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Production & Operations Management
August 2010
Competitiveness, Strategy and Productivity
1. List the key ways in which the organizations compete.
2. Explain the terms: Order qualifiers and Order winners.
3. What are distinctive competencies and how do they affect strategy.
4. Explain the term “Time based strategy” and give 3 examples.
5. Compare the terms strategies and tactics. A Production Manager decides to use overtime for one week in order to meet a critical delivery schedule. Is this decision strategic or tactical?
6. List the factors affecting productivity and some ways to improve productivity.
7. Name 10 ways in which banks compete for customers.
8. Compute the multifactor productivity measure for each of the weeks shown. What do the productivity figures suggest? Assume 40-hour weeks and an hourly wage rate of $12. Overhead is 1.5 times weekly labour cost. Material cost is $6 per pound.
Week Output Workers Material (lbs.)
1 30000 6 450
2 33600 7 470
3 32200 7 480
4 35400 8 480
9. An operation has a 10% scrap rate. As a result, 72 pieces per hour are produced. What is the potential increase in productivity that could be achieved by eliminating the scrap?
10. A manager checked production records and found that a worker produced 160 units while working 40 hours. In the previous week, the same worker produced 138 units while working 36 hours. Did the worker’s productivity increase, decrease, or remain the same? Explain.
11. The following table shows data on the average number of customers processed by several bank service units each day. The hourly wage rate is $25, the overhead rate is 1.0 times labour cost, and material cost is $5 per customer.
Unit Employees Customers processed
A 4 36
B 5 40
C 8 60
D 3 20
a) Compute the labour productivity and multifactor productivity for each unit
b) Suppose a new, more standard procedure is to be introduced that will enable each employee to process one additional customer per day. Compare the expected labour and multifactor productivity rates for each unit. For multifactor productivity assume an 8-hour day.
Capacity Planning
1. Give an example of a product and a service that exhibit the following seasonal demand patterns:
a. Annual
b. Monthly
c. Weekly
d. Daily
2. What is meant by “capacity in chunks” and why is that a factor in capacity planning?
3. How do capacity decisions influence productivity?
4. Briefly discuss how uncertainty affects capacity decisions?
5. A computer repair service has a design capacity of 80 repairs per day. Its effective capacity, however, is 64 repairs/day and the actual output is 62 repairs/day. Which of the following factors would you recommend that the manager investigate: quality problems, absenteeism, or scheduling and balancing? Explain your reasoning.
6. In a job shop, the effective capacity is only 50% of design capacity and actual output is 80% of effective capacity. What design capacity would be needed to achieve an actual output of eight jobs per week?
7. A producer of pottery is considering the addition of a new plant to absorb the backlog of demand that now exists. The primary location being considered will have a fixed cost of $9200 per month and a variable cost of 70 cents per unit produced. Each item is sold to retailers at a price that averages 90 cents.
a) What volume per month is required in order to break even?
b) What profit would be realized on a monthly volume of 61000 units? 87000 units?
c) What volume is needed to obtain a profit of $16000 per month?
d) What volume is needed to provide a revenue of $23000 per month?
e) Plot the total cost and total revenue lines.
8. A firm plans to begin production of a new small appliance. The manager must decide whether to purchase the motors for the appliance from a vendor at $7 each or to produce them in house. There are two processes of manufacturing and either of them could be used for in house production. One would have an annual fixed cost of $160000 and a variable cost of $5 per unit. The other process would have an annual fixed cost of $190000 and a variable cost of $4 per unit. Determine the range of annual income for which each of the alternatives would be best.
9. A company manufactures a product using two machine cells. Each cell has a design capacity of 250 units per day and an effective capacity of 230 units per day. At present, actual output averages 200 units per cell, but the manager estimates that productivity improvements soon will increase the output to 225 units per day. Annual demand is currently 50000 units. It is forecasted that within two years, annual demand will triple. How many cells should the company plan to use to satisfy predicted demand under these conditions? Assume 240 working days per year.
