six sigma in supply chain, taguchi method and robust design

Assignment 10

(Solution) Six Sigma in Supply Chain, Taguchi Method

and Robust Design

Dr. Jitesh J. Thakkar

Department of Industrial and Systems Engineering

Indian Institute of Technology Kharagpur

Instruction

• Total No. of Questions: 15. Each question carries one point.

• All questions are objective type. In some of the questions, more than one answers are correct.

• This assignment includes true/false statement questions.

Dr. Jitesh J. Thakkar, IIT Kharagpur

Question 1

Birla Tyres purchases rims from DEL Ltd. an external supplier.

DEL Ltd. takes 10 days in manufacturing and delivering an order.

Birla Tyres requires 10,000 units of rims annually. Its ordering

cost is Rs 60,000.00 per order and its carrying costs are Rs 180.00

per unit per year. The maximum usage per day could be 50 per

day. What will be reorder level and safety stock?


a) 274 and 400 respectively

b) 226 and 500 respectively

c) 400 and 274 respectively

d) 500 and 226 respectively

Solution 1

Answer: d (500 and 226) • EOQ = Sqrt (2×Annual Demand×Ordering cost per

unit/Carrying cost per unit)

• Maximum daily usage is 50 units and average daily usage is 27.4 (10,000 annual demand ÷ 365 days).

• Safety Stock = (Maximum daily usage – average daily usage) × Lead Time = (50-27.4) × 10 = 226 units.

• Reorder Level = Safety Stock + Average Daily Usage × Lead Time

• Reorder Level = 226 units + 27.4 units × 10 = 500 units.


Question 2

a) Best case scenario

b) Optimal case scenario

c) Worst case scenario

d) None of these

A Design of an experiment is too sensitive. What

will the designer will do to plan for the

unexpected?


Solution 2


Answer: c (Worst case scenario)

A worst-case scenario is a concept in

robust design wherein the planner, in

planning for potential disasters, considers

the most severe possible outcome that can

reasonably be projected to occur in a

given situation.

Question 3

Taguchi’s robust design uses certain data which are as follows 12, 15, 18, 20, 22, 27, 32, 38, 40, 46, 53, and 57. What will be the SN ratio for the design process?

a) 1.5854

b) 2.0944

c) 2.7854

d) 3.1466


Solution 3

Answer: b (2.0944)


• Mean = 𝜇 =𝑥1+𝑥2.…+𝑥12

12=

12+15….+57

12= 31.66667

• The standard deviation is given by

𝜎 =1

𝑛−1× (𝑥𝑖 − 𝜇)2𝑛

𝑖=1 =

1

12−1× (𝑥𝑖 − 31.66667)212

𝑖=1 = 15.11973

• Signal to noise ratio = 𝜇

𝜎=

31.66667

15.11973= 2.0944

Indian Cricket Association runs a mail-order

business for cricket kit equipment. Annual

demand for cricket bat is 16000. The annual

holding cost per unit is Rs 150.00 and the cost to

place an order is Rs 3000.00. What will be

economic order quantity?

a) 600

b) 700

c) 800

d) 900

Question 4


Answer: c (800) • Best quantity to order for maximum profit is the Economic

Order Quantity (EOQ)

• To calculate EOQ the following formula is used.

𝑬𝑶𝑸 =𝟐𝑫𝑪𝒑

𝑪𝒉

• Where D = Annual Demand

• 𝑪𝒑 = Cost to place a single order

• 𝑪𝒉 = Cost to hold one unit inventory for a year

𝑬𝑶𝑸 =𝟐𝑫𝑪𝒑

𝑪𝒉 =

𝟐×𝟏𝟔𝟎𝟎𝟎×𝟑𝟎𝟎𝟎

𝟏𝟓𝟎= 𝟖𝟎𝟎 𝒖𝒏𝒊𝒕𝒔

Solution 4


Which of the following is a 4-level array in the

Taguchi’s Orthogonal Array Table?

Question 5

a) 𝐿4(23)

b) 𝐿27(313)

c) 𝐿25(56)

d) 𝐿16(45)


Solution 5

Answer: d (𝐿16(45))

Taguchi’s OA-based Experimental Design

Matrix Notation

𝐿𝑁(2

𝑘)


Total Number of Runs

Number of Factors

Number of Levels per Factor

Question 6

A push/pull view of the supply chain categorizes

processes based on whether they are initiated in

response to a customer order (pull) or in

anticipation of a customer order (push). This

view is very useful when considering strategic

decisions relating to supply chain design.


a) True

b) False

Solution 6

Answer: a (True)


A push/pull view of the supply chain categorizes

processes based on whether they are initiated in

response to a customer order (pull) or in

anticipation of a customer order (push). This

view is very useful when considering strategic

decisions relating to supply chain design.

Question 7

For a sample of data given below what will

be the SN ratio when response is to be

maximized by Taguchi?

2, 5, 7, 11, 14, 18, 21, 24, 26, 29, 30, 34, 37

a) 15.893

b) 16.358

c) 16.478

d) None of these Dr. Jitesh J. Thakkar, IIT Kharagpur

Solution 7 Answer: a (15.893) • To maximize robustness, when Target performance is the best, Taguchi uses

the signal to noise ratio

𝑆𝑁𝑡 = −10 log(𝑦 2

𝑠2)

• When response is to be maximized, Taguchi uses

𝑆𝑁𝑡 = −10 log(

1𝑦2

𝑛)

• When response is to be minimized, Taguchi uses

𝑆𝑁𝑡 = −10 log( 𝑦2

𝑛)

• Here response maximised formula is used and the by doing

calculation we get 15.893 as the SN ratio.


