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Problem 1. In business and educational settings, computer pr…

Problem 1. In business and educational settings, computer presentations use liquid crystal display (LCD) projectors. The most common failure mode of these projectors is the failure of the lamp and many projector manufacturers include the expected lamp life in their technical specification documents. A manufacturer clams that users can expect 500 hours of projection time for each lamp used under normal operating conditions. To test this claim, a public university placed identical lamps in 3 projector models supplied by this manufacturer and tested a total of 10 projectors. A university staff recorded the projector’s working hours before each lamp burned out. LCD Model Projection Hours LCD Model Projection Hours LCD Model Projection Hours 1 182 2 332 3 280 1 244 2 418 3 360 1 387 2 584     1 600+ (censored) 2 600+ (censored)       Failure Time # of Parts at Risk R(t) 182 10   244 9   280 8   332 7   360 6   387 5   418 4   584 3   600+ 2   a. Use the Kaplan-Meier method to compute the reliability value of the last column in the table above. (5 points) b. Assume failure times follow an exponential distribution with failure rate λ. Derive the likelihood function for this dataset. (10 points) c. Calculate the failure rate value. (5 points) d. Taking a closer look at this dataset, it seems that the lamps of LCD Model 2 have consistently longer lives than the lamps of the other two models. As a reliability engineer, what is your suggestion to make a further investigation of this suspicion? Please utilize the discussions in the Ford Case Study to suggest some reliability analysis and reliability comparison tools. (10 points)