10. A manager must decide how many machines of a certain type to purchase. Each machine can process 100 customers per day. One machine will result in a fixed cost of $2000 per day, while two machines will result in a fixed cost of $3800 per day. Variable cost will be $20 per customer, and revenue will be $45 per customer.
a) Determine the break-even point for each range.
b) If estimated demand is 90 to 120 customers per day, how many machines should be purchased?
11. The manager of a car wash must decide whether to have one or two wash lines. One line will mean a fixed cost of $6000 a month, and two lines will mean a fixed cost of $10500 a month. Each line would be able to process 15 cars an hour. Variable costs will be $3 per car, and revenue will be $5.95 per car. The manager projects an average demand of between 14 and 18 cars an hour. Would you recommend one or two lines? The car wash is open 300 hours a month.
12. A small firm intends to increase the capacity of a bottleneck operation by adding a new machine. Two alternatives, A and B, have been identified, and the associated costs and revenues have been estimated. Annual fixed costs would be $40,000 or A and $30,000 for B. Variable costs per unit would be $10 for A and $11 for B and revenue per unit would be $15.
a. Determine each alternative’s break-even point in units.
b. At what volume of output would the two alternatives yield the same profit?
c. If expected annual demand is 12000 units, which alternative would yield the higher profit?
Cash Flows and Present worth
1. A Paint manufacturer intends to expand the capacity by investing Rs. 50 lakh in an automatic blending machine. The production capacity of the machine is 1200 litres per day. The material cost of the paint is Rs. 55 per litre and the processing cost is Rs. 15 per litre. The projected annual demand (in thousand litres) for 5 years is given below:
2011 2012 2013 2014 2015 2016
230 215 245 280 340 300
If the selling price of the paint is Rs. 78 per litre, calculate the break-even period for an expected rate of return of 12%. Consider 300 working days in a year.
2. Analyze the following investment required to set up a retail Mall and the expected returns from it over a period of six years. If the minimum expected rate of return is 15%, would you recommend the investments? All figures are in Rs. Lakhs.
2011 2012 2013 2014 2015 2016
Investments 15 - 7 - 3 -
Annual total costs - 13 17.5 16 18 20.5
Annual Revenue - 15.5 24 25 29.5 32
Annual total costs - 13 17.5 16 18 20.5
Annual Revenue - 15.5 24 25 29.5 32
Decision Theory
Option Motel approved Motel rejected
Renew lease $500,000 $4,000,000
Relocate $5,000,000 $100,000
What course of action would you recommend using:
a) Maximax criterion
b) Maximin criterion
c) Laplace criterion
d) Minimax regret criterion
2. In the previous question, if the probability of the motel getting approved is 0.35, then answer the following questions:
a. Which alternative will get selected if the management uses maximum expected monetary value as the decision criterion?
b. Represent this problem in the form of a decision tree
c. If the management has been offered the option of a temporary lease while the town planning department is processing the motel’s application, would you advise the management to sign the lease? The lease will cost $24,000.
3. Construct a graph that can be used for sensitivity analysis for the preceding problem.
a. How sensitive is the solution in terms of the probability estimate of 0.35?
b. Suppose that the probability for approval gets revised to 0.45, how sensitive is the solution to this revised estimate? Explain.
c. Suppose the management is confident of all the estimated payoffs except for $4 Million. If the probability of approval is 0.35, for what range of payoff for renew/reject will the alternative selected using maximum expected value remain the same?
4. The conditional pay-offs in crores of rupees for the three models of a car for the various likely sales figures are as follows:
Sales (units)
Model 1 lakh 2 lakh 3 lakh
X 30 10 10
Y 55 20 3
Z 15 35 65
X 30 10 10
Y 55 20 3
Z 15 35 65
Find the pay-offs using (a) Maximax, (b) Maximin and (c) Laplace criteria.
