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Setting up reliability goals for systems
Reliabilit) Engineering I (1980)43 48
SETTING UP RELIABILITY GOALS FOR SYSTEMS
D. V. PETKAR
Reliability Evaluation Laboratory, Bhabha Atomic Research Centre, Bombay 400 085, India
ABSTRACT
The quality of life of people of any country depends to a very large extent on the quality and reliability oJproducts and services like transport, communications, power, broadcasting, telecasting, etc. Psychological and physical discomforts are felt by people only when things fail thereby reducing or removing the service. Everybody feels that 'immortal" services should be available, but services are created by man and are mortal like him. However, there is a need to have a reliability goal whereby one can guarantee the continuity of a service for a certain length of time/distance with a known risk of failure. Reliability of services is dependent on the reliability of systems comprising them and the management. In this paper the author has tried to focus attention on the need to have reliability goals as distinct from availability goals. The paper gives the basis for setting up reliability goals for a system as well as its subsystems. The allocation of reliability goals .['or the subsystems is based on the operating experience with similar systems or on the basis of the knowledge of the system or both. Two typical cases of a nuclear power station and a particle accelerator are considered and reliability goals for both system and subsystems are arrived at. The author concludes by stating that reliability goals in respect of simple items produced in large quantities and used anywhere in the world are a necessity. This is so because cost of maintenance is bound to be large with such items.
l.
INTRODUCTION
Man, through being an intelligent animal, has been able to improve upon the surroundings in which he has been born. He has by his intelligence and hard work created a culture and improved the quality of life of mankind in general. The quality of life of people of any country depends to a very large extent on the quality and 43 Reliability Engineering 0143-8174/80/0001-0043/$02.25 © Applied Science Publishers Ltd, England, 1980 Printed in Great Britain
44
D.V.
PETKAR
reliability of products and services like transport, communications and power. Thus the standards of quality and reliability in respect of products and services are going to decide the standard of quality of life. Thus it becomes important to lay down the standards for reliability in respect of both products and services in such a way that aspects of the quality of life get reflected in these standards. Modern civilization is dependent on power, communications and transport services. The measure for the quality of these services is generally given in terms of percentage non-availability over a period, for example, a year. However, what one would like to have is uninterrupted service for a certain length of time/distance with a certain confidence level. This approach would be valid even for entertainment services like the motion picture industry, television, etc., the interruption of which resulting only in psychological discomfort rather than both psychological and physical discomfort.
2.
SYSTEM A N D SUBSYST[:M R E L I A B I L I T Y
The reliability of a complex system, consisting of parts exhibiting constant failure rate, exhibits exponential distribution. It is also known that the reliability of a complex maintained system consisting of parts with constant and non-constant failure rates and mixed ages also exhibits exponential distribution during the usefullife period after the initial infant-mortality period. Let a given system S consist of N independent subsystems A l to AN. The system operates in such a way that if any one of the N subsystems fail the system fails. Let Z s and ZA1 to ZAN be the failure rates of the system and subsystems respectively. Then we have N
Zs = ~ ',ZA,
(1)
i=l
The problem now is what should be the failure rate of the subsystem and what should be the basis for allocation ? The basis for the allocation can be the operating experience of similar systems and one can think of relative contribution of the subsystem to the unscheduled outage rate of the system. Let OR s and ORAl to ORAN represent the outage rate of the system and its subsystems respectively. Let KAI to KANalso represent the fractional contribution of the subsystem to the outage rate of the system. Then we have N
OR s = ~ ',ORAl i=l
(2)
RELIABILITY GOALS FOR SYSTEMS
45
ORAi KA~---- O R s
(3)
ZAi = KAiZ s
(4)
and
3.
SYSTEM RELIABILITY GOAL
System reliability is defined as the probability that the system will perform its function without failure for the specified period of time under the specified conditions. For example, in the case of a power station the reliability can be defined as the probability that the power station will not fail to supply power for a specified period of time under the specified power demand conditions. In the case of a transport system, reliability can be defined as the probability that the vehicle will transport people or goods or both, a given distance in a given time under the specified road and traffic conditions. Let us set a reliability goal for the power station as follows. The power station will be able to supply stated power for a specified period of 1000 h under constant power demand conditions with a confidence of 0-99. From the exponential distribution this gives us a failure rate of 10-5/h. Similarly, a reliability goal can be set for a vehicle as follows. The vehicle will transport people or goods or both a distance of 1000 km without breakdown in 20 h with a confidence of 0.99. This will give a failure rate of 10- 5/km. This assumes that in a properly maintained vehicle the failures are r a n d o m and independent of age, i.e. exponential distribution is valid.
