플랜트 엔지니어를 위한 신뢰성 엔지니어링 원칙

그림 8의 예에서 볼 수 있듯이 두 개의 개별 회귀선을 그릴 때 데이터 세트가 더 잘 작동합니다. 첫 번째 라인은 0.5의 베타 모양 매개변수를 보여 초기 수명 실패를 나타냅니다. 두 번째 선은 3.0의 베타 모양을 나타내어 실패 위험이 시간의 함수로 증가함을 나타냅니다. 복잡한 장비, 특히 기계 장비는 새롭거나 최근에 재건할 때 "런인(run-in)" 오류가 발생하는 것이 일반적입니다. 따라서 초기 시작 직후에 실패 위험이 가장 높습니다.

시스템이 시스템 유형에 따라 몇 분, 몇 시간, 며칠, 몇 주, 몇 년 또는 몇 년이 걸릴 수 있는 실행 기간을 통해 작동하면 시스템은 다른 위험 패턴에 들어갑니다. 이 예에서 시스템은 시작 기간을 종료하면 시간의 함수로 실패 위험이 증가하는 기간에 들어갑니다.

다중 베타는 신뢰성 엔지니어에게 시간의 함수로서 위험을 보다 정확하게 추정할 수 있도록 합니다. 이 지식으로 무장하면 완화 조치를 취할 수 있는 더 나은 위치에 있습니다. 예를 들어, 초기 수명 기간 동안 우리는 제조/재구축, 설치 및 시작의 정밀도를 향상시키는 경향이 있습니다. 또한 고위험 기간 동안 모니터링 기술을 추가하거나 모니터링 빈도를 늘릴 수 있습니다. 도입 기간 후에 시스템에 영향을 미치는 것으로 생각되는 시간 종속적 마모 오류를 대상으로 하는 모니터링 기술을 도입하거나 그에 따라 모니터링 빈도를 늘리거나 경우에 따라 "어려운" 예방 유지 관리 작업을 예약할 수 있습니다.

시스템 안정성 추정

작동 상황 및 필요한 임무 시간과 관련하여 구성 요소 또는 기계의 신뢰성이 설정되면 플랜트 엔지니어는 시스템 또는 프로세스의 신뢰성을 평가해야 합니다. 다시 말하지만, 간결함과 단순성을 위해 직렬, 병렬 및 공유 부하 중복 시스템(r/n 시스템)에 대한 시스템 안정성 추정치를 논의합니다.

시리즈 시스템
시리즈 시스템에 대해 논의하기 전에 안정성 블록 다이어그램에 대해 논의해야 합니다. 사용하기 복잡한 도구가 아니라 신뢰성 블록 다이어그램은 처음부터 끝까지 프로세스를 간단히 매핑합니다. 시리즈 시스템의 경우 하위 시스템 A 다음에 하위 시스템 B가 오는 식입니다. 직렬 시스템에서 하위 시스템 B를 사용할 수 있는 능력은 하위 시스템 A의 작동 상태에 따라 다릅니다. 하위 시스템 A가 작동하지 않으면 시스템은 하위 시스템 B의 상태에 관계없이 다운됩니다(그림 9).

To calculate the system reliability for a serial process, you only need to multiply the estimated reliability of Subsystem A at time (t) by the estimated reliability of Subsystem B at time (t). The basic equation for calculating the system reliability of a simple series system is:

Where:
Rs(t) – System reliability for given time (t)
R1-n(t) – Subsystem or sub-function reliability for given time (t)

So, for a simple system with three subsystems, or sub-functions, each having an estimated reliability of 0.90 (90%) at time (t), the system reliability is calculated as 0.90 X 0.90 X 0.90 =0.729, or about 73%.

Figure 9. Simple Serial System

Parallel Systems
Often, design engineers will incorporate redundancy into critical machines. Reliability engineers call these parallel systems. These systems may be designed as active parallel systems or standby parallel systems. The block diagram for a simple two component parallel system is shown in Figure 10.

Figure 10. Simple parallel system – the system reliability is increased to 99% due to the redundancy.

To calculate the reliability of an active parallel system, where both machines are running, use the following simple equation:

Where:
Rs(t) – System reliability for given time (t)
R1-n(t) – Subsystem or sub-function reliability for given time (t)

The simple parallel system in our example with two components in parallel, each having a reliability of 0.90, has a total system reliability of 1 – (0.1 X 0.1) =0.99. So, the system reliability was significantly improved.

There are some shortcut methods for calculating parallel system reliability when all subsystems have the same estimated reliability. More often, systems contain parallel and serial subcomponents as depicted in Figure 11. The calculation of standby systems requires knowledge about the reliability of the switching mechanism. In the interest of simplicity and brevity, this topic will be reserved for a future article.

Figure 11. Combination System with Parallel and Serial Elements

r out of n Systems (r/n Systems)
An important concept to plant reliability engineers is the concept of r/n systems. These systems require that r units from a total population in n be available for use. A great industrial example is coal pulverizers in an electric power generating plant. Often, the engineers design this function in the plant using an r/n approach. For instance, a unit has four pulverizers and the unit requires that three of the four be operable to run at the unit’s full load (see Figure 12).

Figure 12. Simple r/n system example – Three of the four components are required.

The reliability calculation for an r/n system can be reduced to a simple cumulative binomial distribution calculation, the formula for which is:

Where:
Rs =System reliability given the actual number of failures (r) is less than or equal the maximum allowable (k)
r =The actual number of failures
k =The maximum allowable number of failures
n =The total number of units in the system
p =The probability of survival, or the subcomponent reliability for a given time (t).