Question 8

What are Taguchi’s contributions?

a) Quality Engineering Philosophy – Targets

and Loss functions

b) Methodology – System, Parameter, Tolerance

design steps

c) Experimental Design – use of Orthogonal

arrays

d) All are correct.


Solution 8

Answer: d (All are correct)


The following are Taguchi’s Contributions: a) Quality Engineering Philosophy – Targets and

Loss functions

b) Methodology – System, Parameter, Tolerance

design steps

c) Experimental Design – use of Orthogonal

arrays

d) Analysis – use Signal-to-Noise (S/N ratios)

Question 9

The cost of scrapping a part is Rs 13.00

when it deteriorates from a target by ±0.25

mm. what will be the quality loss

coefficient if the target value for the

product’s response is 1.5 mm?

a) 8.32

b) 16.54

c) 29.92

d) 35.46


Solution 9

Answer: a (8.32) • The most common quadratic loss function is in the

form of : 𝐿 = 𝑘(𝑦 − 𝑚)2

• Where – L: Total loss due to deviation from target

– m: Target value for the product response

– k: Quality loss co-efficient

– y: Random variable of interest

• Here L = 13.00

• y = 0.25

• m = 1.5

• Putting these values in the equation, we get k = 8.32


Question 10

Which is not an assumption taken while

calculating Economic Order Quantity (EOQ)?

a) The ordering cost is constant.

b) The rate of demand is random.

c) The lead time is fixed.

d) The replenishment is made instantaneously;

the whole batch is delivered at once.


Solution 10 Answer: b The following are some of the assumptions while calculating Economic Order Quantity (EOQ): The ordering cost is constant.

The rate of demand is constant.

The lead time is fixed.

The purchase price of the item is constant i.e. no discount is available.

The replenishment is made instantaneously, the whole batch is delivered at once.


Question 11

A great deal of inventory piles up along the

supply chain due to

a) Good quality of suppliers – production may go

rapidly.

b) Poor management of logistics and not monitoring

the lead time.

c) Machine breakdown resulting from poor quality

culture causing production interruption.

d) Quality of finished products may be high causing

no need to inspect and waist time.


Solution 11

Answer: b and c A great deal of inventory piles up along the supply chain due to

Poor quality of suppliers – production may stop if there are no materials and parts in the buffer stock.

Poor management of logistics and not monitoring the lead time.

Machine breakdown resulting from poor quality culture causing production interruption – again buffers are needed.

Quality of finished products may not be high enough to support JIT models of operations in your customer’s operations.


Question 12 Taguchi focused on off-Line Quality Control. What is the meaning of off-Line Quality Control?

a) A commitment to quality that goes beyond internal

company issues to suppliers and customers

b) None of these.

c) Improving quality and reducing costs in the

product or process at the production stage.

d) Improving quality and reducing costs in the

product or process at the design stage.


Solution 12

Answer: d


Off-line quality control methods are quality and

cost control activities conducted at the product

and process design stages to improve product

manufacturability and reliability, and to reduce

product development and lifetime costs.

Parameter design is an off-line quality

control method.

Question 13 By Minimizing SN ratio one can maximize

robustness of a design.

a) True

b) False

c) None of these


Solution 13

Answer: b (False) • By maximizing SN ratio one can maximize

Robustness of a design.

• Smallest sensitivity to noise gives better

Robustness of a design.


Question 14 Suppose a genetic algorithm uses chromosomes of the form x = abcdef with a fixed length of six genes. Each gene can be any digit between 0 and 9. Let the fitness of individual x be calculated as:

𝑓 𝑥 = 4𝑎 + 3𝑓 − 𝑏 + 𝑐 − 2𝑑 + 5𝑒

Let the initial population consist of four individuals with the following chromosomes:

𝑥1 = 654532

𝑥2 = 239285

𝑥3 = 871201

𝑥4 = 418594

Which gene has the minimum fitness using Genetic Algorithm?


a) 𝑥1

b) 𝑥2

c) 𝑥3

d) 𝑥4

Solution 14

Answer: c (𝑥3) 𝑓(𝑥1)= 4 × 6 + 3 × 2 − 5 + 4 − 2 × 5 + 5 × 3 = 26

𝑓(𝑥2)= 4 × 2 + 3 × 5 − 3 + 9 − 2 × 2 + 5 × 8 = 47

𝑓(𝑥3)= 4 × 8 + 3 × 1 − 7 + 1 − 2 × 2 + 5 × 0 = 23

𝑓(𝑥4)= 4 × 4 + 3 × 4 − 1 + 8 − 2 × 5 + 5 × 9 = 54

The lowest value has minimum fitness and

the highest value has the maximum fitness.


Question 15

Which of the following is a Noise factor of

Taguchi’s robust design?

a) Operating Temperature

b) Position of the gas pedal

c) Dimensions of parts

d) Deposition time in silicon wafer fabrication


Solution 15 Answer: a Control Factors :–Design factors that are to be set at optimal

levels to improve quality and reduce sensitivity to noise –

Dimensions of parts, type of material, etc.

Noise Factors :–Factors that represent the noise that is

expected in production or in use – Dimensional variation,

Operating Temperature, etc.

Adjustment Factor :– Affects the mean but not the variance of

a response – Deposition time in silicon wafer fabrication.

Signal Factors :– Set by the user to communicate desires of

the user – Position of the gas pedal


Thank you

Dr. J

itesh

J. T

ha

kka

r, IIT K

ha

ragp

ur

six sigma in supply chain, taguchi method and robust design

Documents