4.
CASE STUDIES
Two cases are studied in this paper. One is that of a nuclear power station and the other is that of a particle accelerator. Both the systems are fairly complex and consist of electronic and electrical, pneumatic, hydraulic, electro-mechanical, mechanical and civil structural parts. These, from the point of view of reliability terminology, can be classified into: 1. 2.
Parts with constant failure rates with time, and Parts with non-constant failure rates with time.
Both of the systems are maintained systems and will indicate a constant failure rate after the initial infant-mortality period. Thus a Reliability Index, viz. failure rate, can be assigned to both the systems and their subsystems.
46
D . V . PETKAR
4.1. Case 1: Nuclear p o w e r reactor A number of nuclear power reactors are operating in the world and the International Atomic Energy Agency (IAEA) collects operating experience data. In order to achieve some kind of uniformity in data collection, IAEA has classified the reactor system into 10 major subsystems.~ The operating experience data is useful in allocating the causes for system down time to various subsystem failures. Thus the factors KA, as referred to in Section 2 above can be evaluated. Table 1 gives the failure rate requirements in respect of each of the reactor subsystems for a required reactor operating time of 1000 h with 99 ~o confidence. TABLE
I
REACTOR SUBSYSTEMS A N D FAILURE RATES
Subsystem
Failure rate
( IO 6/h)
Reactor and accessories Fuel Reactor control and inslrumentation Nuclear auxiliary system Main heat removal system Steam generators Feedwater systems Turbine generators systems Electrical power supply Miscellaneous System
0.4 0.2 0"6 0. I 3.0 2.5 0.1 2.5 0.3 0.3 10.0
4.2. Case 2. Particle accelerator A particle accelerator is a research tool and experiments may demand that it should operate for at least 200h continuously with 99')~, confidence. Its major subsystems are:
1. 2. 3. 4. 5. 6. 7. 8. 9.
Magnet Radio frequency Injection Vacuum Control Target Electrical supply Air conditions Miscellaneous
lfwe assume as a first approximation that these subsystems are equally complex and contribute equally to the accelerator down time then each of the above subsystems should have failure rates of the order of 5 × 10-6/h.
RELIABILITY GOALS FOR SYSTEMS 5.
47
COMPONENT FAILURE RATES
We see from above that the subsystem failure rates are of the order of 10-6/h. Subsystems themselves will consist of a number of component parts whose failure rates thus have to be one or two orders of magnitude less, i.e. in the range 10- 7_ I 0- a/h. To establish the order of these failure rates with 90 % confidence will require component test times in the range 2.3-230 x 10 6 h allowing for only one failure. This necessitates a large sample size of components if the waiting time for the decision is to be only 1000 h. This is costly, and maybe one should go into details of the factors which control the failure rates.
6.
FAILURE RATE CONTROLLING FACTORS
Causes for component failure in general can be classified into two groups, viz: (a) internal to the component, i.e. inherent, (b) external to the component, i.e. environmental. In general, the component failure rates are observed to be controlled by: 1. 2. 3. 4. 5. 6. 7. 8.
Design Materials and parts Manufacturing processes Quality control and inspection procedures Transportation and storage conditions Installation Servicing and maintenance Operation and operations conditions
It is quite clear that the first four of the above factors decide the inherent reliability and the last four use reliability. As the requirements for component reliability are high, the best way is to have better control on the controlling factors and screen the components effectively to eliminate the components with inherent defects.
7.
CONCLUSIONS
I have considered typical cases so as to focus the attention on having reliability goals. This approach should by no means be restricted only to costly and complex systems. It is also applicable to simple systems produced in large numbers and used at different places over the world. Every-product goes through the life cycle of: 1 concept and definition, 2 design and development, 3 manufacturing and installation, 4 operation and maintenance, before it is discarded.
48
D.V. PETKAR
it is felt that a reliability goal and the machinery to implement this goal is essential in respect of every item whether simple or complex. This will be the only way to build reliability into our products and actions.
