A B E F. G I J 1 All failure times are in operating hours Motor Drive Mechanism Electronics 2 Failure Number 3 1 1 116 8 4 2 1 15 19 5 3 1 6 4 15 208 219 221 224 255 7 5 16 37 59 62 8 6 21 9 7 22 260 83 10 8 25 292 11 9 41 293 42 12 13 95 114 169 191 199 232 44 14 46 12 13 15 52 344 347 352 359 359 366 366 369 16 66 259 17 281 68 93 18 16 19 17 118 130 20 381 18 19 21 134 382 22 388 20 21 136 147 23 399 24 22 179 25 23 24 227 269 26 27 28 Forty-eight motors were subject to a reliability test for 400 operating hours 29 36 drive mechanisms were independently tested for 400 operating hours 30 The electronic component subsystem was tested in which 20 component subsystems were operated until 15 failures were generated The Hooper Company manufactures several different vacuum cleaners. One model that the company is particularly proud of is the Hooper WG-7024 Self-Propelled Upright Vacuum called the Wind Gust. The Wind Gust has a 3M Filtrete HEPA filter bag that is part of the highly- efficient 3M Filtrete System, a 15 cleaning width with dual brush agitator, an attached deluxe- stretch hose, multiple height adjustments, a 31-ft power cord with quick cord release, fingertip on/off controls, a full bag indicator, and a full one-year warranty. From a design perspective, the Wind Gust consists of four primary subsystems: (1) the frame and housing, including the Fitration (bag) components, (2) the motor, (3) the drive mechanism, and (4) the electronics. It is only the last three subsystems that are of a reliability concern. It is estimated that the typical user of an upright vacuum will operate the appliance an average of 58 minutes a week or approximately 50 hours a year. The warranty agreement requires Hooper to replace the entire vacuum cleaner at cost regardless of the failure mode. Replacement cost is estimated to be $285 including shipping costs and allowing for factory restoration of the failed unit. Forty-eight motors were subject to a reliability test for 400 operating hours and 36 drive mechanisms were independently tested for 400 operating hours. The electronic component subsystem was also subject to a reliability test in which 20 component subsystems were operated until 15 failures were generated. The results of the testing for each of the three components is in the spreadsheet titled "Case Study 3 dataset". (a) Complete the following table by selecting the distribution that has the best R2 value when performing a least-squares analysis. Use operating hours as the unit of time. Consider only the exponential, Weibull, normal, and lognormal distributions in your analysis. Subsystem Failure distribution Least-square parameter estimates MTTF based on least-square estimates Motor Drive Mechanism Electronics (b) Assuming that all subsystems are independent of each other, compute the following performance mcasurements for the entire vacuum cleaner system: (i) R(I year) (ii) R(5 years) (11)Median number of years to failure (iv)90 percent design life in operating hours (1) Expected warranty cost per unit (c) In order to improve the overall product reliability, the Hooper Company CEO has mandated that the following initiatives be taken: Motor: The motor is purchased from a small company that has been experiencing manufacturing problems. All motors sold to Hooper must now undergo factory burn-in testing in order to achieve 90 percent reliability at 50 customer operating hours. Any units that fail during burn-in are rejected. Drive Mechanism: The primary failure mode is early wearout of the drive belts. By implementing statistical process control during drive belt production, Hooper can reduce variability (ie, the standard deviation of the failure times) by 25 percent while not impacting the MTTE. Electronies: The primary failure mode is opens in the electrical wiring at specific high-stress points due to repeated bending, twisting, and other strains of the wiring. In order to reduce the number of such failures, duplicate (parallel) wiring has been installed in critical locations. This has the effect of making the electronics subsystem behave in an active redundant manner. Assuming that all corrective actions have been implemented, repeat part (b) and compute new system performance measurements. A B E F. G I J 1 All failure times are in operating hours Motor Drive Mechanism Electronics 2 Failure Number 3 1 1 116 8 4 2 1 15 19 5 3 1 6 4 15 208 219 221 224 255 7 5 16 37 59 62 8 6 21 9 7 22 260 83 10 8 25 292 11 9 41 293 42 12 13 95 114 169 191 199 232 44 14 46 12 13 15 52 344 347 352 359 359 366 366 369 16 66 259 17 281 68 93 18 16 19 17 118 130 20 381 18 19 21 134 382 22 388 20 21 136 147 23 399 24 22 179 25 23 24 227 269 26 27 28 Forty-eight motors were subject to a reliability test for 400 operating hours 29 36 drive mechanisms were independently tested for 400 operating hours 30 The electronic component subsystem was tested in which 20 component subsystems were operated until 15 failures were generated The Hooper Company manufactures several different vacuum cleaners. One model that the company is particularly proud of is the Hooper WG-7024 Self-Propelled Upright Vacuum called the Wind Gust. The Wind Gust has a 3M Filtrete HEPA filter bag that is part of the highly- efficient 3M Filtrete System, a 15 cleaning width with dual brush agitator, an attached deluxe- stretch hose, multiple height adjustments, a 31-ft power cord with quick cord release, fingertip on/off controls, a full bag indicator, and a full one-year warranty. From a design perspective, the Wind Gust consists of four primary subsystems: (1) the frame and housing, including the Fitration (bag) components, (2) the motor, (3) the drive mechanism, and (4) the electronics. It is only the last three subsystems that are of a reliability concern. It is estimated that the typical user of an upright vacuum will operate the appliance an average of 58 minutes a week or approximately 50 hours a year. The warranty agreement requires Hooper to replace the entire vacuum cleaner at cost regardless of the failure mode. Replacement cost is estimated to be $285 including shipping costs and allowing for factory restoration of the failed unit. Forty-eight motors were subject to a reliability test for 400 operating hours and 36 drive mechanisms were independently tested for 400 operating hours. The electronic component subsystem was also subject to a reliability test in which 20 component subsystems were operated until 15 failures were generated. The results of the testing for each of the three components is in the spreadsheet titled "Case Study 3 dataset". (a) Complete the following table by selecting the distribution that has the best R2 value when performing a least-squares analysis. Use operating hours as the unit of time. Consider only the exponential, Weibull, normal, and lognormal distributions in your analysis. Subsystem Failure distribution Least-square parameter estimates MTTF based on least-square estimates Motor Drive Mechanism Electronics (b) Assuming that all subsystems are independent of each other, compute the following performance mcasurements for the entire vacuum cleaner system: (i) R(I year) (ii) R(5 years) (11)Median number of years to failure (iv)90 percent design life in operating hours (1) Expected warranty cost per unit (c) In order to improve the overall product reliability, the Hooper Company CEO has mandated that the following initiatives be taken: Motor: The motor is purchased from a small company that has been experiencing manufacturing problems. All motors sold to Hooper must now undergo factory burn-in testing in order to achieve 90 percent reliability at 50 customer operating hours. Any units that fail during burn-in are rejected. Drive Mechanism: The primary failure mode is early wearout of the drive belts. By implementing statistical process control during drive belt production, Hooper can reduce variability (ie, the standard deviation of the failure times) by 25 percent while not impacting the MTTE. Electronies: The primary failure mode is opens in the electrical wiring at specific high-stress points due to repeated bending, twisting, and other strains of the wiring. In order to reduce the number of such failures, duplicate (parallel) wiring has been installed in critical locations. This has the effect of making the electronics subsystem behave in an active redundant manner. Assuming that all corrective actions have been implemented, repeat part (b) and compute new system performance measurements