5. The director of social services of a county has learnt that the state has mandated additional information requirements, which is going to place additional burden on their department. He has identified three alternatives to handle the increased work load. An unknown factor is the caseload for the coming year when the new data will be collected on a trial basis. The estimated cost for various options and caseloads are as follows:
Caseload
Options Moderate High Very High
Reassign staff $50,000 $60,000 $85,000
Hire new staff $60,000 $60,000 $60,000
Redesign the process $40,000 $50,000 $90,000
of data collection
If reliable estimates of caseload probabilities are not available, what decision would be appropriate using each of the following criteria?
Options Moderate High Very High
Reassign staff $50,000 $60,000 $85,000
Hire new staff $60,000 $60,000 $60,000
Redesign the process $40,000 $50,000 $90,000
of data collection
If reliable estimates of caseload probabilities are not available, what decision would be appropriate using each of the following criteria?
a) Maximin
b) Maximax
c) Minimax regret
d) Laplace criterion
6. In the previous example, the caseload probabilities are estimated as 0.10 for moderate, 0.30 for high and 0.60 for very high.
a. Which alternative will yield the minimum expected cost?
b. Construct a design tree of the problem. Indicate the expected costs for the three decision branches.
c. Determine the expected value of perfect information using an opportunity loss table.
Process Selection and Facility Layout
1. Explain the 5 process types, and indicate the kinds of situations in which each would be used.
2. Discuss the advantages and disadvantages of automation
3. What is a flexible manufacturing system, and under what set of circumstances is it most appropriate?
4. What are the main advantages and disadvantages of product layout?
5. What are the main advantages and disadvantages of process layout?
6. Identify the fixed-path and variable-path material handling equipment commonly found in Super markets?
7. What is cellular manufacturing? What are its main benefits and limitations?
8. Explain the concept of Group Technology.
9. An assembly line with 17 tasks is to be balanced. The longest task is 2.4 minutes, and the total time for all tasks is 18 minutes. The line will operate for 450 minutes per day.
a. What are the minimum and maximum cycle times?
b. What range of output is theoretically possible for the line?
c. What is the minimum number of workstations needed if the maximum output rate is to be sought?
d. What cycle time will provide an output rate of 125 units per day?
e. What potential output will result if the cycle time is (i) 9 minutes? (ii) 15 minutes?
10. A manufacturer of pencil sharpeners is planning to add a new line of sharpeners, and you have been asked to balance the process, given the following tasks and precedence relationships. Assume that cycle time is to be the minimum possible.
Task Length (min) Immediate follower
a 0.2 b
b 0.4 d
c 0.3 d
d 1.3 g
e 0.1 f
f 0.8 g
g 0.3 h
h 1.2 end
a. Do each of the following:
i. Draw precedence diagram
ii. Assign tasks to stations in order of greatest number of following tasks
iii. Determine the percentage idle time
iv. Compute the rate of output that could be expected from this line assuming a 420-minute working day.
b. Answer these questions:
i. What is the shortest cycle time that will permit use of only two workstations? Is this cycle time feasible? Identify the tasks you would assign to each station.
ii. Determine the percentage of idle time that would result if two stations were used.
iii. What is the daily output under this arrangement?
iv. Determine the output rate that would be associated with the maximum cycle time.
11. As part of a major plant renovation project, the industrial engineering department has been asked to balance a revised assembly operation to achieve an output of 240 units per eight-hour day. Task times and precedence relationships are as follows.
Task duration (min) Precedes task
a 0.2 b
b 0.4 c
c 0.2 f
d 0.4 e
e 1.2 g
f 1.2 g
g 1.0 end
Do each of the following:
a. Draw the precedence diagram
b. Determine the minimum cycle time, the maximum cycle time, and the calculated cycle time.
c. Determine the minimum number of stations needed.
d. Assign tasks to workstations on the basis of greatest number of following tasks. Use longest processing time as a tiebreaker. If ties still exist, assume indifference in choice.
e. Compute the percentage of the idle time for the assignment in part d.
