Reliability, Failure Analysis and Asset Management

Introduction

Electrical installations are expected to deliver safe, continuous and economical service over many years. Reliability engineering provides the language and methods for judging whether equipment will perform its required function, how often it may fail, how quickly it can be restored, and whether continued operation is justified. Asset management extends this analysis across the entire life cycle: acquisition, installation, operation, maintenance, renewal and disposal.

These subjects are particularly important in electrical engineering because failures may cause more than production loss. A failed protection system, deteriorated cable, defective transformer or unreliable emergency supply can expose people to electric shock, arc flash, fire and loss of essential services. Decisions must therefore combine probability, consequence, safety, regulatory compliance and cost.

This chapter develops failure-rate, bathtub-curve, MTBF, MTTR, availability, criticality, life-cycle cost and root-cause analysis concepts. It then integrates them into an ISO 55000-aligned asset-management decision process.

Learning objectives

By the end of this chapter, the reader should be able to:

1. Explain reliability, maintainability and availability and distinguish their measures.
2. Interpret failure-rate data and the bathtub curve without misapplying its assumptions.
3. Calculate and interpret MTBF, MTTR, steady-state availability and related measures.
4. Rank electrical assets using criticality and risk.
5. Compare maintenance strategies using life-cycle cost and failure consequences.
6. Apply structured root-cause analysis to an electrical failure.
7. Explain how asset-management decisions support safety, governance and ISO 55000 principles.

1. Fundamental concepts

Reliability and failure

Reliability is the probability that an item performs its required function, under stated conditions, for a specified time interval. The phrase “required function” is essential. A transformer may remain energized but fail to regulate voltage adequately; a circuit breaker may carry normal current but fail to interrupt a fault. Functional requirements should therefore state capacity, performance, environment, duty cycle and safety obligations.

Let T be the random variable representing time to failure. The reliability function is:

where R(t) is dimensionless and t is time. The cumulative distribution function is F(t) = P(T ≤ t), so:

The probability density function f(t), when it exists, is related by f(t) = dF(t)/dt. The hazard or instantaneous failure rate is:

Here λ(t) has units of failures per unit time. It represents the conditional rate of failure at time t, given survival to t. It is not simply the fraction of installed equipment that fails at that instant.

The cumulative hazard is:

and, under the usual continuous-time assumptions:

For a constant failure rate λ, this becomes the exponential model:

This model assumes independent failures, a constant operating environment and no aging-related change in hazard. It is useful for random failures during a stable operating period, but it should not be used automatically for every asset.

Maintainability and repair

Maintainability is the probability that a failed item can be restored to a specified condition within a stated time, using prescribed procedures and resources. Repair time includes diagnosis, isolation, access, replacement or repair, testing and return to service. Waiting for permits, spares or specialist personnel may be included in operational downtime even if it is not hands-on repair time.

For a repair time random variable D, maintainability is:

A mean value of repair time alone does not describe the whole restoration process. Two systems can have the same MTTR while one has highly predictable repairs and the other has occasional extremely long outages.

Availability

Availability is the probability that an item is capable of performing its function when required. It differs from reliability because an item may fail and subsequently be repaired.

For a repairable asset in steady operation, with statistically stable failure and repair processes:

where MTBF is mean time between failures and MTTR is mean time to repair. Both must use the same time unit. This is often called inherent or basic availability when only active repair time is included. Operational availability may additionally include logistics, administration, waiting for permits and delayed access.

For an item that is nonrepairable during a mission, availability is not interchangeable with reliability. A standby generator that fails once and is replaced may be treated differently from a protective relay required to function once during an emergency.

2. Failure-rate models and the bathtub curve

The bathtub curve is a conceptual representation of changing failure rate over an asset population or life cycle. It has three commonly described regions:

1. Infant mortality: high early failure rate, often caused by manufacturing defects, installation errors, poor commissioning, incompatible components or inadequate workmanship.
2. Useful life: approximately constant failure rate, where random stresses dominate.
3. Wear-out: increasing failure rate caused by aging, fatigue, insulation deterioration, corrosion, thermal cycling, bearing wear or depletion of life-limited components.

The curve is not a universal law and may not describe every component. Modern electronic components may exhibit a long constant-rate period with limited wear-out, whereas cables, batteries, capacitors, bearings and insulation systems often show pronounced aging. The observed curve also depends on the definition of failure, maintenance policy, population selection and data censoring.

A constant-rate exponential model has mean time to failure:

MTTF is normally used for nonrepairable items; MTBF is used for repairable systems under a defined failure-and-repair process. In a constant-rate exponential model, the mean is 1/λ, but this relationship does not apply to an arbitrary time-varying failure rate.

A useful aging model is the Weibull distribution:

where β is the shape parameter and η is the characteristic life, in the same time unit as t. Its hazard rate is:

If β < 1, the failure rate decreases, consistent with infant mortality. If β = 1, the failure rate is constant and the model reduces to the exponential distribution. If β > 1, the failure rate increases, consistent with wear-out. Weibull analysis requires appropriate failure-time data and careful treatment of units, censored observations and multiple failure modes.

A planned replacement interval should not be selected merely because an asset is old. Preventive replacement is most justified when age increases failure probability, the failure consequence is significant, the replacement interval is technically effective, and the total cost and safety benefit exceed those of other strategies.

3. Reliability data and performance measures

MTBF, MTTF and failure rate

For a population of repairable assets observed over total operating time Tₒ and experiencing n relevant failures, a simple empirical estimate is:

The hat indicates an estimate. This calculation assumes that the included exposure time and failure definitions are consistent. Scheduled inspections, nuisance alarms and duplicate reports should not be counted as failures unless they represent loss of the defined function.

