QUESTION 5 [20 Marks] (a) Table 3 shows the data for the Loan application and errors. Table 3 n np n np Subgroup number 1 2 3 4 5 6 7 8 9 10 500 500 500 500 500 500 500 500 500 500 20 21 19 15 18 20 19 28 17 20 Subgroup number 11 12 13 14 15 16 17 18 19 20 500 500 500 500 500 500 500 500 500 500 19 18 10 11 10 9 10 11 9 8 Table 3: Loan application and errors i) Based on the given data in Table 3, calculate the Centre Line (CL), Upper Control Limit (UCL) and Lower Control Limit (LCL) for p-chart. [8 Marks) [C01, PO1, C3] ii) Construct a p-chart for the data. (5 Marks] [C01, PO1, C3] iii) Explain whether the process in control or not. [2 marks] [C01, PO1, C3] (b) Explain TWO (2) basic functions of control chart. [5 Marks] Appendix A Q Ox ox (n) C4 Tables of Constants for Control charts Institute of Table 8A - Variable Data ref: AIAG manual for SPC Quality & Reliability X bar and R Charts X bar and s charts Chart for Chart for Averages Chart for Ranges (R) Averages Chart for Standard Deviation (s) Divisors Divisors Control to Control to Limits Estimate Factors for Control Limits estimate Factors for Control Factor Limits Factor Limits subgroup size A2 dz D3 D4 Az B3 B4 2 1.880 1.128 3.267 2.659 0.7979 3.267 3 1.023) 1.693 2.574 1.954 0.8862 2.568 4 0.729 2.059 2.282 1.628 0.9213 2.266 5 0.577 2.326 2.114 1.427 0.9400 2.089 6 0.483 2.534 2.004 1.287 0.9515 0.030 1.970 7 0.419 2.7041 0.076 1.924 1.182 0.9594 0.118 1.882 8 0.373 2.847 0.136 1.864 1.099 0.9650 0.185 1.815 9 0.337) 2.970 0.184 1.816 1.032 0.9693 0.239 1.761 10 0.308 3.078 0.223 1.777 0.975 0.9727 0.284 1.716 15 0.223 3.4721 0.347 1.653 0.789 0.9823 0.428 1.572 25 0.153 3.931 0.459 1.541 0.606 0.9896) 0.565 1.435 IN O 8 Centerline 0 x Control Limits UCL = +A LCL = X - AR R X bar and R Charts CL; = CLR = R dz UCLR = D.R LCL R = DR UCL; = 7 +4,5 | LCL; = 7 4,5 UCL, = 0.5 LCL = B,S | S X bar and s Charts CL; = X CL = 5 - C4