This equation is somewhat more complicated. In our pulverizer example, assuming a subcomponent reliability of 0.90, the equation works out as a summation of the following:
P(0) =0.6561
P(1) =0.2916

So, the likelihood of completing the mission time (t) is 0.9477 (0.6561 + 0.2916), or approximately 95%.

Field Data Collection
To employ the reliability analysis methods described herein, the engineer requires data. It is imperative to establish field data collection systems to support your reliability management initiatives. Likewise, as much as possible, you’ll want to employ common nomenclature and units so that your data can be parsed effectively for more detailed analysis. Collect the following information:

A good general system for data collection is described in the IEC standard 300-3-2. In addition to providing instructions for collecting field data, it provides a standard taxonomy of failure modes. Other taxonomies have been established, but the IEC standard represents a good starting point for your organization to define its own. Likewise, DOE standard NE-1004-92 offers a very nice standard nomenclature of failure causes.

An important benefit derived from your efforts to collect good field data is that it enables you to break the “random trap.” As I mentioned earlier, the bathtub curve has been much maligned – particularly in the Reliability-Centered Maintenance literature. While it’s true that Weibull analysis reveals that few complex mechanical systems exhibit time-dependent wearout failures, the reason, at least in part, is due to the fact that the reliability of complex systems is affected by a wide variety of failure modes and mechanisms.

When these are lumped together, there is a “randomizing” effect, which makes the failures appear to lack any time dependency. However, if the failure modes were analyzed individually, the story would likely be very different (Figure 13). For certain, some failure modes would still be mathematically random, but many, and arguably most, would exhibit a time dependency. This kind of information would arm reliability engineers and managers with a powerful set of options for mitigating failure risk with a high degree of precision. Naturally, this ability depends upon the effective collection and subsequent analysis of field data.

Figure 13. Good field data collection enables you to break the random trap.

This brief introduction to reliability engineering methods is intended to expose the otherwise uninitiated plant engineer to the world of quantitative reliability engineering. The subject is quite broad, however, and I’ve only touched on the major reliability methods that I believe are most applicable to the plant engineer. I encourage you to further investigate the field of reliability engineering methods, concentrating on the following topics, among others:

More detailed understanding of the Weibull distribution and its applications

More detailed understanding of the exponential distribution and its applications

The Gaussian distribution and its applications

The log-normal distribution and its applications

Confidence intervals (binomial, chi-square/Poisson, etc.)

Beta distribution and its applications

Bayesian applications of reliability engineering methods

Stress-strength interference analysis

Testing options and their applicability to plant reliability engineering

Reliability growth strategies and management

More detailed understanding of field data collection.

Most important, spend time learning how to apply reliability engineering methods to plant reliability problems. If your interest in reliability engineering methods is high, I encourage you to pursue professional certification by the American Society for Quality as a reliability engineer (CRE).

References
Troyer, D. (2006) Strategic Plant Reliability Management Course Book, Noria Publishing, Tulsa, Oklahoma.

Bernowski, K (1997) “Safety in the Skies,” Quality Progress , January.

Dovich, R. (1990) Reliability Statistics, ASQ Quality Press, Milwaukee, WI.

Krishnamoorthi, K.S. (1992) Reliability Methods for Engineers, ASQ Quality Press , Milwaukee, WI.

MIL Standard 721

IEC Standard 300-3-3

DOE Standard NE-1004-92

Appendix:Select reliability engineering terms from MIL STD 721
Availability – A measure of the degree to which an item is in the operable and committable state at the start of the mission, when the mission is called for at an unknown state.

Capability – A measure of the ability of an item to achieve mission objectives given the conditions during the mission.

Dependability – A measure of the degree to which an item is operable and capable of performing its required function at any (random) time during a specified mission profile, given the availability at the start of the mission.

Failure – The event, or inoperable state, in which an item, or part of an item, does not, or would not, perform as previously specified.

Failure, dependent – Failure which is caused by the failure of an associated item(s). Not independent.

Failure, independent – Failure which occurs without being caused by the failure of any other item. Not dependent.

Failure mechanism – The physical, chemical, electrical, thermal or other process which results in failure.

Failure mode – The consequence of the mechanism through which the failure occurs, i.e. short, open, fracture, excessive wear.

Failure, random – Failure whose occurrence is predictable only in the probabilistic or statistical sense. This applies to all distributions.

Failure rate – The total number of failures within an item population, divided by the total number of life units expended by that population, during a particular measurement interval under stated conditions.

Maintainability – The measure of the ability of an item to be retained or restored to specified condition when maintenance is performed by personnel having specified skill levels, using prescribed procedures and resources, at each prescribed level of maintenance and repair.

Maintenance, corrective – All actions performed, as a result of failure, to restore an item to a specified condition. Corrective maintenance can include any or all of the following steps:localization, isolation, disassembly, interchange, reassembly, alignment and checkout.

Maintenance, preventive – All actions performed in an attempt to retain an item in a specified condition by providing systematic inspection, detection and prevention of incipient failures.

Mean time between failure (MTBF) – A basic measure of reliability for repairable items:the mean number of life units during which all parts of the item perform within their specified limits, during a particular measurement interval under stated conditions.

Mean time to failure (MTTF) – A basic measure of reliability for non-repairable items:The mean number of life units during which all parts of the item perform within their specified limits, during a particular measurement interval under stated conditions.

Mean time to repair (MTTR) – A basic measure of maintainability:the sum of corrective maintenance times at any specified level of repair, divided by the total number of failures within an item repaired at that level, during a particular interval under stated conditions.

Mission reliability – The ability of an item to perform its required functions for the duration of specified mission profile.

신뢰성 – (1) The duration or probability of failure-free performance under stated conditions. (2) The probability that an item can perform its intended function for a specified interval under stated conditions. For non-redundant items this is the equivalent to definition (1). For redundant items, this is the definition of mission reliability.