Assignment #5- stat final

docx

School

Lambton College *

*We aren’t endorsed by this school

Course

2004

Subject

Statistics

Date

Feb 20, 2024

Type

docx

Pages

Uploaded by mannnu123

Faculty of Business, Health & Technology Course Number QEM 2004 Section Number Group 2 Course Title Advanced Statistics Semester/Year 2 nd Sem/2023 Instructor Dr. Mohammed Mehdizadeh ASSIGNMENT No. 5 Assignment Title Acceptance Sampling Submission Date 14/12/2023 Due Date Student Name Student ID Signature* MANPREET SINGH C0895959 MS *By signing above you attest that you have contributed to this submission and confirm that all work you have contributed to this submission is your own work. Any suspicion of copying or plagiarism in this work will result in an investigation of Academic Misconduct and may result in a “0” on the work, an “F” in the course, or possibly more severe penalties. 1

Instructions: - Late submission may result in “0” mark for this assignment. - Submission via email is Not acceptable. - Please write your answers as clean and readable as possible on letter size papers. - Questions should be solved in detail to earn full mark. - Write your name and student ID as clean and readable as possible on the cover page. - Write name of all students in your group and one person per group submit the assignment Problem a) Find a single-sampling plan for which p 1 = 0.01, alpha = 0.03, p 2 = 0.18, and beta = 0.11 and Lot size is 3000. Answer) Measurement type: Go/no go Lot quality in proportion defective Lot size: 3000 Use binomial distribution to calculate probability of acceptance Method Acceptable Quality Level (AQL) 0.01 Producer’s Risk (α) 0.03 Rejectable Quality Level (RQL or LTPD) 0.18 Consumer’s Risk (β) 0.11 Generated Plan(s) Sample Size 20 Acceptance Number 1 Accept lot if defective items in 20 sampled ≤ 1; Otherwise reject. Proportion Defective Probability Accepting Probability Rejecting AOQ ATI 0.01 0.983 0.017 0.00977 70.2 0.18 0.102 0.898 0.01821 2696.5 2

Average Outgoing Quality Limit(s) (AOQL) AOQL At Proportion Defective 0.04110 0.07747 3

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

b) Find a single-sampling plan for which p 1 = 0.01, alpha = 0.05, p 2 = 0.15, and beta = 0.15 Answer) Measurement type: Go/no go Lot quality in proportion defective Lot size: 3000 Use binomial distribution to calculate probability of acceptance 4

Method Acceptable Quality Level (AQL) 0.01 Producer’s Risk (α) 0.05 Rejectable Quality Level (RQL or LTPD) 0.15 Consumer’s Risk (β) 0.15 Generated Plan(s) Sample Size 22 Acceptance Number 1 Accept lot if defective items in 22 sampled ≤ 1; Otherwise reject. Proportion Defective Probability Accepting Probability Rejecting AOQ ATI 0.01 0.980 0.020 0.00973 82.2 0.15 0.137 0.863 0.02036 2592.8 Average Outgoing Quality Limit(s) (AOQL) AOQL At Proportion Defective 0.03739 0.07069 5

c) Draw the OC curve for this part and find the level of lot quality ( p ) that will be rejected 90% of the time Answer) Method Acceptable Quality Level (AQL) 0.01 Producer’s Risk (α) 0.03 Rejectable Quality Level (RQL or LTPD) 0.18 Consumer’s Risk (β) 0.11 Generated Plan(s) Sample Size 20 Acceptance Number 1 6

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Accept lot if defective items in 20 sampled ≤ 1; Otherwise reject. Proportio n Defective Probability Accepting Probability Rejecting AOQ ATI 0.010 0.983 0.017 0.00977 70.2 0.180 0.102 0.898 0.01821 2696.5 0.181 0.100 0.900 0.01797 2702.2 Average Outgoing Quality Limit(s) (AOQL) AOQL At Proportion Defective 0.04110 0.07747 7

We used the pa vs. p graph to measure the lot quality level (p). The discovery of a 90% rejection rate suggests that p(a) ought to be 0.10. As a result, a line drawn from p(a) = 0.1 extrapolates to the graph and, upon repeating at the top, to a neighbouring number. Use Minitab to get the precise amount. As a result, Minitab gives us the wrong percentage, 0.181. A 0.900 rejection probability and a 0.100 p(a) will be present. Consequently, for the 0.900 rejection, p will have a value of 0.181. d) Draw the OC curve for this part b and find the level of lot quality ( p ) that will be rejected 90% of the time. Answer) Method Acceptable Quality Level (AQL) 0.01 Producer’s Risk (α) 0.05 Rejectable Quality Level (RQL or LTPD) 0.15 Consumer’s Risk (β) 0.15 Generated Plan(s) Sample Size 22 Acceptance Number 1 Accept lot if defective items in 22 sampled ≤ 1; Otherwise reject. Proportio n Defective Probability Accepting Probability Rejecting AOQ ATI 0.0100 0.980 0.020 0.00973 82.2 0.1500 0.137 0.863 0.02036 2592.8 0.1655 0.100 0.900 0.01646 2701.7 8

We used the pa vs. p graph to measure the lot quality level (p). The discovery of a 90% rejection rate suggests that p(a) ought to be 0.10. Thus, we can get a number that is close by by drawing a line from p(a) = 0.1 to the graph and back to p. Use Minitab to get the precise amount. Minitab indicates that the incorrect percent is 0.1655. A 0.900 rejection probability and a 0.100 p(a) will be present. Consequently, the value of p for the 0.900 rejection will be 0.1655. In this case, a lot size of 3000 was utilized. e) For sample size and the acceptance of part a and p=0.02, what are AOQ and ATI? Answer) 9

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

f) Find a single-sampling plan for which p 1 = 0.01, alpha = 0.05, p 2 = 0.17, and beta = 0.15 and Lot size is 5000. what are AOQ and ATI? 10

Answer) Measurement type: Go/no go Lot quality in proportion defective Lot size: 5000 Use binomial distribution to calculate probability of acceptance Method Acceptable Quality Level (AQL) 0.01 Producer’s Risk (α) 0.05 Rejectable Quality Level (RQL or LTPD) 0.17 Consumer’s Risk (β) 0.15 Generated Plan(s) Sample Size 19 Acceptance Number 1 Accept lot if defective items in 19 sampled ≤ 1; Otherwise reject. Proportio n Defective Probability Accepting Probability Rejecting AOQ ATI 0.01 0.985 0.015 0.00981 95.1 0.17 0.142 0.858 0.02403 4293.3 Average Outgoing Quality Limit(s) (AOQL) AOQL At Proportion Defective 0.04336 0.08136 11