REFERENCE I. FATTAH, A. and SKJOELDI:BRAND,R. Performance analysis of nuclear power plants from operating
experience data, Proceedings of a Symposium on Reliability of Nuclear Power Plants, Innsbruck, 14-18 April 1975, IAEA, Vienna, (1975), pp.91-102
SETTING UP RELIABILITY GOALS FOR SYSTEMS
D. V. PETKAR
Reliability Evaluation Laboratory, Bhabha Atomic Research Centre, Bombay 400 085, India
ABSTRACT
The quality of life of people of any country depends to a very large extent on the quality and reliability oJproducts and services like transport, communications, power, broadcasting, telecasting, etc. Psychological and physical discomforts are felt by people only when things fail thereby reducing or removing the service. Everybody feels that 'immortal" services should be available, but services are created by man and are mortal like him. However, there is a need to have a reliability goal whereby one can guarantee the continuity of a service for a certain length of time/distance with a known risk of failure. Reliability of services is dependent on the reliability of systems comprising them and the management. In this paper the author has tried to focus attention on the need to have reliability goals as distinct from availability goals. The paper gives the basis for setting up reliability goals for a system as well as its subsystems. The allocation of reliability goals .['or the subsystems is based on the operating experience with similar systems or on the basis of the knowledge of the system or both. Two typical cases of a nuclear power station and a particle accelerator are considered and reliability goals for both system and subsystems are arrived at. The author concludes by stating that reliability goals in respect of simple items produced in large quantities and used anywhere in the world are a necessity. This is so because cost of maintenance is bound to be large with such items.
l.
INTRODUCTION
Man, through being an intelligent animal, has been able to improve upon the surroundings in which he has been born. He has by his intelligence and hard work created a culture and improved the quality of life of mankind in general. The quality of life of people of any country depends to a very large extent on the quality and 43 Reliability Engineering 0143-8174/80/0001-0043/$02.25 © Applied Science Publishers Ltd, England, 1980 Printed in Great Britain
44
D.V.
PETKAR
reliability of products and services like transport, communications and power. Thus the standards of quality and reliability in respect of products and services are going to decide the standard of quality of life. Thus it becomes important to lay down the standards for reliability in respect of both products and services in such a way that aspects of the quality of life get reflected in these standards. Modern civilization is dependent on power, communications and transport services. The measure for the quality of these services is generally given in terms of percentage non-availability over a period, for example, a year. However, what one would like to have is uninterrupted service for a certain length of time/distance with a certain confidence level. This approach would be valid even for entertainment services like the motion picture industry, television, etc., the interruption of which resulting only in psychological discomfort rather than both psychological and physical discomfort.
2.
SYSTEM A N D SUBSYST[:M R E L I A B I L I T Y
The reliability of a complex system, consisting of parts exhibiting constant failure rate, exhibits exponential distribution. It is also known that the reliability of a complex maintained system consisting of parts with constant and non-constant failure rates and mixed ages also exhibits exponential distribution during the usefullife period after the initial infant-mortality period. Let a given system S consist of N independent subsystems A l to AN. The system operates in such a way that if any one of the N subsystems fail the system fails. Let Z s and ZA1 to ZAN be the failure rates of the system and subsystems respectively. Then we have N
Zs = ~ ',ZA,
(1)
i=l
The problem now is what should be the failure rate of the subsystem and what should be the basis for allocation ? The basis for the allocation can be the operating experience of similar systems and one can think of relative contribution of the subsystem to the unscheduled outage rate of the system. Let OR s and ORAl to ORAN represent the outage rate of the system and its subsystems respectively. Let KAI to KANalso represent the fractional contribution of the subsystem to the outage rate of the system. Then we have N
OR s = ~ ',ORAl i=l
(2)
RELIABILITY GOALS FOR SYSTEMS
45
ORAi KA~---- O R s
(3)
ZAi = KAiZ s
(4)
and
3.
SYSTEM RELIABILITY GOAL
System reliability is defined as the probability that the system will perform its function without failure for the specified period of time under the specified conditions. For example, in the case of a power station the reliability can be defined as the probability that the power station will not fail to supply power for a specified period of time under the specified power demand conditions. In the case of a transport system, reliability can be defined as the probability that the vehicle will transport people or goods or both, a given distance in a given time under the specified road and traffic conditions. Let us set a reliability goal for the power station as follows. The power station will be able to supply stated power for a specified period of 1000 h under constant power demand conditions with a confidence of 0-99. From the exponential distribution this gives us a failure rate of 10-5/h. Similarly, a reliability goal can be set for a vehicle as follows. The vehicle will transport people or goods or both a distance of 1000 km without breakdown in 20 h with a confidence of 0.99. This will give a failure rate of 10- 5/km. This assumes that in a properly maintained vehicle the failures are r a n d o m and independent of age, i.e. exponential distribution is valid.
