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

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Question;Problem No. 1A 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:SampleNo. Number ofDefective Units SampleNo. Number ofDefective Units1 8 11 42 5 12 33 3 13 54 9 14 65 4 15 26 5 16 57 8 17 08 5 18 39 3 19 410 6 20 2A. [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. 2A 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# SampleMean SampleNo. SampleMean SampleNo. SampleMean1 3.86 14 3.81 27 3.812 3.90 15 3.83 28 3.863 3.83 16 3.86 29 3.984 3.81 17 3.82 30 3.965 3.84 18 3.86 31 3.886 3.83 19 3.84 32 3.767 3.87 20 3.87 33 3.838 3.88 21 3.84 34 3.779 3.84 22 3.82 35 3.8610 3.80 23 3.89 36 3.8011 3.88 24 3.86 37 3.8412 3.86 25 3.88 38 3.7913 3.88 26 3.90 39 3.85A. [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. 3An appliance store carries a certain brand of TV which has he following characteristics:Average daily demand 2 unitsOrdering cost $25 per orderCarrying Cost 35% of unit cost per yearUnit cost $400 per unitAverage Lead time 4 daysStandard deviation of daily demand 0.8 unitStandard deviation of lead time 0.6 daysThe 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. 4A 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 weekOrdering cost (for all suppliers) $75 per orderHolding cost 20% of the unit costWorking weeks 50 a yearThe retailer has narrowed down the choices to two suppliers. The following shows the price-break schedule for each supplier:SUPPLIER A SUPPLIER BQuantity Unit Price Quantity Unit Price1-299 $14.00 1-249 $14.10 300-699 13.80 250-449 13.90 700+ 13.60 450+ 13.70A. [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. 5A 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 dayStandard deviation of demand 30The store operates 300 days a yearHolding cost 35 percent of the unit costOrdering costs $120 per orderProduction lead time (setup time) 3 daysStock out policy No more than 7%Unit cost $9.25Given 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 QUESTIONBONUS 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 dayThe store operates 300 days a yearHolding cost 30 percent of the unit costOrdering cost $90 per orderUnit cost $10.75Given 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 0.090.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.53590.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.57530.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.61410.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.65170.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.68790.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.72240.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.75490.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.78520.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.81330.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.83891.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.86211.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.88301.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.90151.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.91771.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.93191.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.94411.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.95451.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.96331.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.97061.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.97672.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.98172.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.98572.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.98902.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.99162.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.99362.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.99522.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.99642.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.99742.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.99812.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.99863.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.99903.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.99933.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.99953.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.99973.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.99983.5 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998For Z = 2.0The figures in the table show the cumulative area under the curve from minus infinity to a given positive z value

Paper#52411 | Written in 18-Jul-2015

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