness of flange Depth of slot Hardness Frequency 30 20 60 90 30 40 50 20 Percentage 8.82 5.88 17.65 26.47 8.82 11.77 14.71 5.88 9 Percentage of defects Pareto Analysis (2) 30 25 20 15 10 5 0 4 3 7 6 1 5 2 8 Defect code 10 Preparation to use the control chart Choose the sample Sample size Sampling Frequency Choose the instrument for measurement Design the form used to collect the data 11 Non target based X-bar and Range chart Target based X-bar and standard deviation chart Non target based Target based Making the Control Chart 12 X-bar and R Chart(1) Step 1 Write the measurement of the quality characteristic in a Form. Step 2 Calculate Mean and Range for each sample. n X X i 1 n i R X max X min 13 X-bar and R Chart(2) Step 3 Determine and draw a center line and trial control limits for every chart. X- bar chart g Center Line Control Limit X X i i 1 g X 3s X 3sˆ 3R (UCLX , LCLX ) X X X A2 R n nd 2 14 15 X-bar and R Chart(3) R - Chart g R Center Line R Control Limits R 3s R i 1 i g R R UCLR R 3d3 D4 R LCLR R 3d3 D3 R d d2 2 3d 3 D4 1 d2 3d3 D3 max 0,1 d2 16 X-bar and R Chart(4) Step 4 Plotting the range value at R-Chart. Determine whether the point plotted in the statistical control. If not, identify the assignable causes that related to the out-of-control point and then perform the improvement to eliminate the assignable causes. 17 X-bar and R Chart(5) Step 5 Eliminate the out-of-control point after performing the improvement. Use the rest of sample to revise the center line and the control limits. Step 6 Implement the control chart. 18 Example 1 Consider a process by which coils are manufactured. Samples of size 5 are randomly selected from the process, and the resistance values (in ohms) of the coils are measured. The data values are given in Table 7-2, as are the sample mean X bar and the range R. 19 Example 1 (continue) Table 7-2 Sample Observations X bar R 1 3 . . . 22 23 25 20,22,21,23,22 25,18,20,17,22 . . . 21,18,18,17,19 21,24,24,23,23 19,20,21,21,22 21.6 20.40 . . . 18.6 23.00 20.6 3 8 . . . 4 3 3 Sum 521.00 87 Comments New vendor High Temp. Wrong die 20 Example 1 (continue) The initial of R-chart 87 R 3.48 25 Center Line UCLR (2.114)(3.48) 7.357 Trial Control Limits LCLR (0)(3.48) 0 9 8 7 Range 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Sample 21 Example 1 (continue) R-chart Revision 1 79 R 3.29 24 Revised Center Line Revised Control Limit UCLR (2.114)(3.29) 6.96 LCLR (0)(3.29) 0 8 7 6 Range 5 4 3 2 1 0 1 22 43 54 65 76 87 98 109 11 25 10 12 11 13 12 14 13 15 14 16 15 17 16 18 17 19 18 20 19 21 20 22 21 23 22 24 23 24 Sample 22 Example 1 (Continue) The initial of X-bar chart 500.6 X 20.858 24 Center Line UCLX 20.858 (0.577)(3.29) 22.76 Trial Control Limits LCLX 20.858 (0.577)(3.29) 18.96 25 X bar 20 15 10 5 0 11 22 43 54 65 76 10 12 11 13 121413 15 14 16 15 17 16 18 17 19 18 20 19 2120 22 21 23 22 24 23 25 24 87 98 109 11 Sample 23 Example 1 (Continue) R-chart Revision 2 72 R 3.27 22 Revised Center Line UCLR (2.114)(3.27) 6.92 Revised Control Limits LCLR (0)(3.27) 0 8 7 6 Range 5 4 3 2 1 0 1 22 43 54 65 76 87 8 9 9 10 10 12 11 13 12 14 13 15 14 16 15 11 Sample 16 17 17 18 18 19 19 20 2021 2124 22 25 24 Example 1 (Continue) X-bar chart for revision 1) 459 X 20.86 22 Center Line UCLX 20.86 (0.577)(3.27) 22.752 Control Limits LCLX 20.86 (0.577)(3.27) 18.975 25 20 X bar 15 10 5 0 11 22 43 5 4 6 5 76 78 9 8 10 11 11 12 9 10 13 13 14 14 15 15 16 16 17 17 18 18 19 12 Sample 20 20 21 21 24 22 25 19 25 Standardized Control Chart (1) It is used when the sample size is not the same. The Statistic is standardized by subtraction the sample mean from the grand mean and divide it by the standard deviation. The standard value represents the deviation from the mean with the unit of standard deviation. The control limits for the standardized control chart is ± 3. 26 Standardized Control Chart (2) The mean control chart : Grand mean g X n X i i i 1 g n i 1 i g The estimation of Standard Deviation process sˆ (n i 1 g 1) si2 (n i 1 The standardized value i i 1) Xi X Zi ŝ / ni The Zi values are plotted in the control chart with CL=0, UCL=3 dan LCL=-3. 27 Standardized Control Chart (3) Range control chart The value of ri Ri ri sˆ ri d 2 The value of ki k i d3 The ki values are plotted in the control chart with CL=0, UCL=3 dan LCL=-3. 