12. A workshop operates for 400 minutes in a day. The manager of the workshop wants an output of 200 units per day for the assembly line that has the elemental tasks shown in the table below.
Task duration (min) Precedes task
a 0.2 b
b 0.4 c
c 0.2 f
d 0.4 e
e 1.2 g
f 1.2 g
g 1.0 end
Do each of the following:
a. Construct a precedence diagram.
b. Assign tasks according to the ‘most following tasks’ rule.
c. Assign tasks according to the ‘greatest positional weight’ rule.
d. Compute the balance delay for each rule. Which one yields the better set of assignments in this instance?
13. Arrange six departments into a 2 X 3 grid so that the following conditions are satisfied:
1 is close to 2,
5 is close to 2 & 6,
4 is close to 3,
3 is not close to 1 & 2
Develop a Muther-type grid using the letters A, O, X. Assume that any pair of combinations not mentioned have an O rating.
14. Determine the placement of departments for a newly designed facility that will minimize total transportation costs using the data in the following tables. Assume that reverse distances are same. The locations are shown in the grid. Assume a transportation cost of Rs. 15 per metre. Calculate the total transportation cost of the solution.
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Location A
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Location B
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Location C
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Location D
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Distance between locations (metres)
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From/To
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A
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B
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C
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D
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A
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-
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40
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80
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70
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B
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-
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40
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50
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C
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-
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60
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D
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-
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No. of trips per day between departments
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From/To
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1
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2
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3
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4
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1
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-
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10
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20
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80
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2
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-
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40
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90
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3
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-
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55
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4
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-
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Inventory Management
1. What are the requirements for effective inventory management?
2. Briefly describe each of the costs associated with inventory.
3. Explain briefly how a higher carrying cost can result in a decrease in inventory.
4. Under what circumstances would the amount of safety stock held be: a) Large, b) Small, c) Zero?
5. What is meant by the term service level? Generally speaking, how is service level related to the amount of safety stock held?
6. Describe briefly the A-B-C approach to inventory control.
7. Explain how a decrease in setup time can lead to a decrease in the average amount of inventory a firm holds, and why that would be beneficial.
8. What tradeoffs are involved in each of these aspects of inventory management?
a. Buying additional amounts to take advantage of quantity discounts.
b. Treating holding cost as a percentage of unit price instead of as a constant amount.
c. Conducting cycle counts once a quarter instead of once a year.
9. The manager of an automobile repair shop hopes to achieve a better allocation of inventory control efforts by adopting an A-B-C approach to inventory control. Given the monthly usage in the following table, classify the items in A,B, and C categories according to dollar usage. Consider cumulative consumption levels of up to 70%, 70-90% and 90-100% for A-B-C classification:
Item Usage (units) Unit Cost ($)
4021 50 1400
9402 300 12
4066 40 700
6500 150 20
9280 10 1020
4050 80 140
6850 2000 15
3010 400 20
4400 7000 5
a. Determine the economic order quantity.
b. What is the average number of bags on hand?
c. How many orders per year will there be?
d. Compute the total cost of ordering and carrying flour.
e. If ordering costs were to increase by $1 per order, how much would that affect the minimum total annual cost?
11. A produce distributor uses 800 packing crates a month, which it purchases at a cost of $10 each. The manager has assigned an annual carrying cost of 35% of the purchase price per crate. Ordering costs are $28. Currently the manager orders once a month. How much could the firm save annually in ordering and carrying costs by using EOQ?
12. A food processor uses approximately 27000 glass jars a month for its fruit juice product. Because of storage limitations, a lot size of 4000 jars has been used. Monthly holding cost is 18 cents per jar, and reordering cost is $60 per order. The company operates an average of 20 days a month.
a. What is the economic order quantity?
b. If the manager is able to follow EOQ, then how many orders will he place in a year?
c. What will be the average inventory level if the manager follows EOQ methodology for inventory management?
d. What loss is the company incurring by its present order size?
e. If the ordering cost is reduced to $40 per order the what will be the revised EOQ?
