Reliability, Failure Analysis and Asset Criticality

Introduction

Production systems create value only when equipment performs its required function safely, consistently and economically. Reliability engineering examines the probability that an asset will perform its intended function for a specified time under stated conditions. Maintenance management complements reliability by restoring or preserving that function. Together, they support decisions about inspection intervals, spare parts, maintenance tactics, replacement and risk control.

Reliability should not be confused with durability. Durability concerns the length of useful life; reliability concerns successful performance over a specified operating period. An old but well-maintained pump may be reliable, while a new pump installed incorrectly may be unreliable. Reliability is therefore influenced by design, manufacture, installation, operation, environment, maintenance and human factors.

Learning Objectives

On completing this chapter, the learner should be able to:

1. Define reliability, availability, maintainability, MTBF and MTTR.
2. Calculate basic reliability and availability measures.
3. Classify failures and interpret failure-rate behaviour.
4. Use Pareto analysis to prioritise chronic losses.
5. Assess equipment criticality using consequence and likelihood.
6. Conduct a practical failure mode and effects analysis (FMEA).
7. Explain reliability-centred maintenance (RCM) and select suitable tasks.
8. Compare life-cycle costs and make basic replacement decisions.
9. Recognise data, ethical, safety and governance limitations in reliability decisions.

1. Core Reliability Concepts

1.1 Function and functional failure

An asset performs one or more functions, each with a required performance standard. For example, a cooling-water pump may be required to deliver 100 m³/h at 4 bar, without leakage and without exceeding vibration limits. A functional failure occurs when the asset cannot meet one or more specified standards. Failure is therefore relative to a required function, not merely to physical deterioration.

Failure may be:

• Complete: the function is totally lost.
• Partial: performance remains, but below the required standard.
• Intermittent: the function is lost and recovered unpredictably.
• Degraded: performance gradually falls because of wear, fouling or ageing.
• Incipient: a detectable condition indicates that functional failure is developing.

1.2 Reliability function

Let T be the random variable representing time to failure. Reliability at time t is the probability that failure has not occurred by t:

Here, R(t) is dimensionless reliability, P denotes probability, and F(t) is the cumulative distribution function of failure time. The expression applies to a defined population, operating condition and failure criterion.

For an exponential failure-time model with constant failure rate λ:

λ is the failure rate, normally expressed as failures per operating hour, and t is operating time. This model assumes statistically independent failures, a constant hazard rate and no ageing effect. It is often useful for random failures during a stable operating period, but it is inappropriate when wear-out is dominant.

The mean time to failure (MTTF) for a non-repairable item is:

For the exponential model, MTTF = 1/λ. MTTF applies to non-repairable items; MTBF is generally used for repairable assets.

1.3 Failure rate and the bathtub curve

The hazard or instantaneous failure rate is:

where f(t) is the probability density of failure time. The familiar bathtub curve has three broad regions:

1. Early-life failures: high but decreasing rate, often associated with design defects, poor installation or commissioning errors.
2. Useful life: approximately constant random-failure rate.
3. Wear-out: increasing rate caused by fatigue, corrosion, erosion, ageing or accumulated damage.

The bathtub curve is a conceptual model, not a universal law. Many modern electronic and complex systems do not show a pronounced wear-out phase, and inappropriate time-based replacement can introduce installation-related failures.

1.4 Series and parallel systems

For a series system, all components must work. If component failures are independent:

For two independent components, R_s = R₁R₂. Thus, adding components in series reduces system reliability.

For a parallel redundant system, at least one component must work:

These equations assume clearly defined system logic and statistical independence. Common-cause failures, shared utilities and human errors can invalidate the apparent benefit of redundancy.

2. Maintainability, Availability and Maintenance Metrics

2.1 Maintainability and MTTR

Maintainability is the probability that a failed asset can be restored to a specified condition within a stated time, using defined procedures and resources. It depends on accessibility, modular design, diagnostics, tools, skills, spares and work control.