28 The Control Limits base on Target X-bar control chart CLX X 0 3s 0 (UCLX , LCLX ) X 0 X 0 As 0 n R control chart CLR d 2s 0 UCLR R 3s R d2s 0 3d3s 0 d2 3d3 s 0 D2s 0 LCLR R 3s R d2s 0 3d3s 0 d2 3d3 s 0 D1s 0 29 The Average and Standard Deviation Control Chart Xi n 2 i 1 X i n X n s i 1 i X n 1 2 i 1 2 n n 1 E( s) c4s s s s 1 c 2 4 30 The Average and Standard Deviation Control Chart (No Standard) Standard Deviation chart g Center Line CLs s s i 1 i g UCLs s 3s s s 3s 1 c42 Control Limit 3s 1 c42 UCLs s B4 s c4 3s 1 c42 LCLs s B3 s c4 31 The Average and Standard Deviation Control Chart (No Standard) Average X-bar chart (grand mean) g Center Line X X i i 1 g X 3s X X 3 Control Limit (UCLX , LCLX ) X 3s c4 n s n X A3 s 32 The Average and Standard Deviation Control Chart (There is a Standard) Standard Deviation Chart Center Line CLs c4s 0 UCLs c4s 0 3s s c4s 0 3s 0 1 c42 Control Limit UCLs c4 3 1 c42 s 0 B6s 0 LCLs c4 3 1 c42 s 0 B5s 0 33 The Average and Standard Deviation Control Chart (There is a Standard) Average X-bar chart Center Line CLX X 0 Control Limit UCL X , LCLX X 0 As 0 34 Control Chart Pattern (Natural) UCL Sample Average 35 CL 20 LCL 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sample 35 Control Chart Pattern (Sudden Shifts in the Level) UCL Sample Average 35 CL 20 LCL 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sample 36 Control Chart Pattern (Sudden Shifts in the Level) Change in proportions of materials coming from different sources. New worker or machine. Modification of production method or process. Change in inspection device or method. 37 Control Chart Pattern (Gradual Shifts in the Level) UCL Sample Average 35 CL 20 LCL 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sample 38 Control Chart Pattern (Gradual Shifts in the Level) The incoming quality of raw material or components changed over time. The maintenance program changed. The style of supervision changed. New operator. A decrease in worker skill due to fatigue. A gradual improvement in the incoming quality of raw materials. 39 Control Chart Pattern (Trending) UCL Sample Average 35 CL 20 LCL 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sample 40 Control Chart Pattern (Trending) Gradual deterioration of equipment. Worker fatigue. Deterioration of environmental conditions. Improvement or deterioration of operator skill. Gradual change in homogeneity of incoming material quality. 41 Control Chart Pattern (Cyclic) UCL Sample Average 35 CL 20 LCL 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sample 42 Control Chart Pattern (Cyclic) Temperature or other recurring changes in physical environment. Worker fatigue. Differences in measuring or testing devices which are used in order. Regular rotation of machines or operators. 43 Control Chart Pattern (Freaks) UCL Sample Average 35 CL 20 LCL 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sample 44 Control Chart Pattern (Freaks) The use of a new tool for a brief test period. The failure of a component. 45 Control Chart Pattern (Bunches) UCL Sample Average 35 CL 20 LCL 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sample 46 Control Chart Pattern (Bunches) The use of a new vendor for a short period of time. The use of different machine for a brief time period. A new operator used for a short period. 47 Control Chart Pattern (Mixture) UCL Sample Average 35 CL 20 LCL 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sample 48 Control Chart Pattern (Mixture) The differences in the incoming quality of material from two vendors. Overcontrol. Two or more machines being represented on the same control chart. 49 Control Chart Pattern (Stratification) UCL Sample Average 35 CL 20 LCL 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sample 50 Control Chart Pattern (Stratification) Incorrect calculation of control limits. Incorrect subgrouping. 51 Process Capability • Capability Process Estimation is performed when the process is in control. • Hitung standar deviasi proses. • Proportion nonconforming item is performed by viewing the average, standard deviasi process, and specification limits (not the control limits). 52 Example 2 The coil resistance specification is 21±3 ohms. The sample with size 5 is taken with the result Rbar equal to 3.50 and the process average estimation is 20.864. Determine the proportion of nonconforming output with assumption that the coil resistance data is normal distribution. 53 Example 2 (continue) sˆ R 3.50 1.505 d 2 2.326 0.0287 0.0188 LSL=18 X 20.864 sˆ 1.505 USL=24 X 54