A sudden failure of a mechanism or a sudden stop in the operation of electronics often indicates that the resource provided by the manufacturer has been exhausted. Reliability is a property of an object maintain efficiency for a certain time or operating time without forced breaks. Engineers establish this parameter at the design stage, using complex statistical models and data on the durability of materials. Understanding the nature of failures allows not only to predict service life, but also to competently build a maintenance strategy.

Unlike maintainability, which characterizes the possibility of recovery, reliability refers to the period of continuous operation before the first failure. Probability of failure-free operation is a key quantitative indicator used in GOST standards and international specifications. If a system ceases to perform its functions, this means that its internal reliability is lower than the requirements of the external environment or operating conditions. Analyzing the causes of such events requires a detailed consideration of the theoretical foundations and practical assessment methods.

Theoretical foundations and definitions of reliability

In technical thermodynamics and reliability theory, an object is understood as any element of a system, be it a separate part, assembly, device or complex software and hardware complex. Reliability is one of the four main properties of reliability, along with durability, maintainability and storability. It describes the ability of an object to have no failures over a specified period of time under certain operating conditions. This is a probabilistic characteristic that cannot be guaranteed with 100% accuracy for a specific instance, but is statistically significant for a batch of products.

There is a fundamental difference between sudden and gradual failures. Sudden failures occur abruptly and are often associated with external influences or hidden defects in materials that could not be detected during incoming inspection. Gradual failures, on the other hand, result from the accumulation of irreversible changes such as wear, insulation aging or metal fatigue. It is critically important to understand that failure-free operation characterizes the period before the first failure of any type occurs.

To evaluate this property, various mathematical distribution models are used. The most common is the exponential distribution, which is valid for the period of normal operation when the failure rate is constant. However, for the running-in or aging stages, other functions such as the Weibull distribution are used. Engineers operate with the concept MTBFto quantify product quality.

  • πŸ› οΈ Sudden failure: an unpredictable event requiring immediate intervention.
  • πŸ“‰ Gradual withdrawal: the result of normal wear and tear that can be predicted.
  • ⏳ Hours: the duration or volume of operation of an object before failure occurs.

No-failure analysis is impossible without a clear definition of the boundaries between a serviceable and a faulty state. Technical conditions must strictly regulate permissible deviations of parameters. If the output of a device is outside the specified limits, the object is considered inoperable, even if it is physically intact. Therefore, when calculating reliability indicators, specific failure criteria specified in the documentation are always taken into account.

Mathematical model of reliability

The reliability function R(t) represents the probability that the object will operate without failure until time t. It is related to the failure-free operation time distribution function F(t) by the relation R(t) = 1 - F(t).

Quantitative indicators and calculation methods

To numerically express the property of failure-free operation, a number of specific indicators are used. The main one is the probability of failure-free operation P(t), which shows the proportion of objects that have remained operational by time t. This parameter always lies in the range from 0 to 1 and decreases over time. For systems being restored, they are often used mean time between failures (MTBF), which is calculated as the ratio of the total operating time of all objects to the total number of failures.

Failure rate Ξ»(t) is another important characteristic that describes the distribution density of the time of failure, provided that a failure has not occurred before this moment. The graph of the failure rate versus time is often called the β€œlife curve” or β€œbathtub”, since it has three characteristic sections: a running-in period with high intensity, a period of normal operation with constant intensity, and an aging period with a sharply increasing intensity. Calculations are carried out taking these phases into account.

When designing systems, engineers use various methods to improve reliability. One of them is redundancy, when the functions of the main element are duplicated by spare ones. There is a hot backup, when the element is energized, and a cold one, when it turns on only when the main one fails. Structural and time-based reservations are also used. All these measures are aimed at increasing the overall resource of the system.

Indicator Designation Unit of measurement The essence of the indicator
Probability of failure-free operation P(t) Dimensionless (0-1) Share of objects operating without failure until time t
Mean time between failures MTBF Hours, cycles Mathematical expectation of time between failures
Failure Rate Ξ»(t) 1/hour Failure probability density at a given moment
Gamma percentage resource LΞ³ Hours, km Operating time during which a failure will not occur with probability Ξ³
πŸ’‘

Reliability is not a constant value; it depends on operating conditions and operating time of the object.

Calculating the reliability of complex systems often requires the use of logical-probabilistic methods. The reliability block diagram may differ from the electrical or functional diagram. For example, elements connected in series in an electrical circuit are also connected in series in a reliability circuit, since the failure of any one of them leads to the failure of the entire circuit. A parallel connection in a reliability scheme corresponds to redundancy. The accuracy of calculations directly affects the safety and economic efficiency of operation.

Factors influencing the maintenance of performance

The actual reliability of an object depends significantly on the conditions in which it is operated. Even an ideally designed device can quickly fail if the temperature is violated or exposed to aggressive environments. Climatic factors such as humidity, temperature, atmospheric pressure and dust have a direct impact on the rate of degradation of materials. Mechanical influences, including vibration and shock loads, can cause fatigue failure.

Quality maintenance plays a critical role in maintaining high levels of reliability. Timely replacement of consumables, lubrication of rubbing parts and monitoring of parameters can extend the period of normal operation. Ignoring routine maintenance leads to accelerated wear and tear of the system into the zone of catastrophic failure. The human factor during maintenance is also a significant source of errors.