Mean time to repair (MTTR) is the average active repair time. In practice, organisations must distinguish active repair time from total downtime, which may include waiting for diagnosis, permits, materials, craftsmen and production release.

For an exponential repair-time model with repair rate μ:

M(t) is maintainability by time t and μ is the repair rate, measured in repairs per hour. For this model, MTTR = 1/μ. The model assumes independent repair times and a constant repair rate.

2.2 Availability

Availability is the probability that an asset is capable of performing its function when required. Several definitions must be distinguished.

Inherent availability considers only corrective maintenance and active repair time:

Achieved availability includes preventive-maintenance time but generally excludes logistics and administrative delays. Operational availability includes realistic downtime such as waiting for spares, permits, technicians and production scheduling:

Availability is dimensionless and normally reported as a percentage. MTBF and MTTR must use the same time unit. High reliability does not automatically mean high availability: a rare but very long repair can produce poor availability.

Worked Example 1: MTBF, MTTR and availability

A packaging machine operates for 4,800 scheduled hours in a year. It experiences 12 functional failures and accumulates 60 hours of active corrective repair. Ignore planned maintenance for inherent availability.

Assuming operating time is approximated by scheduled time minus active repair time:

MTBF = (4,800 − 60) ÷ 12 = 395 h

MTTR = 60 ÷ 12 = 5 h

Therefore:

Aᵢ = 395 ÷ (395 + 5) = 0.9875

Inherent availability is approximately 98.75%. If the 60 hours exclude waiting for parts and technicians, operational availability will be lower and must be calculated from actual calendar uptime and downtime.

Worked Example 2: exponential reliability

A fan has a constant failure rate of 0.0004 failures per hour. Reliability over 1,000 hours is:

R(1,000) = e^(−0.0004×1,000) = e^(−0.4) ≈ 0.6703

The probability of surviving 1,000 hours is approximately 67.0%, under the stated exponential assumptions.

3. Failure Analysis and Data Quality

Failure analysis seeks to identify physical, human and organisational causes rather than merely recording symptoms. A useful investigation separates:

• Symptom: what was observed, such as high temperature.
• Failure mode: how the function was lost, such as bearing seizure.
• Physical cause: the mechanism, such as lubricant starvation.
• Root cause: the underlying management or design condition, such as an unsuitable lubrication interval or inaccessible grease point.
• Consequence: the effect on safety, environment, quality, delivery and cost.

A disciplined investigation normally includes event chronology, evidence preservation, interviews, inspection, maintenance records, operating data and causal verification. The “five whys” method is useful for simple causal chains, while fault-tree analysis, fishbone diagrams and statistical analysis are useful for more complex cases. A root cause should be supported by evidence and should lead to a controllable corrective action.

3.1 Data requirements

Reliability decisions depend on consistent records. A minimum failure record should include asset identity, function, failure date and time, operating conditions, failure mode, cause, detection method, downtime categories, repair action, parts used and return-to-service time. Codes should be standardised through an equipment hierarchy and failure taxonomy.

Common data problems include duplicate work orders, confusing planned work with failures, missing start or finish times, changing equipment configurations and reporting only visible failures. A calculated MTBF is not meaningful if the numerator and denominator are inconsistent.

3.2 Pareto analysis

Pareto analysis ranks categories by their contribution to a selected loss measure, such as downtime hours, maintenance cost, number of failures or safety events. It is based on the practical observation that a relatively small number of categories may account for a large proportion of loss; the 80/20 ratio is a heuristic, not a law.

Procedure:

1. Define the population, period and measure.
2. Group events using consistent categories.
3. Sort categories from largest to smallest.
4. Calculate cumulative totals and percentages.
5. Investigate the vital few, while checking that high-consequence rare events are not hidden by frequency rankings.

Pareto analysis identifies where to investigate; it does not itself prove causation.

