讲解：Faulty Phones、R、R、ModellingR|SQL

Course work: Faulty PhonesBackgroundThe famous technology company, Apricot, is selling phones with a life-time warranty. With thiswarranty, Apricot promises to repair faulty phones or replace them free of charge. To maximize theirprofits, Apricot has asked you for a report and a set of recommendations on the best strategy for thiswarranty scheme. The main consideration that should be addressed in the report is cost of the scheme.Modelling AssumptionsYou are asked to make the following modelling assumptions in your analysis:• In any given day, assuming a phone has had i faults (for i=0,1,2,...,n−1) the probability ofhaving another fault is p, independently of all previous days, and the new fault is to be repairedwith probability qi+1 within the same day.• If a phone is not repaired, it is replaced instead.• If a phone has its n’th fault it is immediately replaced.• The expected cost to Apricot to repair the i’th fault of a phone is £(q×100×2i).• Replacing a phone costs Apricot £R.• Apricot’s products fall into one of three classes:1. Low quality - n=3, R=410, p=5×10−4for 25% of the production line.2. Medium quality - n=4, R=850, p=2×10−4, for 52% of the production line.3. High quality - n=4, R=950, p=10−4, for 23% of production line.• Replacement phones initially have zero faults and are subject to the same warranty.• Replacement phones always have the same quality class as the originals.• The probability of experiencing more than one fault within a single day is sufficiently smalland is to be ignored.Points to addressApricot is interested in understanding the expected daily cost of the warranty scheme for every phoneand the optimal replacement strategy. In particular, Apricot can invest in its maintenance departmentto increase q, which increases the proportion of faults that can be repaired but also increases theaverage repair cost.You are to compute the expected daily costs for each of the three quality classes. First, report thesecosts for q=0.8 then produce plots showing the expected total daily costs for all values of q from0 to 1 and each of the three quality classes. Lastly, recommend the best value of q, up to an errorof 1%, in two cases:• Different values may be used for different quality classes to optimize the total cost of each class;• The same value is to be used in all quality classes to optimize the total cost;and report on the total expected daily costs in each case.Finally, suppose that the replacement phone is picked randomly from the production line so thatthe quality of the replacement is not necessarily the same as the original, write down the transitionprobability matrix of the Markov chain that you would use for this case.HINT: Write down the transition probability matrix for a Markov chain whose current staterepresents the number of faults a customeFaulty Phones代做、R编程设计调试、R语言代写、r’s phone has experienced (and had repaired) up to thecurrent day. Compute the stationary distribution of this Markov chain, and then compute the longterm average cost of the scheme.Further Points to Note• Collaboration and Plagiarism: Students are allowed to discuss the methods used withother students, but your submitted project must be all your own work. Particularly pleasenote the following:– Coursework reports must be written in a student’s own words and any code in theircoursework must be their own code. If some text or code in the coursework has beentaken from other sources, these sources must be properly referenced.– Failure to reference work that has been obtained from other sources or to copy the wordsand/or code of another student is plagiarism and if detected, this will be reported to theSchool’s Discipline Committee. If a student is found guilty of plagiarism, the penaltycould involve voiding the course.– Students must never give hard or soft copies of their coursework reports or code to anotherstudent. Students must always refuse any request from another student for a copy oftheir report and/or code.– Sharing a coursework report and/or code with another student is collusion, and if detected,this will be reported to the School’s Discipline Committee. If found guilty of collusion,the penalty could involve voiding the course.– Further information: https://www.hw.ac.uk/students/doc/plagiarismguide.pdf.• Submission: The report should be submitted through Vision using Turnitin. It should not besubmitted by email or handed in as a paper copy.• Deadline: The deadline for submission is 3:30 pm on Monday, November 4th (local time);projects may be submitted early. Late projects will be marked in line with the UniversityCoursework Policy.• Assessment This coursework will contribute 10% to the final mark for the course. Thiscoursework will be marked using the marking rubric found in the same folder as this project onVISION.• Feedback Marks and feedback for the project will be available from Monday, November 18th.Report SpecificationThe report should meet the following specifications:1. The report must be typed.2. The report must not be more than three sides of A4 including graphs and tables, but notincluding the Appendix.3. The report must not contain any R code or your calculations.4. The report should give the results of the analyses that have been carried out and your commentson and conclusions from these results, but should be as readable as possible by non-specialists.5. The Appendix must contain all code and workings for all calculations in your analysis. Itshould also include the definition of the Markov chain(s) you are using for the model and thecorresponding P matrices.6. Note this report is for a group of non-specialists and so should be understandable by them.转自：http://www.3daixie.com/contents/11/3444.html