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##### STATS Multiple Problems-A machine produces a product and the operator of the machine

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Problem No. 1;A machine produces a product and the operator of the machine would like to develop an SPC chart to control the proportion of non-conforming (defective) units produced. She/he takes twenty samples of 250 units each and records the number of defective units found in each sample in the following table;Sample;No.;Number of;Defective Units;Sample;No.;Number of;Defective Units;1 8 11 4;2 5 12 3;3 3 13 5;4 9 14 6;5 4 15 2;6 5 16 5;7 8 17 0;8 5 18 3;9 3 19 4;10 6 20 2;A. [2 points] What type of control chart (X-bar, R, p, or c) is appropriate for this process? Why? (No explanation, no credit);B. [4 points] Calculate the control limits for a 2-sigma control chart for this process.;C. [4 points] Given the sample data above, is the process in or out of control? EXPLAIN (be specific as to why). No explanation, no credit! You must draw a control chart (Use Excel for this purpose and copy the graph into your Word document).;?;Problem No. 2;A chocolate manufacturer would like to develop a process control chart to control the weight of chocolate bars it produces. Historically, the process has had a standard deviation of 0.25. The operator has taken 39 samples of size 7 each and calculated the following sample means;Sample;#;Sample;Mean;Sample;No.;Sample;Mean;Sample;No.;Sample;Mean;1 3.86 14 3.81 27 3.81;2 3.90 15 3.83 28 3.86;3 3.83 16 3.86 29 3.98;4 3.81 17 3.82 30 3.96;5 3.84 18 3.86 31 3.88;6 3.83 19 3.84 32 3.76;7 3.87 20 3.87 33 3.83;8 3.88 21 3.84 34 3.77;9 3.84 22 3.82 35 3.86;10 3.80 23 3.89 36 3.80;11 3.88 24 3.86 37 3.84;12 3.86 25 3.88 38 3.79;13 3.88 26 3.90 39 3.85;A. [3 points] Calculate the control limits for a 2-sigma x-bar control chart for this process.;B. [3 points] Assuming the R-chart for the process is in control, is this process in control? Why or Why not? EXPLAIN (be specific as to why). No explanation, no credit.;C. [4 points] The specifications for the product are as follows: 3.8 ? 0.4 oz. Calculate the Capability ratio and index. Interpret them (be specific).;?;Problem No. 3;An appliance store carries a certain brand of TV which has he following characteristics;Average daily demand 2 units;Ordering cost \$25 per order;Carrying Cost 35% of unit cost per year;Unit cost \$400 per unit;Average Lead time 4 days;Standard deviation of daily demand 0.8 unit;Standard deviation of lead time 0.6 days;The firm currently orders the product 85 units at a time and operates 250 days a year.;A. [4 points] With the current lot-size policy, what is the annual holding and ordering costs?;B. [3 points] With the current lot size, what is the average time (in days) between orders?;C. [3 points] Calculate EOQ for the TVS.;Problem No. 4;A retailer needs to choose between two suppliers for one of its products. The only criterion used for the decision is the cost. The following information about the product is available;Demand 200 a week;Ordering cost (for all suppliers) \$75 per order;Holding cost 20% of the unit cost;Working weeks 50 a year;The retailer has narrowed down the choices to two suppliers. The following shows the price-break schedule for each supplier;SUPPLIER A SUPPLIER B;Quantity Unit Price Quantity Unit Price;1-299 \$14.00 1-249 \$14.10;300-699 13.80 250-449 13.90;700+ 13.60 450+ 13.70;A. [4 points] Which supplier should the retailer choose? Explain and support your answer with appropriate calculations. Do NOT exceed the box for explanation.;B. [3 points] What is the optimal lot size for the item? (Note: There has to be only ONE choice, regardless of supplier).;C. [3 points] What is the total annual cost of inventory for the chosen (best) lot size?;Problem No. 5;A retailer is considering a P-system of inventory control for one of its products. However, the total cost of the system (including safety stock) is a concern. The following information about this item is gathered;Average demand for the product 120 units per day;Standard deviation of demand 30;The store operates 300 days a year;Holding cost 35 percent of the unit cost;Ordering costs \$120 per order;Production lead time (setup time) 3 days;Stock out policy No more than 7%;Unit cost \$9.25;Given this information, determine the following;A. [5 points] Assuming a P system with a review period of 14 days, calculate the safety stock needed to support the desired stockout policy.;B. [5 points] Annual total cost of the P-system (Grand total cost of inventory for the year);Problem No. 6;[5 points] A retailer currently holds 45 units of safety stock for one of its products. Demand for this product averages 100 units a week with the standard deviation of 12 and the lead time for it is 3 weeks. The current industry standard for this firm is 2% stockout. Is this retailer competitive? WHY? You must show your calculation and explanation below, otherwise there will be no credit.;SHOW BOTH YOUR KEY FIGURES AND YOUR EXPLANATION IN THE FIELD FOR THIS QUESTION;BONUS PROBLEM # 2;[5 points] A retailer is considering a P-system of inventory control for one of its products. However, the first question is what the review period (P) should be. The following information about this item is gathered;Average demand for the product 150 units per day;The store operates 300 days a year;Holding cost 30 percent of the unit cost;Ordering cost \$90 per order;Unit cost \$10.75;Given this information, determine the best estimate for the P (Review Period);CUMULATIVE STANDARD NORMAL DISTRIBUTION TABLE (z-TABLE);Z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09;0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359;0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753;0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141;0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517;0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879;0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224;0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549;0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852;0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133;0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389;1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621;1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830;1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015;1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177;1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319;1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441;1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545;1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633;1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706;1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767;2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817;2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857;2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890;2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916;2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936;2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952;2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964;2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974;2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981;2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986;3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990;3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993;3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995;3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997;3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998;3.5 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998;For Z = 2.0;The figures in the table show the cumulative area under the curve from minus infinity to a given positive z value

Paper#19526 | Written in 18-Jul-2015

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