a
Interpretation:
Value of R(t) and F(t)
Concept Introduction:
Probability is the likelihood of an event to occur.. It ranges between 0 to 1. O implies no chance of occurance while 1 implies 100% chance of occurance.
b
Interpretation:
The expected number of failures
Concept Introduction:
Probability Distribution Function is a likelihood of an event to occur for discrete random variables. Graphically, it shows how likely variables will fall under the probability area.
Exponential distribution is a probabilitydistribution which finds probability of an event to occur between independent constant rate and continous rate.
c
Interpretation:
Value of r(1) yield good approximation or not.
Concept Introduction:
d
Interpretation:
Expected number of items that fail between 1 year and 1 year+ 1 week
Concept Introduction:
Normal distribution is the probability function with continuous series. It is bell shaped distribution function where mean, median and mode are same.
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Production and Operations Analysis, Seventh Edition
- Determine the optimum preventive maintenance frequency for each of the pieces of equipment if breakdown time is normally distributed: (Round "Probability Ratio" to 4 decimal places, and all other answers to 2 decimal places. Negative values should be indicated by a minus sign.) Use Table. Equipment. A201 B400 C850 Equipment A201 B400 CB50 Equipment Average Time (days) between Breakdowns A201 B400 C850 20 30 45 Preventive Maintenance Cost Click here for the Excel Data File: $330 $230 $580 Probability Ratio Standard Deviation 3 Breakdown Cont $2,230 $3,530 $4,825 Interval (days)arrow_forwardA local cab company maintains a fleet of 10 cabs. Each time a cab breaks down, it isrepaired the same day. Assume that breakdowns of individual cabs occur completely atrandom at a rate of two per year.a. What is the probability that any particular cab will run for a full year withoutsuffering a breakdown?arrow_forwardA product engineer has developed the following equation for the cost of a system component: C = (10P)2, where C is the cost in dollars and P is the probability that the component will operate as expected. The system is composed of 3 identical components, all of which must operate for the system to operate. The engineer can spend $254 for the 3 components. What is the largest component probability that can be achieved? (Do not round your intermediate calculations. Round your final answer to 4 decimal places.) Probability 0.8466arrow_forward
- A producer of pocket calculators estimates that the calculators fail at a rate of one every five years. The calculators are sold for $25 each with a one-year free replacement warranty but can be purchased from an unregistered mail-order source for $18.50 without the warranty. What length of period of the warranty equates the replacement costs of the calculator with and without the warranty?arrow_forwardThe warehouse management system (WMS) of RoyaTech's Delaware Valley warehouse tracks service level at the warehouse. A service level failure at the warehouse is an event where a customer's order could not be shipped out in full by the promised shipping time. RoyalTech's ordering system prevents customers from placing orders on products that are not in-stock at the warehouse. Therefore, we can make the statement that "the WMS is guaranteed to show 100% service level at the warehouse." Choose the most appropriate statement in response: O True, because orders will be placed only for products that are available. O False, because service level can never be 100%. O False, because resource constraint or human error may delay the shipping even though inventory is available in the system. O False, because WMS calculations are faulty.arrow_forwardA product engineer has developed the following equation for the cost of a system component: C = (10P)2, where is the cost in dollars and Pis the probability that the component will operate as expected. The system is composed of two identical components, both of which must operate for the system to operate. The engineer can spend $173 for the two components. To the nearest two decimal places, what is the largest component probability that can be achieved?arrow_forward
- The Worthington Gear Company installed a bank of 10 robots about three years ago. The robots greatly in-creased the firm’s labor productivity, but recently attention has focused on maintenance. The firm does no pre-ventive maintenance on the robots because of the variability in the breakdown distribution. Each machine hasan exponential breakdown (or interarrival) distribution with an average time between failures of 200 hours. Eachmachine hour lost to downtime costs $30, which means that the firm has to react quickly to machine failure.The firm employs one maintenance person, who needs 10 hours on average to fix a robot. Actual maintenancetimes are exponentially distributed. The wage rate is $10 per hour for the maintenance person, who can be putto work productively elsewhere when not fixing robots. Determine the daily cost of labor and robot downtime.arrow_forwardA customer orders 60,000 car batteries. If experience has shown that 5.5% of the batteries produced will be defective, how many batteries must be produced to ensure production of 60,000 good ones?arrow_forwardA purchasing agent receiving a kickback from a vendor is a common error in the acquisition and payment cycle and it is difficult to detect. * FALSE TRUEarrow_forward
- a factory that produces a small number of items per day. In about 30% of working days the factory produces 7 units of the product, in 45% of working days it produces 8 units, and the rest of working days it produces 9 units. After production is completed, each unit is thoroughly inspected. Each unit fails inspection with probability ??. If two or more units fail inspection on the same day, the factory closes for a week to re-calibrate equipment. Say the factory opens today after being closed for a week, write a mathematical expression to calculate the probability that the factory will remain open at least 30 days before closing again.arrow_forward1. Three hundred identical cathode ray tubes (CRTS) placed into service simultaneously on January 1, 1976, experienced the following numbers of failures through December 31, 1988: 1983 Year Number of failures 1984 1985 1986 1987 1988 13 19 16 34 21 38 Assume that there were no failures before 1983. a. Based on these data, estimate the cumulative distribution function (CDF) of a CRT chosen at random. Using the results of part (a), estimate the probability that a CRT chosen at random 13.1 Reliability of a Single Component 753 b. Lasts more than 5 years. c. Lasts more than 10 years. d. Lasts more than 12 years. e. That has survived for 10 years fails in the 11th year of operation.arrow_forwardAssume that a system is composed of two independent and identical units in parallel and at least one unit must operate normally for system success. The unit failure and repair rates are 0.002 failures per hour and 0.01 repairs per hour, respectively. The failed system is never repaired. Calculate the value of the system approximate effective failure rate.arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,