Worked Example 3: downtime Pareto

A line records downtime by cause: sensor faults 42 h, material jams 30 h, motor trips 18 h, changeover delays 10 h and other causes 5 h. Total downtime is 105 h. Sensor faults account for 40.0%, material jams for 28.6%, and motor trips for 17.1%. The cumulative percentage after the first three categories is 85.7%. The improvement team should initially examine these three categories, but it should separately review any “other” event involving serious risk.

4. Asset Criticality Assessment

Criticality expresses the relative importance of an asset to business and stakeholder outcomes. It is not the same as equipment value. A low-cost valve may be highly critical if its failure causes a hazardous release or shuts down the entire plant.

A practical assessment considers:

• personnel safety and process safety;
• environmental consequences;
• product quality and regulatory compliance;
• production loss and customer impact;
• repair cost and required lead time;
• redundancy and recovery options;
• detectability and escalation potential.

A simple semi-quantitative model is:

Scores may be rated from 1 to 5, with documented definitions. The multiplication is a prioritisation convention, not a probability calculation unless the scales are statistically calibrated. A risk matrix should therefore be supplemented by engineering judgement and specific review of catastrophic scenarios.

Criticality must be periodically reassessed after process changes, altered production rates, new hazards, obsolescence or changes in redundancy.

5. Failure Mode and Effects Analysis

FMEA is a structured, bottom-up method that examines how an item can fail and what results. A worksheet generally contains function, failure mode, effect, cause, existing controls, detection method, recommended action, responsible person and due date.

Traditional FMEA often assigns:

• Severity (S): consequence of the effect;
• Occurrence (O): likelihood or frequency of the cause;
• Detection (D): likelihood that current controls will fail to detect the problem before the effect occurs.

The traditional risk priority number is:

Each rating must have a documented scale, commonly 1 to 10. RPN is a screening aid, not a physical risk measure. It can rank a frequent low-severity failure above a rare catastrophic failure, depending on the scores. High-severity items should receive attention regardless of RPN, and modern practice often uses action priority rules or separate severity gates.

FMEA quality depends on a multidisciplinary team including operations, maintenance, engineering, quality, safety and, where relevant, suppliers. Controls should be distinguished as prevention controls and detection controls. Recommended actions should alter design, operating practice, inspection, training or maintenance—not merely request that personnel “be careful.”

6. Reliability-Centred Maintenance

RCM is a structured process for determining what must be done to ensure that an asset continues to perform its required functions in its operating context. Its logic is:

1. Define the asset and operating context.
2. Identify functions and performance standards.
3. Identify functional failures.
4. Identify failure modes and causes.
5. Determine effects and consequences.
6. Select technically feasible and worth-doing maintenance tasks.
7. Define default actions when no proactive task is suitable.
8. Implement, measure and revise the programme.

The principal task categories are:

• On-condition task: inspect a measurable condition and act before functional failure, such as vibration monitoring.
• Scheduled restoration: restore capability at a defined interval, where age-related failure is sufficiently predictable.
• Scheduled discard: replace at a defined interval, where useful life and failure risk justify it.
• Failure-finding task: periodically test a hidden protective function, such as an emergency shutdown system.
• Redesign: change the equipment, process or operating context when maintenance cannot manage the risk.
• Run-to-failure: accept failure and repair after failure when consequences and total cost are acceptable.

RCM rejects the assumption that every item should receive frequent time-based maintenance. A task is justified when it is technically feasible, applicable to the failure behaviour and economically or risk-wise worthwhile. Safety and environmental consequences can justify a task even where direct financial savings are small.

7. Life-Cycle Costing and Replacement Decisions

Purchase price is only one element of ownership cost. Life-cycle cost (LCC) includes acquisition, installation, energy, operation, preventive and corrective maintenance, downtime, training, disposal and residual value. A general undiscounted form is:

C₀ is initial acquisition and installation cost, Cₒ,ₜ operating cost in period t, Cₘ,ₜ maintenance cost, C_d,ₜ downtime or consequence cost, and Sₙ residual or salvage value at the end of n periods. All terms must use the same monetary basis.

