1
Basic Concepts

1.1. Introduction

Definitions of terms and parameters used throughout this book are given in this chapter. They are based1 mainly on [IEC 15a] and its companion standard [IEC 16a], although not all standards (even IEC ones) are in line with [IEC 15a]. The assessments of the production availability and the reliability parameters are most of the time based on the assumption that the failure rate is a constant, so the meaning of this assumption is given as well as its limits. In addition to this, the characteristics of the so-called "bathtub curve" are provided. The bathtub curve is mainly relevant for the early phase that is crucial for a proper evaluation of the economics of a project.

1.2. Definition of terms

1.2.1. Risk

During the life of a plant, events may occur which could impact human life, environment, equipment or project profitability. These events can then be named unwanted events. Then for each of these four categories, a curve (see Figure 1.1) characterized by (1) its frequency of occurrence (or its probability) and (2) its severity (amount of the consequence to human life, environment, equipment or project profitability) can be determined. This curve is called a risk:

• - The severity axis could be the plant production unavailability and the probability axis the probability of reaching this production unavailability.
• - The severity axis could be the potential number of deaths and the probability axis the probability of occurrence of these events.

[IEC 13a] considers the risk as a combination of the probability and the severity without considering the magnitude of the consequences. Then this definition is to be discarded, as risk causing the plant to be in the red is not at all to be considered on the same level as a risk causing a decrease of 10% in the plant profitability.

Figure 1.1. Risk in the two-dimension space

For safety (or environmental) risks, a major step is to be carried out before trying to assess the risks: the identification of the hazards (i.e. the potential sources of impact on human life and on the environment2) and their characterization. This theme is not considered in this book.

1.2.2. Time definitions

Figure 1.2 shows the failure-to-repair cycle of a repairable item (TBF = operating Time Between Failures, RT = Repair Time).

Figure 1.2. Failure-to-repair cycle

The Mean operating Time Between Failures (MTBF) is calculated as follows:

The word "operating" was introduced into the definition to prevent the use of S(operation time + repair time) as the numerator.

The Mean Repair Time (MRT) is calculated as follows:

The acronym MTTR was used in the past instead of MRT. [IEC 15a] considers the MTTR as the Mean Time To Restoration, an acronym no longer used in this book as the restoration time is a mixture of repair times, start-up times, mobilization times, etc., which are different physical events.

For non-repairable items, there is obviously no Repair Time (and then no MRT) and the acronym MTTF (Mean operating Time To Failure) is used instead of MTBF.

The Mean operating Time To Failure is calculated as follows:

1.2.3. Failures and repairs

1.2.3.1. Definitions

A failure is the loss of the ability to perform as required. The failure causes are the set of circumstances that lead to the failure. The failure modes are the effects by which the failure is observed. The failure effects are the consequences of the failure. Figure 1.3 shows an example of the relationship of failure causes, failure modes and failure effects for a pressure safety valve.

Figure 1.3. Relationship of failure causes, failure modes and failure effects

Failure modes are often classified in several ways depending on the intent of their use, e.g. according to [LEE 12]:

• - Condition category (used for maintenance purposes) that emphasizes the causes.
• - Performance category that emphasizes the effects.
• - Safety category: see section 1.2.4.4.
• - Detection category: see section 1.2.4.4.

These categories are used for defining the purpose of Failure Mode and Effects Analysis (section 4.2).

"The failure mechanism is the physical, chemical, thermodynamic or other process or combination that leads to the failure. It is an attribute of the failure event that can be deduced technically" (from [ISO 16]).

The circumstances that induce or activate the processes are termed the root causes of failure.

1.2.3.2. Measures

Several definitions are provided in the standards, which are as follows:

• - The instantaneous failure rate ?(t) (also named failure rate, hazard function, hazard rate, force of mortality):

also written as [IEC 16a]:

• - The instantaneous failure intensity z(t) (also named failure intensity, failure frequency, Rate of OCcurrence Of Failures [ROCOF]):

where:

• - E(x): expectation of x
• - N(t): number of failures in the time interval [0, t].
• - The conditional failure intensity ?v(t) (also named Vesely failure rate):

Using [1.7], it can be shown that:

The probability of failure upon demand (the probability of starting failure) is the ratio of the total start failures to the number of attempted item starts [IEE 07a]:

An instantaneous repair rate µ(t) can also be defined:

Within this book, reliability data3 are data on failure frequencies (and probabilities of failure to start), repair times and failure mode percentages.

1.2.3.3. Phases of use of an item

The three phases of use of any item are:

• - OFF, i.e. standby phase or on-guard phase;
• - transition OFF - ON, i.e. (nearly instantaneous) switch to running phase;
• - ON, i.e. running phase.

These are shown in Figure 1.4.

Figure 1.4. The three phases of use of an item

The qualification of the three phases of use of normally running items and on-guard items along their life are as follows:

• 1) For normally running items (the ones considered in production availability studies): standby phase (or even mothballed phase if the standby period exceeds several weeks), transition standby phase to running phase and running phase. Each of these phases has its own reliability characteristics:
  • i) Standby failure rate for the standby phase: it is, most of the time, considered as negligible.
  • ii) Probability of failure upon demand ? for the standby phase to running phase: this parameter is often considered for rotating machines (also named failure to start) only and is given in reliability data books (Chapter 6).
  • iii) Failure rate ? for the running phase: the failure rate provided within the reliability data books. According to [JAN 15], a major gas turbine manufacturer bases its gas turbine maintenance requirements on independent counts of starts and running hours, e.g. hot gas path inspection is to be performed every 24,000 hr or 1,200 starts, whichever criteria limit is reached first. They implemented this approach as life limiters are different for starts and running hours: definitively ? and ? are not to be considered in the same way.
• 2) For on-guard items (the ones considered in reliability studies): on-guard phase, transition on-guard phase to running phase and running phase. Each of these phases has its own reliability characteristics:
  • i) Failure rate ? for the on-guard phase (standby failure rate): this parameter is used for calculating PFDavg and PFH (section 1.2.4.3). It is given in reliability data books.
  • ii) Probability of failure upon demand ? for the on-guard phase to running phase: this parameter is most of the time not considered. As a consequence, PFDavg and PFH considered in reliability calculations are too high, causing often to recommend a too-high proof test frequency.
  • iii) Failure rate ? for the running phase: the failure rate is not considered as the running phase is short compared to the standby phase.

Based on [NUR 03], it could be considered that standby failure rate is most appropriate for shutoff valves but that standby failure rate and probability of failure upon demand ? are to be considered for on-guard rotating machines such as emergency diesel generators.

A causal analysis coupled with expert judgment [PIE 92] allows us to determine the standby failure rate, the probability of failure upon demand ? and the failure rate ? (for the running phase) from field data.

REMARK 1.1.- The PFDavg (see section...