Assignment 10 (Solution) 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.

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 Design of an experiment is too sensitive. What will the designer will do to plan for the unexpected? a) Best case scenario b) Optimal case scenario c) Worst case scenario d) None of these

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

Answer: b (2.0944) Solution 3 Mean = μ = x 1+x 2. +x 12 12 = 12+15.+57 12 = 31.66667 The standard deviation is given by σ = 1 1 n i=1 = n 1 (x i μ) 2 12 (x 12 1 i=1 i 31.66667) 2 = 15.11973 Signal to noise ratio = μ σ = 31.66667 15.11973 = 2.0944

Question 4 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

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 = 2DC p Where D = Annual Demand Cp = Cost to place a single order C h = Cost to hold one unit inventory for a year EOQ = Solution 4 C h 2DC p = 2 16000 3000 C h 150 = 800 units

Question 5 Which of the following is a 4-level array in the Taguchi s Orthogonal Array Table? a) L 4 (2 3 ) b) L 27 (3 13 ) c) L 25 (5 6 ) d) L 16 (4 5 )

Solution 5 Answer: d (L 16 (4 5 )) Taguchi s OA-based Experimental Design Matrix Notation L N (2 k ) Number of Factors Total Number of Runs 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

Answer: a (15.893) Solution 7 To maximize robustness, when Target performance is the best, Taguchi uses the signal to noise ratio SN t = 10 log( y2 s 2) When response is to be maximized, Taguchi uses 1 y SN t = 10 log( 2 n ) When response is to be minimized, Taguchi uses y 2 SN t = 10 log( 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: x 1 = 654532 x 2 = 239285 x 3 = 871201 x 4 = 418594 Which gene has the minimum fitness using Genetic Algorithm? a) x 1 b) x 2 c) x 3 d) x 4

Solution 14 Answer: c (x 3 ) f(x 1 )= 4 6 + 3 2 5 + 4 2 5 + 5 3 = 26 f(x 2 )= 4 2 + 3 5 3 + 9 2 2 + 5 8 = 47 f(x 3 )= 4 8 + 3 1 7 + 1 2 2 + 5 0 = 23 f(x 4 )= 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