⚠️ Attention: Operating equipment outside of the specified modes (overcurrent, overspeed, overheating) sharply reduces the failure rate and can lead to irreversible damage.

Internal factors related to production quality are also critical. Defects in materials, violations of assembly technology, flux residues on the boards or insufficient tightening of connections are hidden defects that appear during the running-in period. Statistical quality control at the manufacturing plant allows us to eliminate defective products, but does not provide a 100% guarantee. Therefore, in critical applications, additional training of products is carried out before installation.

πŸ“Š What most often leads to failure of your equipment?
Wear and tear of materials: Violation of operating conditions: Installation errors: Factory defects:

Test methods and statistics collection

To confirm the declared reliability indicators, special tests are carried out. Accelerated testing allows you to obtain data on failures in a short time by creating extreme conditions (high temperature, humidity, vibration). The results obtained are then recalculated to normal operating conditions using acceleration factors. This is standard practice for electronics and mechanics.

Collecting failure statistics during actual operation is the most reliable, but also the longest method. Manufacturers analyze warranty cases, service center reports and telemetry data. Big Data technologies make it possible to process huge amounts of information, identifying patterns and weak points of structures. Based on this data, changes are made to the design of the next generations of products.

There are different types of reliability tests:

  • πŸ“Š Definition tests: are carried out until a specified number of failures are received to evaluate the indicators.
  • πŸ›‘ Control tests: the purpose is to accept or reject a batch of products.
  • πŸ” Research tests: are needed to study the causes of failures and physical degradation processes.

An important aspect is the correct classification of failures during testing. Failures are divided into independent and dependent, structural and production, removable and irreparable. Only a thorough analysis allows us to draw correct conclusions about the reliability of an object. Errors in classification can lead to an incorrect assessment of the resource.

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Strategies for Improving System Reliability

Engineers apply a set of measures to increase reliability at all stages of the product life cycle. At the design stage, elements with a load reserve are selected, circuit solutions that are resistant to interference are applied, and overload protection is provided. The use of better materials and improved production technologies also contribute. Reservation remains one of the most effective, albeit expensive methods.

During operation, the maintenance strategy must match the nature of the failures. For elements with sudden failures, the condition-based maintenance method is effective, when parameters are constantly monitored and replacement is made when approaching a critical level. For items with gradual wear and tear, preventive maintenance may be used, although the current trend is moving towards predictive analytics.

The introduction of automatic diagnostic systems makes it possible to detect incipient defects at early stages. Built-in tests and monitoring tools transmit information about the state of the object to the operator. This allows you to plan repairs and avoid downtime. Intelligent systems are able to adapt themselves to changing conditions, redistributing the load between nodes.

⚠️ Attention: Excessive complexity of the protection and diagnostic system can itself reduce the overall reliability due to an increase in the number of elements susceptible to failure.

Training personnel in proper operation and maintenance techniques is an integral part of the reliability improvement strategy. Most premature failures are due to improper handling. Clear instructions, understandable interfaces and protection from the β€œfool” help to minimize the influence of the human factor.

Economic aspect and cost optimization

Increased reliability always comes with increased costs for design, production and maintenance. There is an optimal level of reliability at which the total costs of creating and operating an object are minimal. Increasing reliability too much may not be economically feasible if the cost of duplicating or using highly reliable components outweighs the possible damage from rare failures.

When calculating economic efficiency, not only direct costs of repair and replacement are taken into account, but also indirect losses from equipment downtime, product losses, fines for failure to fulfill obligations and reputational risks. For critical facilities, such as nuclear power plants, aviation or medical equipment, the requirements for reliability are as high as possible, and saving on reliability is unacceptable.

Modern approaches to asset management (Asset Management) are based on full life cycle analysis (LCC - Life Cycle Cost). Investments in reliable equipment pay off through lower operating costs and increased useful life. A proper balance between cost of ownership and reliability is the key to successful engineering.

How to calculate the probability of failure-free operation for a sequential system?

For a system with a series connection of elements, the probability of failure-free operation is equal to the product of the probabilities of failure-free operation of each element: P_system = P1 P2 ... *Pn. Since all P < 1, the reliability of the system is always lower than the reliability of the most reliable element.

What is the difference between MTBF and average life time?

MTBF (Mean Time Between Failures) is the average time between failures for recoverable systems. Mean Time To Failure (MTTF) is used for non-recoverable objects and denotes the average time until the first failure. For an exponential distribution, these quantities are numerically equal, but conceptually different.

Is it possible to improve the reliability of old equipment?

Yes, this is possible through modernization, replacing worn-out components with more modern analogues, improving operating conditions (installing filters, voltage stabilizers) and optimizing operating modes. However, the physical wear and tear of the main structures may be irreparable.

What is Weibull distribution law?

This is a two- or three-parameter distribution widely used to describe the lifetime of objects. It flexibly describes different periods of a product’s life (breaking-in, normal operation, aging) by changing the shape parameter. Allows you to more accurately model real failure processes than the exponential distribution.

Why do you need to test new products?

Run-in (training) is necessary to identify and eliminate defects during the running-in period. During this period, failure rates are high due to hidden manufacturing defects. The artificial creation of loads allows you to β€œburn out” weak elements before the start of real operation, increasing the final reliability.