13. A chemical firm produces sodium bisulfate in 100-pound bags. Demand for this product is 20 tons per day. The production capacity is 50 tons per day. Setup costs $100, and storage and handling costs are $5 per ton a year. The firm operates 200 days a year. (Note 1 ton = 2000 pounds).
a. How many bags per production run are optimal?
b. What would the average inventory be for this lot size?
c. Determine the approximate length of a production run, in days.
d. About how many runs per year would there be?
e. How much could the company save annually if the setup cost could be reduced to $25 per run?
14. A mail-order house uses 18000 boxes a year. Carrying costs are 60 cents per box a year, and ordering costs are $96. The following price schedule applies. Determine
a. The optimal order quantity
b. The number of orders per year
Number of boxes Price per box ($)
1000 to 1999 1.25
2000 to 4999 1.20
2000 to 4999 1.20
5000 to 9999 1.15
10000 or more 1.10
15. A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $8 per stone for quantities of 600 stones or more, $9 per stone for orders of 400 to 599 stones, and $10 per stone for lesser quantities. The jewelry firm operates 200 days per year. Usage rate is 25 stones per day, and ordering costs are $48.
a. If carrying costs are $2 per year for each stone, find the order quantity that will minimize total annual cost.
b. If annual carrying costs are 30% of unit cost, what is the optimal order size?
c. If lead time is 6 working days, at what point should the company reorder?
16. Given this information:
Lead-time demand = 600 pounds
Standard deviation of lead-time demand = 52 pounds
Acceptable stockout risk during lead time = 4%
a. What amount of safety stock is appropriate?
b. When should this item be reordered?
c. What risk of stockout would result from a decision not to have any safety stock?
17. Regional Supermarket is open 360 days per year. Daily use of cash register tape averages 10 rolls. Usage appears normally distributed with a standard deviation of 2 rolls per day. The cost of ordering tape roll is $1, and carrying costs are 40 cents per roll a year. Lead time is 3 days.
a. What is the EOQ?
b. What ROP will provide a lead time service level of 96%?
c. What is the expected number of units short per cycle with 96%? Per year?
d. What is the annual service level?
18. Caring Hospital’s dispensary reorders doses of a drug when the supply on hand falls to 18 units. Lead time for resupply is 3 days. Given the typical usage over the last 10 days, what service level is achieved with the hospital’s reorder policy?
Day 1 2 3 4 5 6 7 8 9 10
Units 3 4 7 5 5 6 4 3 4 5
Quality Management
1. Explain the terms ‘Quality of Design’ and ‘Quality of Conformance’.
2. Use the dimensions of quality to describe typical characteristics of these products and services:
a. A television set
b. A restaurant meal (product)
c. A restaurant meal (service)
d. Painting a house
3. Compare the dimensions of product quality versus those of service quality.
4. What is ISO9000 and why is it important for global business to have ISO9000 certification?
5. Explain each of these methods:
a) The plan-do-study-act cycle
b) The 5W2H approach
a) The plan-do-study-act cycle
b) The 5W2H approach
6. What are the key elements of the TQM approach? What is the driving force behind TQM?
7. Briefly explain the terms ‘Benchmarking’ and ‘Run charts’.
8. Explain the costs associated with quality issues.
9. Explain in brief, the Six Sigma methodology in Total Quality Management.
10. Prepare a cause-and-effect diagram to analyze the possible causes of late delivery of parts ordered from a supplier.
11. Prepare a scatter diagram for the following data set and analyze the relationship between the variables:
Temp.(F) 65 63 72 66 82 58 75 86 77 65
Error rate 1 2 0 0 3 3 1 5 2 1
Error rate 1 2 0 0 3 3 1 5 2 1
Quality Control
1. List the steps in Control process.
2. What is the purpose of a control chart? Explain the key concepts that underlie the construction and interpretation of control charts.
