Q8. In a reliability test in the company, the time-to-failure values of ten mechanical items of...

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Q8. In a reliability test in the company, the time-to-failure values of ten mechanical items of the same design running under identical condition were recorded and are as given in the following table (Q8): Table Q8 Unit No. 1 Time to failure (hours) 1432 2 654 3" 1357 4" 737 5 350 6 478 7 1820 8 1056 964 561 9 10 * Units 3, 4 and 10 had not failed at the end of the test period. Using the median rank method for estimating the failure probability and assuming that the guaranteed life before failure is zero, a) b) c) d) Calculate and tabulate the median ranks for the data supplied. Plot the cumulative per cent failure versus time to failure on the Weibull graph paper supplied. Estimate the shape factor and the characteristic time to failure n for the distribution. Infer from the value of whether the failure is an early failure, a random failure or a wear-out failure. Estimate the reliability of an item at 1500 hours, its failure probability between 1500 and 1600 hours, and the probability that the item that is functional at 1500 hours will fail before reaching 1600 hours. Formulae that may be used for Question 8 are given below: New_increment= N+1-(Order_number_of_previous_failed_item) N+1-(Number_of_previous_items) Academic Year 2023/24 Order_number=New_increment + previous_order_number Median_rank= Order number-0.3 where N is the total number of items in the sample. N+0.4 6 Q8. In a reliability test in the company, the time-to-failure values of ten mechanical items of the same design running under identical condition were recorded and are as given in the following table (Q8): Table Q8 Unit No. 1 Time to failure (hours) 1432 2 654 3" 1357 4" 737 5 350 6 478 7 1820 8 1056 964 561 9 10 * Units 3, 4 and 10 had not failed at the end of the test period. Using the median rank method for estimating the failure probability and assuming that the guaranteed life before failure is zero, a) b) c) d) Calculate and tabulate the median ranks for the data supplied. Plot the cumulative per cent failure versus time to failure on the Weibull graph paper supplied. Estimate the shape factor and the characteristic time to failure n for the distribution. Infer from the value of whether the failure is an early failure, a random failure or a wear-out failure. Estimate the reliability of an item at 1500 hours, its failure probability between 1500 and 1600 hours, and the probability that the item that is functional at 1500 hours will fail before reaching 1600 hours. Formulae that may be used for Question 8 are given below: New_increment= N+1-(Order_number_of_previous_failed_item) N+1-(Number_of_previous_items) Academic Year 2023/24 Order_number=New_increment + previous_order_number Median_rank= Order number-0.3 where N is the total number of items in the sample. N+0.4 6