Assignment 7 (Solution) Control Charts, Process capability and QFD

Transcription

1 Assignment 7 (Solution) Control Charts, Process capability and QFD Dr. Jitesh J. Thakkar Department of Industrial and Systems Engineering Indian Institute of Technology Kharagpur

2 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.

3 Question 1 What are the control limits of p-chart for the following data of 20 samples of 100 pairs of jeans? Sample Number of defectives Proportion Defectives Total 180 a) UCL = and LCL = b) UCL = and LCL = c) UCL = and LCL = d) UCL = and LCL =

4 Solution 1 Answer: b (UCL = and LCL = ) p = Total Defectives Total Sample observation = = 0.09 UCL = p + z p (1 p ) n = (1 0.09) 100 = LCL = p z p 1 p n = (1 0.09) =

5 Question 2 A hospital manager receives a certain number of complaints each day about the hospitals service. Complaints for 15 days are given in the table shown. What are the control limits when one will construct a control chart using three sigma limits? a) UCL and LCL are 5±3 5 b) UCL = 0 and LCL = c) UCL = and LCL = 0 d) None of these

6 Days Table of Question 2 Number of complaints D3ays Number of complaints Total 75

7 Solution 2 Answer: c (UCL = and LCL = 0) Total defects c = = 75 Samples 15 = 5 UCL = c + z c = = LCL = c z c = = If LCL is negative then it is taken as zero.

8 Common Data Question (Question 3 & 4)

9 Common data Question The following data is a common data given for x-bar and range chart calculations in Question Number 3 and 4. Sample 1 Sample 2 Sample 3 Sample 4 Sample x-bar R

10 Data Sample Size = m A 2 A 3 d 2 D 3 D 4 B 3 B

11 Question 3 What is the value of central line and UCL for Range chart? a) Central Line = 3.25 and UCL = 4.68 b) Central Line = 5.24 and UCL = c) Central Line = 4.71 and UCL = d) Central Line = 4.68 and UCL =

12 Solution 3 Answer: d (Central Line = 4.68 and UCL = ) Central Line = R = 5 i=1 n R i = = 4.68 UCL = D 4 R = = Here sample size is 3 so value of D 4 from chart is

13 Question 4 What will be the lower control limit for x-bar chart for the previous problem? a) b) c) d) None of these

14 Answer: a (10.51) x = x = n i=1 n k i=1 k X i x i Solution 4, where n is the number of observations, where k is the number of subgroups UCL = x + A 2 R LCL = x A 2 R By putting the values we will get LCL = approximately.

15 Question 5 p Charts calculate the percent defective in a sample whereas c Charts counts number of defects in item. a) True b) False

16 Answer: a (True) Solution 5 Described in the video lecture

17 Question 6 A is an attributes control chart used with data collected in sub groups of varying size. Fill in the blank with appropriate option. a) C chart b) P chart c) U chart d) NP chart

18 Solution 6 Answer: c (U chart) A u-chart is an attributes control chart used with data collected in subgroups of varying sizes. U- charts show how the process, measured by the number of nonconformities per item or group of items, changes over time. Nonconformities are defects or occurrences found in the sampled subgroup.

19 Question 7 What is the importance of the capability analysis? a) Capability analysis determines whether the inherent variability of the process output fails within the acceptable range of the variability allowed by the design specifications for the process output. b) Capability analysis determines whether the invariability of the process output fails within the acceptable range of the variability allowed by the design specifications for the process output. c) Both of the above d) None of the above

20 Solution 7 Answer: a Capability analysis determines whether the inherent variability of the process output fails within the acceptable range of the variability allowed by the design specifications for the process output.

21 Question 8 Process Capability Analysis differs fundamentally from control charting because a) It focuses on improvement not control b) It focuses on variable not attribute, data involved c) Capability study address range of individual outputs d) All of the above

22 Solution 8 Answer: d (All of the above) Process Capability Analysis differs fundamentally from control charting because It focuses on improvement not control It focuses on variable not attribute, data involved Capability study address range of individual outputs Control charting addresses ranges of sample measures

23 Question 9 For a process the upper specification limit is 18.5 and the lower specification limit is 12.5 with a standard deviation of What will be the process capability ratio of the process for six sigma process? a) b) c) d) 1.828

24 Solution 9 Answer: b (1.724) Process capability ratio = C p = USL LSL 6σ = Here USL = Upper Specification Limit LSL = Lower Specification Limit =

25 Question 10 We are studying two processes for machining a part. Process A produces parts which have a mean length of 150 and a standard deviation of 3. Process B produces parts which have a mean length of 155 and standard deviation of 1. The design specifications for the part are 150±10. Data given is for Z = area under the standard normal curve to the left of Z will be What will be the value of process capability ratio for process B and C pk for process A? a) and respectively b) and respectively c) and respectively d) None of these

26 Solution 10 Answer: b (3.333 and respectively) Process capability ratio for B = C p = USL LSL = USL μ μ LSL C pk for A = min, 3σ 3σ = min, σ = = 1.111

27 Question 11 Which of the following statements are wrong? I. Natural variation exceeds design specifications: process is not capable of meeting specification all the time. II. Design specification and natural variations are same: process is capable of meeting specification most of the time. a) Only I b) Only II c) Both I and II d) None of these

28 Solution 11 Answer: d (None of these) Both the statements are correct statements

29 Question 12 What QFD (Quality Function Deployment) do? a) QFD develop and manufacture towards measured goals. b) QFD gives passive reaction to customer goals. c) QFD optimises products and processes. d) None of these

30 Solution 12 Answer: a and c QFD (Quality Function Deployment) - Listens to e the customer. - develop and manufacture towards measured goals. - optimises products and processes.

31 Question 13 Twenty samples of size 4 are taken from a stable process. The average means of the sample means is 42.5, and the average range of the samples is 1.5. What is the UCL for the R-chart? a) 0.00 b) c) d) 43.37

32 Solution 13 Answer: c (3.423) Average of Ranges of 20 samples = R = chart) 20 i=1 20 R = 1.5 ( Central Line for R Upper Control Limit of R Chart = D 4 R = = (D 4 = for sample size 4)

33 Question 14 What causes design to fail? a) Not enough basic knowledge at hand when a design project starts b) Too little activity in the beginning of the project c) Bad and/or non existing demand specifications d) All of these

34 Solution 14 Answer: d (All of these) The following are the causes of designs to fail: - Not enough basic knowledge at hand when a design project start - Corporate Management view is to simplistic - Too little activity in the beginning of the project - Unspecified demands and constraints - Bad and/or non existing demand specifications - Time is not enough to be thorough - Unrealistic time frames - Bad co-operation between marketing/customer design, engineering and manufacturing

35 Question 15 What is the roof of the house of quality in QFD indicates? a) Relationship Matrix b) Co-relationship Matrix c) Conflict Matrix d) Target Specification

36 Solution 15 Answer: b and c ( Co-relationship Matrix and Conflict Matrix)

37 Thank you