3. Briefly explain the purpose of each of these control charts:
a) x-bar chart
b) Range chart
c) p-Chart
d) c-Chart
a) x-bar chart
b) Range chart
c) p-Chart
d) c-Chart
4. What is a run? How are run charts useful in process control?
5. Explain the terms ‘median run test’ and ‘up/down run test’. Why is it usually desirable to use both of them?
6. Define and explain the terms control limits and process variability.
7. Answer the following questions about inspection:
a) What level of inspection is optimal?
b) What factors guide the decision of how much to inspect?
c) What are the main considerations in choosing between centralized inspection and on-site
inspection?
d) What points are potential candidates for inspection?
a) What level of inspection is optimal?
b) What factors guide the decision of how much to inspect?
c) What are the main considerations in choosing between centralized inspection and on-site
inspection?
d) What points are potential candidates for inspection?
8. What is meant by process capability index? How is it determined?
9. Classify each of the following as either a Type 1 error or Type 2 error:
a) Putting an innocent person in jail
b) Releasing a guilty person from jail
c) Eating (on not eating) a cookie that fell on the floor
d) Not seeing a doctor as soon as possible after ingesting poison
a) Putting an innocent person in jail
b) Releasing a guilty person from jail
c) Eating (on not eating) a cookie that fell on the floor
d) Not seeing a doctor as soon as possible after ingesting poison
10. Specifications for a part for a DVD player state that the part should weigh between 24 and 25 grams. The process that produces the parts yields a mean of 24.5 grams with a standard deviation of 0.2 grams. The output follows normal distribution.
a) What percentage of parts will not meet the weight specs?
b) Within what values 95.44% of sample means of this process fall, if samples of n=16 are taken and the process is in control (random)?
a) What percentage of parts will not meet the weight specs?
b) Within what values 95.44% of sample means of this process fall, if samples of n=16 are taken and the process is in control (random)?
11. An automatic filling machine is used to fill 1-litre bottles of cola. The machine’s output is approximately normal with a mean of 1.0 litre and a standard deviation of 0.01 litre. Output is monitored using means of samples of 25 observations.
a) Determine upper and lower control limits that will include roughly 97% of the sample means when the process is in control.
b) Given these sample means: 1.005, 1.001, 0.998, 1.002, 0.995 and 0.999, is the process in control?
a) Determine upper and lower control limits that will include roughly 97% of the sample means when the process is in control.
b) Given these sample means: 1.005, 1.001, 0.998, 1.002, 0.995 and 0.999, is the process in control?
12. Given the following data for the number of defects per spool of cable, using three-sigma limits, is the process in control?
Spool 1 2 3 4 5 6 7 8 9 10
Defects 2 3 1 0 1 3 2 0 2 1
Spool 11 12 13 14
Defects 3 1 2 0
13. Using samples of 200 credit card statements, an auditor found the following:
Sample 1 2 3 4
Statements 4 2 5 9
With errors
a. Determine the fraction defective in each sample
b. If the true fraction of defective for this process is unknown, what is your estimate of it?
c. What is your estimate of the mean and standard deviation of the sampling distribution of fractions defective for this sample size?
d. What control limits would give an alpha risk of 0.03 for this process?
e. What alpha risk would control limits of 0.047 and 0.003 provide?
f. Using control limits of 0.047 and 0.003, is the process in control?
g. Suppose that the long term fraction defective of the process is known to be 2%. What are the values of the mean and the standard deviation of the sampling distribution?
h. Construct a control chart for the process, assuming a fraction defective of 2%, using two-sigma control limits. Is the process in control?
14. A production process consists of a three-step operation. The scrap rate is 10% for the first step and 6% for the other two steps.
a. If the desired daily output is 450 units, how many units must be started to allow for the loss due to scrap?
b. If the scrap rate for each step could be cut in half, how many units would this save in terms of the scrap allowance?
c. If the scrap represents a cost of $10 per unit, how much is it costing the company per day for the original scrap rate?
