CHAPTER 4s Reliability Operations Management, Eighth Edition, by William J. Stevenson Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin

Reliability Reliability: The ability of a product, part, or system to perform its intended function under a prescribed set of conditions Failure: Situation in which a product, part, or system does not perform as intended Normal operating conditions: The set of conditions under which an item’s reliability is specified

Improving Reliability Component design Production/assembly techniques Testing Redundancy/backup Preventive maintenance procedures User education System design

Quantifying Reliability Reliability is Probability If a component or item has a reliability of 0.8, it means that it has a 80% probability of functioning as intended, the probability it will fail is 1-0.8 = 0.2 which is 20%

Reliability is a Probability Probability that the product or system will: Function when activated Function for a given length of time Independent events Events whose occurrence or nonoccurrence do not influence each other. Redundancy The use of backup components to increase reliability.

Rule 1 .90 .80 Lamp 1 Lamp 2 .90 x .80 = .72 Both the lamps should be lighted up in order to ensure visibility If two or more events are independent and success is defined as probability that all of the events ,occur then the probability of success is equal to the product of probabilities Reliability of the System = (Reliability of component 1) (Reliability of Component 2)

Rule 2 If two events are independent and “success” is defined as probability that at least one of the events will occur, then the probability of either one plus 1.00 minus that probability multiplied by the other probability Lamp 2 is an example of redundancy here, as it being backup Lamp increases the reliability of the system from 0.9 to 0.98 Lamp 2 (backup) .90 .80 Lamp 1 .90 + (1-.90)*.80 = .98

Rule 3 If three events are involved and success is defined as the probability that at least one of them occurs, the probability of success is equal to the probability of the first one ( any of the events), plus the product of 1.00 minus that probability and the probability of the second event ( any of the remaining events), plus the product of 1.00 minus each of the two probabilities and the probability of third event and so on. This rule can be extended to cover more than three events.

Rule 3 .70 .80 1 – P(all fail) .90 1-[(1-.90)*(1-.80)*(1-.70)] = .994 Lamp 3 (backup for Lamp 2) Lamp 2 (backup for Lamp1) 1 – P(all fail) 1-[(1-.90)*(1-.80)*(1-.70)] = .994 Lamp 1

2. Time based Reliability “Failure Rate” Figure 4S.1 Few (random) failures Infant mortality Failures due to wear-out Time, T Failure Rate

What can we observe in the Bath Tub Curve Phase I You can see that quite a few of the products fail shortly put into service, not because they wear out but they are defective to begin with. Phase II The rate of failure decreases rapidly once the truly defective items are WEEDED OUT (Eliminating inferior products/Services). During phase II, there are fewer failures because the inferior/defective have already been eliminated. This phase is free of worn out items and as seen is the LONGEST PERIOD here.

What can we observe in the Bath Tub Curve Phase III In the third phase, failure occurs because the products have completed the normal life of their service life and thus worn out. As we can see the graphs steeps up in this phase indicating an increase in the failure rate. HOW CAN WE COLLECT INFORMATION ON THE DISTRIBUTION, LENGTH OF EACH PHASE REQUIRES COLLECTION AND ANALYSIS OF DATA. WE ARE INTERESTED IN CALCULATING MEAN TIME BETWEEN FAILURE FOR EACH PHASE.

Exponential Distribution FOR INFANT MORTALITY STAGE Figure 4S.2 Reliability = e -T/MTBF 1- e -T/MTBF T Time

Exponential Distribution Equipment failures as well as product failures may occur in this pattern. In such case the exponential distribution, such as depicted on the graph for you. Phase I indicates the probability that equipment or product put into service at time 0 will fail before specified T is ability that a product will last until Time T and is represented by area under the curve between O and T.

Exponential Distribution Phase II indicates that the curve to the right of Point T increases in Time but reduces in reliability. We can calculate the reliability or probability values using a table of exponential values. An exponential distribution is completely described using the distribution mean, which reliability engineers call it the MEAN TIME BETWEEN FAILURES. Using T to represent the length of service, we can calculate P before failure as P ( No failure before T)= e-T/MBTF.

Normal Distribution Figure 4S.3 Reliability z

Normal Distribution Product failure due to wear out can be determined by using normal distribution. From our knowledge of statistics we already know that the statistic table for a standardized variable Z represents the area under the normal curve from essentially from the left end of the curve to a specified point z, where z is a standardized value computing use z = T-Mean wear out time Std Deviation of Wear out Time

Normal Distribution The mean life of a certain steam turbine can be modeled using a normal distribution with a mean life of six years, and a standard deviation of one year. Determine each of the following: The probability that a stem turbine will wear out before seven years of service. To probability that a steam turbine will wear out after seven years of service ( i.e. find its reliability) The service life will provide a wear-out probability of 10 percent. Wear out life mean= 6 years. Wear out life standard deviation = 1 year Wear out life is normally distributed.

Normal Distribution Subtract the probability ( reliability) determined in part a from 100 percent 1.00 -0.8413 = 0.1587 We can see that on the Z scale, both a and b gives 1.00 Reliability= 0.1587 z

Availability The fraction of time a piece of equipment is expected to be available for operation MTBF = mean time between failures MTR = mean time to repair

Concurrent Engineering Advantages Manufacturing Personnel are able to identify production capabilities and capacities . Early opportunities for design or procurement of critical tooling, some of which might have long lead times.

Concurrent Engineering Advantages Early consideration of the Technical Feasibility of a particular design or a portion of a design.

Concurrent Engineering Disadvantages Long standing existing boundaries between design and manufacturing can be difficult to overcome.

Computer-Aided Design Computer-Aided Design (CAD) is product design using computer graphics. increases productivity of designers, 3 to 10 times creates a database for manufacturing information on product specifications provides possibility of engineering and cost analysis on proposed designs

Quality Function Deployment QFD: An approach that integrates the “voice of the customer” into the product and service development process. Quality Function Deployment Voice of the customer House of quality

Operations Strategy Invest more in R &D (Research & Development). Shift some emphasis away from short term performance to long term Performance. Work towards continual and gradual improvements instead o big bang approach. Work to shorten the product life cycle.

Operations Strategy Increase emphasis on component commonality. Package products and services. Use multiple platforms. Consider tactics for mass customization. Look for continual improvement. Shorten time to market.