4.
CASE STUDIES
Two cases are studied in this paper. One is that of a nuclear power station and the other is that of a particle accelerator. Both the systems are fairly complex and consist of electronic and electrical, pneumatic, hydraulic, electro-mechanical, mechanical and civil structural parts. These, from the point of view of reliability terminology, can be classified into: 1. 2.
Parts with constant failure rates with time, and Parts with non-constant failure rates with time.
Both of the systems are maintained systems and will indicate a constant failure rate after the initial infant-mortality period. Thus a Reliability Index, viz. failure rate, can be assigned to both the systems and their subsystems.
46
D . V . PETKAR
4.1. Case 1: Nuclear p o w e r reactor A number of nuclear power reactors are operating in the world and the International Atomic Energy Agency (IAEA) collects operating experience data. In order to achieve some kind of uniformity in data collection, IAEA has classified the reactor system into 10 major subsystems.~ The operating experience data is useful in allocating the causes for system down time to various subsystem failures. Thus the factors KA, as referred to in Section 2 above can be evaluated. Table 1 gives the failure rate requirements in respect of each of the reactor subsystems for a required reactor operating time of 1000 h with 99 ~o confidence. TABLE
I
REACTOR SUBSYSTEMS A N D FAILURE RATES
Subsystem
Failure rate
( IO 6/h)
Reactor and accessories Fuel Reactor control and inslrumentation Nuclear auxiliary system Main heat removal system Steam generators Feedwater systems Turbine generators systems Electrical power supply Miscellaneous System
0.4 0.2 0"6 0. I 3.0 2.5 0.1 2.5 0.3 0.3 10.0
4.2. Case 2. Particle accelerator A particle accelerator is a research tool and experiments may demand that it should operate for at least 200h continuously with 99')~, confidence. Its major subsystems are:
1. 2. 3. 4. 5. 6. 7. 8. 9.
Magnet Radio frequency Injection Vacuum Control Target Electrical supply Air conditions Miscellaneous
lfwe assume as a first approximation that these subsystems are equally complex and contribute equally to the accelerator down time then each of the above subsystems should have failure rates of the order of 5 × 10-6/h.
RELIABILITY GOALS FOR SYSTEMS 5.
47
COMPONENT FAILURE RATES
We see from above that the subsystem failure rates are of the order of 10-6/h. Subsystems themselves will consist of a number of component parts whose failure rates thus have to be one or two orders of magnitude less, i.e. in the range 10- 7_ I 0- a/h. To establish the order of these failure rates with 90 % confidence will require component test times in the range 2.3-230 x 10 6 h allowing for only one failure. This necessitates a large sample size of components if the waiting time for the decision is to be only 1000 h. This is costly, and maybe one should go into details of the factors which control the failure rates.
6.
FAILURE RATE CONTROLLING FACTORS
Causes for component failure in general can be classified into two groups, viz: (a) internal to the component, i.e. inherent, (b) external to the component, i.e. environmental. In general, the component failure rates are observed to be controlled by: 1. 2. 3. 4. 5. 6. 7. 8.
Design Materials and parts Manufacturing processes Quality control and inspection procedures Transportation and storage conditions Installation Servicing and maintenance Operation and operations conditions
It is quite clear that the first four of the above factors decide the inherent reliability and the last four use reliability. As the requirements for component reliability are high, the best way is to have better control on the controlling factors and screen the components effectively to eliminate the components with inherent defects.
7.
CONCLUSIONS
I have considered typical cases so as to focus the attention on having reliability goals. This approach should by no means be restricted only to costly and complex systems. It is also applicable to simple systems produced in large numbers and used at different places over the world. Every-product goes through the life cycle of: 1 concept and definition, 2 design and development, 3 manufacturing and installation, 4 operation and maintenance, before it is discarded.
48
D.V. PETKAR
it is felt that a reliability goal and the machinery to implement this goal is essential in respect of every item whether simple or complex. This will be the only way to build reliability into our products and actions.
REFERENCE I. FATTAH, A. and SKJOELDI:BRAND,R. Performance analysis of nuclear power plants from operating
experience data, Proceedings of a Symposium on Reliability of Nuclear Power Plants, Innsbruck, 14-18 April 1975, IAEA, Vienna, (1975), pp.91-102