17 Reliability Supplement to Chapter Four a mearn ervice life that can be modele

Question

17

Reliability Supplement to Chapter Four a mearn ervice life that can be modeled by a normal distribution with a mean of six years and deviation of one-half year 17 ajor television manufacturer has determined that its 40-inch LED televisions have ard a. What probability can you assign to service lives of at least (1) five years? (2) six years? (a seven and one-half years? b. I t the manufacturer offers service contracts of four years on these televisions what can be expected to fail from wear-out during the service period? 18. Refer to Pro blem 17. What service period would achieve an expected wear-out rate of cent? (2) 5 percent? 9. Determine the availability for each of these cases MTBF 40 days, average repair time 3 days b. MTBF 300 hours, average repair time 6 hours 20. A machine can operate for an average of 10 weeks before it needs to be overhauled, a process which takes two days. The machine is operated five days a week. Compute the availability of this machine. (Hint: All times must be in the same units.) 21. A manager must decide between two machines. The manager will take into account each machine's operating costs and initial costs, and its breakdown and repair times. Machine A has a projected average operating time of 142 hours and a projected average repair time of 7 hours. Projected times for machine B are an average operating time of 65 hours and a repair time of 2 hours. What are the projected availabilities of each machine? 22. A designer estimates that she can (a) increase the average time between failures of a part by 5 per and s have an average life of 2.7 years. Battery life is normally distributed with a meanof of S450, or (b) reduce the average repair time by 10 percent at a cost of $200. Whi ent at a cost option would be more cost-effective? the average repair time is 4 hours Currently, the average time between failures is 100 hour 23. Auto batterie 2.7 years and a standard deviation of.3 year. The batteries are warranted to operate for a minimu of 2 y charge. The com ears. If a battery fails within the warranty period, it will be replaced with a new battery pany sells and installs the batteries. Also, the usual $5 installation charge will ved wai a. b. A competitor is offering a warranty of 30 months on its premium battery. The manager of t What percentage of batteries would you expect to fail before the warranty period expires ompany is toying with the idea of using the same battery with a different exterior, labeling as a pre pany have to charge on its "premium" battery to offset the additional cost of replacing batt it mium battery, and offering a 30-month warranty on it. How much more would the con c. What other factors would you take into consideration besides the price of the battery? atteries?

Explanation / Answer

Normal distribution:

Mean = u= 6 years

Standard deviation = sd = 1.5 years

A. The probabilities that we can assign to service life are:

P (0<x<5 years)

Z= (x-u)/sd = -0.6 (x = 5)

Because, P(z= -0.6) = 0.275 [from normal distribution table]

Therefore, probability of TV life to be less than 5 years = 0.275

Because 6 years is mean life of the product therefore probability will be 50% i.e. 0.5

P (0<x<7.5 years)

Z= (x-u)/sd = 1.0 (x = 7.5)

Because, P(z= 1.0) = 0.841 [from normal distribution table]

Therefore, probability of TV life to be less than 7.5 years = 0.841

B. The percentage of products he will be servicing in first 4 years

We need to find the probability of the product surviving in first 4 years

P (0<x<4 years)

Z= (x-u)/sd = -1.3 (x = 4)

Because, P(z= -1.3) = 0.097 [from normal distribution table]

Therefore, probability of TV life to be less than 4 years = 0.097

During service period of 4 years the manufacturer can aspect the 0.097*100= 9.7% of products to wear out

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