For investment comparison, future cash flows should be discounted:

PV is present value, Cₜ is a cash flow at time t, i is the discount rate per period and t is the number of periods. A discounted LCC is the sum of the present values of all relevant costs minus the present value of residual value. Inflation treatment must be consistent: use nominal costs with a nominal discount rate, or real costs with a real discount rate.

Basic replacement logic

Replacement is justified when the expected economic and risk benefits of the proposed asset exceed its acquisition and transition costs. Relevant evidence includes rising corrective cost, increasing downtime, obsolescence, safety exposure, energy inefficiency, poor support and declining performance. A replacement should not be justified solely by age if condition and failure risk remain acceptable.

For assets with unequal lives, comparing total cost over each asset’s own life can be misleading. Equivalent annual cost (EAC) converts a present value into an annual equivalent:

This assumes a constant discount rate i, a service life of n periods and an equivalent annual cash-flow interpretation. The alternative with lower EAC is preferred only if service, risk, capacity and performance are comparable.

8. Applied Case: Illustrative Critical Pump Assessment

Background

An illustrative chemical-processing plant has two cooling-water pumps, one duty and one standby. The duty pump has experienced repeated seal failures and occasional bearing overheating. Cooling loss can force a controlled production shutdown; a seal failure can also create a chemical exposure hazard.

Problem

The maintenance department proposes replacing seals every six months. Operations argues that the real issue is poor alignment and contaminated lubricant. Management requires a defensible maintenance and investment recommendation.

Analysis

The team first confirms the pump function: deliver the specified flow and pressure continuously within vibration, temperature and leakage limits. Failure records over 18 months show 9 seal failures and 4 bearing-related interventions. However, records do not consistently distinguish active repair time from waiting time, so operational availability is recalculated from production logs.

The criticality review assigns high consequence to loss of cooling and very high consequence to hazardous leakage. Existing redundancy reduces production frequency consequences but does not eliminate safety exposure, because the standby pump may be unavailable or the common cooling header may fail.

The FMEA identifies seal leakage, bearing lubrication loss, shaft misalignment and standby-start failure. Controls include visual rounds, vibration checks and a monthly standby test. The team verifies that the standby test does not test operation under full thermal load.

Approach and solution

The RCM review selects:

• condition monitoring of vibration and bearing temperature;
• alignment verification after installation and coupling work;
• contamination control and lubricant sampling;
• a failure-finding test of the standby pump under representative conditions;
• inspection of seal-flush pressure and filtration;
• redesign of the seal-flush arrangement if contamination is confirmed;
• controlled spare seals and bearings because of supplier lead time.

A six-month seal replacement is not automatically retained. If the failure pattern is random or driven by contamination, age-based replacement may waste good seals and create installation-induced failures. The plant also compares the present-value cost of improved sealing and monitoring with replacement by a more robust pump. Safety and compliance costs are included, not only maintenance labour.

Outcome

The recommended decision is conditional: implement the controls for one monitoring cycle, validate failure causes, and proceed with replacement if risk remains above the approved threshold or if the LCC analysis favours the new pump. The case demonstrates that criticality, FMEA, RCM and LCC are complementary rather than competing methods.

Learning points

1. A standby asset is not effective redundancy unless it is capable, available and tested.
2. Repeated symptoms do not establish root cause.
3. Safety consequence can justify action even when failure frequency is low.
4. Maintenance intervals should follow failure behaviour and task applicability.
5. Decisions require reliable downtime, cost and condition data.