15. A teller window at a bank had the following service times (in minutes) for 20 randomly selected customers:
Samples
1 2 3 4
1 2 3 4
4.5 4.6 4.5 4.7
4.2 4.5 4.6 4.6
4.2 4.4 4.4 4.8
4.3 4.7 4.4 4.5
4.3 4.3 4.6 4.9
a. Determine the mean of each sample
b. If the process parameters are unknown, estimate its mean and standard deviation
c. Estimate the mean and the standard deviation of the sampling distribution.
d. What would three-sigma control limits for the process be? What alpha risk would they provide?
e. What alpha risk would control limits of 4.14 and 4.86 provide?
f. Using limits of 4.14 and 4.86, are any sample means beyond the control limits? If so, which one(s)?
g. Construct control charts for means and ranges using table 10.3 in the book. Are any samples beyond the control limits? If so, which ones?
h. Explain why control limits are different for means in parts d and g?
i. If the process has a known mean of 4.4 and a known standard deviation of 0.18, what would three-sigma control limits be for a mean chart? Are any sample means beyond the control limits? If so, which ones?
16. A process that produces computer chips has a mean of 0.03 defective chip and a standard deviation of 0.003 chip. The allowable variation is from 0.03 to 0.05 defective.
a. Compute the capability ratio for the process.
b. Is the process capable?
a. Compute the capability ratio for the process.
b. Is the process capable?
17. As part of an insurance company’s training program, participants learn how to conduct an analysis of clients’ insurability. The goal is to have participants achieve a time in the range of 30 to 45 minutes. Test results for three participants were as follows:
Name Mean Std. Deviation
Name Mean Std. Deviation
Armand 38 min. 3 min
Jerry 37 min 2.5 min
Melissa 37.5 min 1.8 min
a. Which of the participants would you judge to be capable? Explain.
b. Can the value of Cpk exceed the value of Cp for a given participant? Explain.
18. The Good Chocolate Company makes a variety of chocolate candies, including a 12-ounce chocolate bar (340 grams) and box of six 1-ounce chocolate bars (170 grams).
a. Specifications for the 12 ounce bar are 330 grams to 350 grams. What is the largest standard deviation (in grams) that the machine that fills the bar molds can have and still be considered if the average fill is 340 grams?
b. The machine that fills the bar molds for the 6-ounce bars has a standard deviation of 0.8 grams. The filling machine is set to deliver an average of 1.01 ounces per bar. Specifications for the 6-bar box are 160 to 180 grams. Is the process capable? (Variance for the box = 6 x bar variance)
c. What is the lowest setting in ounces for the filling machine that will provide capability in terms of the 6-bar box?
Acceptance Sampling
1. What is the purpose of acceptance sampling? How does it differ from process control?
2. What is an Operating Characteristic Curve, and how is it useful in acceptance sampling?
3. An assembly operation for trigger mechanism of semiautomatic spray gun produces a small percentage of defective mechanisms. Management must decide whether to continue the current practice of 100% inspection or to replace defective mechanisms after final assembly when all guns are inspected. Replacement at final assembly costs $30 each; inspection during trigger assembly costs $12 per hour of labour and overhead. The inspection rate is one trigger per minute.
a. Would 100% inspection during trigger assembly justified if there are (1) 4% defective? (2) 1% defective?
b. At what point would management be indifferent between 100% inspection of triggers and only final inspection?
4. Random samples of n=20 circuit breakers are tested for damage caused during shipment in each lot of 4000 received. Lots with more than one defective are pulled and subjected to 100% inspection.
a. Construct the OC cure for this sampling plan.
b. Construct the AOQ curve for this plan, assuming defectives found during 100% inspection are replaced with good parts. What is the approximate AOQL?
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