9. Governance, Safety and Contemporary Practice

Reliability decisions have ethical consequences. Suppressing failure reports, manipulating downtime, extending inspection intervals without engineering justification or classifying hazardous failures as routine undermines safety and violates professional responsibility. Critical protective systems require traceable testing, competency assurance, management of change and compliance with applicable occupational-safety, environmental, pressure-equipment and process-safety requirements.

Computerised maintenance management systems (CMMS) and enterprise asset-management systems support history, planning and cost control. Sensors, edge devices and machine-learning models can identify abnormal vibration, temperature or energy use. However, predictive analytics should not be treated as an autonomous safety decision. Models require representative data, verification, cybersecurity, alarm governance and human review. False alarms cause alarm fatigue; missed alarms create false confidence. Data ownership, access control and audit trails are increasingly part of asset governance.

Best practice includes clear asset hierarchy, standard failure codes, disciplined work-order closure, calibrated instruments, competent analysis, independent review of high-risk decisions, and periodic validation of maintenance outcomes. Key performance indicators should include availability, schedule compliance, repeat failures, planned-to-corrective work ratio, overdue safety tasks, and risk reduction—not only maintenance cost.

Challenges and Limitations

Reliability calculations often assume independence, constant rates and complete data, while real plants contain common-cause failures, changing loads, deferred work and human interactions. MTBF can be distorted by inconsistent failure definitions or by averaging unlike operating contexts. Availability may be overstated when waiting time is excluded. Pareto charts can favour frequent minor events over rare catastrophic ones. FMEA scores may reflect team opinion rather than measured probability. RCM can become bureaucratic if functions and consequences are poorly defined. LCC depends on uncertain energy prices, failure costs, discount rates and residual values.

These limitations do not make the methods useless; they require transparent assumptions, sensitivity analysis, quality data and professional judgement. Quantitative outputs should inform decisions, not conceal uncertainty.

Chapter Summary

Reliability is the probability that an asset performs its required function for a stated time and condition. Maintainability concerns restoration, while availability combines successful operation and downtime. MTBF, MTTR, MTTF and reliability equations are useful only when their definitions, assumptions and data boundaries are clear. Failure analysis distinguishes symptoms, failure modes, physical causes, root causes and consequences. Pareto analysis prioritises investigation, whereas criticality assessment combines likelihood and consequence to guide risk-based attention. FMEA provides a structured examination of failure modes and controls, while RCM selects technically feasible and economically or risk-justified maintenance tasks. Life-cycle costing broadens decisions beyond purchase price, and replacement analysis should include downtime, risk, energy, obsolescence and residual value. Effective practice depends on trustworthy data, multidisciplinary review, safety governance and continuous learning.

Key Terms

Reliability: Probability that an asset performs its required function for a specified time and condition.

Availability: Probability or proportion of time that an asset is capable of performing its function.

Maintainability: Probability that an asset can be restored within a specified time.

MTBF: Mean time between functional failures for a repairable asset.

MTTR: Mean active time required to repair and restore an asset.

MTTF: Mean time to failure for a non-repairable item.

Failure mode: The manner in which a function is lost.

Failure cause: Physical, human or organisational reason for a failure mode.

Root cause: Underlying cause whose removal prevents recurrence.

Hazard rate: Instantaneous rate of failure conditional on survival to a given time.

Pareto analysis: Ranking of loss categories to identify major contributors.

Asset criticality: Relative importance of an asset based on consequence and likelihood.

FMEA: Structured analysis of functions, failure modes, effects, causes and controls.

RPN: Product of severity, occurrence and detection ratings in traditional FMEA.

RCM: Process for selecting maintenance based on functions, consequences and failure behaviour.

On-condition task: Inspection of a condition with action before functional failure.

Failure-finding task: Test intended to reveal hidden failure of a protective function.

Life-cycle cost: Total ownership cost over an asset’s service life.

Equivalent annual cost: Annualised value used to compare alternatives with different lives.

Common-cause failure: Failure of multiple redundant elements due to a shared cause.

Review Questions

Short Answer Questions

1. Distinguish reliability from availability.
2. Why is MTBF not normally used for a non-repairable item?
3. State two limitations of Pareto analysis.
4. What is the purpose of a failure-finding task?
5. Why must active repair time be distinguished from total downtime?

Long Answer Questions

1. Explain the bathtub curve and discuss when its assumptions may be inappropriate.
2. Describe the stages of an RCM study and the principal maintenance task categories.
3. Explain how criticality assessment should incorporate safety, environmental and production consequences.
4. Compare FMEA with root-cause analysis, including their different purposes.
5. Discuss the components and assumptions of a life-cycle cost analysis.

Analytical / Application Questions

1. An asset operates for 7,200 scheduled hours, has 18 failures and requires 90 active repair hours. Calculate approximate MTBF, MTTR and inherent availability. State your assumptions.
2. A plant’s top downtime categories are pump trips, sensor faults, material jams, changeovers and miscellaneous events. Design a Pareto-analysis procedure and explain how you would avoid overlooking rare catastrophic events.
3. A redundant standby pump is available but is never tested under operating conditions. Assess whether it should receive a high criticality rating and recommend an RCM task set with justification.

Multiple Choice Questions with Answers

Question 1

A machine operates for 2,000 hours, experiences 5 failures, and requires 25 active repair hours. Using operating time as 2,000 − 25 hours, what is its approximate MTBF?

A. 375 hours

B. 395 hours

C. 400 hours

D. 405 hours

Correct Answer: B. 395 hours

Question 2

Under the exponential constant-failure-rate model, reliability is represented by which expression?

A. R(t) = λt

B. R(t) = 1 − e^(−λt)

C. R(t) = e^(−λt)

D. R(t) = MTTR ÷ MTBF

Correct Answer: C. R(t) = e^(−λt)

Question 3

Which measure includes waiting for parts, technicians and production release?

A. Inherent availability

B. Operational availability

C. Active repair time

D. Maintainability

Correct Answer: B. Operational availability

Question 4

What is the main purpose of Pareto analysis?

A. To prove the physical root cause of every failure

B. To rank loss categories and prioritise investigation

C. To calculate the exact probability of catastrophic failure

D. To determine the discount rate for replacement

Correct Answer: B. To rank loss categories and prioritise investigation

Question 5

In traditional FMEA, the risk priority number is calculated as:

A. Severity + occurrence + detection

B. Severity × occurrence × detection

C. Occurrence ÷ severity × detection

D. Detection − occurrence − severity

Correct Answer: B. Severity × occurrence × detection

Question 6

Which RCM task is intended to reveal a hidden failure in a protective function?

A. Scheduled discard

B. Failure-finding task

C. Run-to-failure task

D. Lubrication task only

Correct Answer: B. Failure-finding task

Question 7

A series system requires every independent component to operate. If component reliabilities are 0.98 and 0.95, what is system reliability?

A. 0.030

B. 0.930

C. 0.950

D. 0.931

Correct Answer: D. 0.931

Question 8

Which statement about the traditional FMEA RPN is most accurate?

A. It is a direct probability of failure

B. It always prioritises catastrophic failures correctly

C. It is a screening aid dependent on rating scales

D. It eliminates the need for engineering judgement

Correct Answer: C. It is a screening aid dependent on rating scales

Question 9

In life-cycle costing, which item is normally included?

A. Only purchase price

B. Only corrective labour

C. Acquisition, operation, maintenance, downtime and disposal effects

D. Only salvage value

Correct Answer: C. Acquisition, operation, maintenance, downtime and disposal effects

Question 10

For inherent availability, the standard basic relationship is:

A. MTBF ÷ (MTBF + MTTR)

B. MTTR ÷ (MTBF + MTTR)

C. MTBF × MTTR

D. MTBF − MTTR

Correct Answer: A. MTBF ÷ (MTBF + MTTR)