An empirical failure rate is:

It has units such as failures per operating hour. If n = 0, the estimate λ̂ = 0 does not prove perfect reliability; it reflects insufficient observed failures. Confidence limits or Bayesian methods may be required for zero-failure data.

Worked example: availability

A motor-driven pump operates for 8,000 h and experiences four functional failures. Corrective restoration times are 5, 7, 4 and 8 h.

Total operating exposure is 8,000 h, so:

Mean repair time is:

The steady-state approximation is:

The result assumes the failure and repair process is sufficiently stable and that the four repair times represent the relevant downtime definition. If waiting for a replacement motor added 30 h to one event, operational availability would be lower than the calculated inherent availability.

Availability of series and standby systems

For independent components in a series functional arrangement, every component must work. If component reliabilities are R₁, R₂, …, Rₙ:

For two independent components in parallel, the system works if at least one works:

These equations assume independence and a clearly defined success state. Common-cause failures, shared power supplies, common environmental exposure and maintenance interactions can invalidate the simple parallel benefit. Redundant protection may also create a dangerous misconception: redundancy improves functional availability only if the failure is detected and the remaining channel is capable of performing the safety function.

4. Criticality, risk and maintenance prioritization

Maintenance resources are limited. Criticality analysis helps determine where inspection, spares, condition monitoring, engineering review and renewal should be concentrated. Criticality is not identical to failure frequency. An infrequently failing emergency switchboard may be more critical than a frequently failing nonessential fan.

A practical risk expression is:

Probability may be represented by failure likelihood, while severity can include personnel injury, fire, environmental harm, regulatory breach, production loss, equipment damage and reputation. Multiplication is useful for ranking but can conceal important differences; a low-probability fatal event should not automatically be treated as equivalent to a frequent minor interruption merely because the numerical products match.

A criticality assessment should identify:

• the asset’s required function and operating context;
• credible failure modes and causes;
• consequences to safety, environment, service, production and compliance;
• existing safeguards and their independence;
• detectability and warning time;
• restoration requirements and spare-part constraints;
• legal, insurance and emergency-power obligations.

A qualitative matrix may classify assets as critical, high, medium or low. A quantitative approach may use weighted scores, for example:

where C is a criticality score, S is safety consequence, E environmental consequence, O operational or financial consequence, R regulatory or reputational consequence, and w terms are documented weights. The score is a decision aid, not a physical law. Weights must be agreed, reviewed and tested for sensitivity.

Maintenance strategies can then be selected by failure mode:

Reliability-centered maintenance (RCM) asks what functions are required, how each function can fail, what causes the failure, what happens when it occurs, and which task is technically and economically justified. It avoids the assumption that every asset benefits from more frequent servicing.

5. Root-cause and failure analysis

A symptom is not necessarily a cause. “Breaker tripped” describes an event; it does not establish whether the cause was overload, insulation breakdown, incorrect protection settings, mechanical seizure, wiring error or an unwanted trip signal.

A disciplined investigation normally follows these stages:

1. Make safe and preserve evidence. Isolate energy sources, apply lockout/tagout, control arc-flash hazards and prevent unauthorized reset or alteration.
2. Define the failed function. State what the asset was required to do and under what conditions.
3. Collect facts. Obtain event records, relay oscillography, thermal images, test results, maintenance history, drawings, settings, environmental conditions and operator statements.
4. Construct a timeline. Separate verified observations from assumptions.
5. Identify failure mode and mechanisms. Examples include short circuit, open circuit, loss of insulation, contact erosion, overheating, corrosion or software/configuration error.
6. Analyze causes. Use fault-tree analysis, fishbone diagrams, five-whys questioning, barrier analysis or a combination.
7. Test hypotheses. A proposed cause should explain the evidence and survive attempts at disconfirmation.
8. Select corrective and preventive actions. Address technical, human, organizational and management-system causes.
9. Verify effectiveness. Define a measurable outcome and check it after implementation.

Fault-tree analysis begins with a top event, such as “bus fails to energize,” and logically combines contributing events using AND and OR gates. For independent basic events, an OR combination has probability:

An AND combination has probability:

These simple equations require independence or an appropriate joint model. Common-cause failures violate independence and must be represented explicitly.

Root-cause analysis should not become a search for an individual to blame. If a technician installed a cable incorrectly, investigators should also examine drawing quality, training, supervision, time pressure, verification, procurement and organizational controls. Ethical investigation distinguishes accountability from hindsight bias and protects evidence integrity.

6. Life-cycle cost and renewal decisions

The cheapest purchase price is rarely the lowest total cost. Life-cycle cost includes acquisition, design, installation, energy, inspection, maintenance, downtime, failure consequences, modifications, disposal and residual value.

For a sequence of costs occurring at times t = 0, 1, …, n, the present value is:

C₀ is initial cost, Cₜ is cost in period t, r is the discount rate per period, and Sₙ is residual or salvage value at the end of period n. Costs must be expressed in consistent monetary units and the discount-rate basis must match the time period. If future costs are in nominal currency, the rate should incorporate the relevant inflation assumptions; if costs are real, a real discount rate should be used.

Expected failure cost can be included as:

A rigorous model may use time-varying hazard, multiple failure modes and scenario-dependent consequences rather than one average probability.

Worked life-cycle comparison

Suppose a five-year decision compares two motor-control panels. Panel A costs $20,000 initially and $4,000 per year for energy and maintenance. Panel B costs $28,000 initially and $2,500 per year. Ignore failure consequences and residual value, and use a 5% annual discount rate. The present-value factor for five equal end-of-year costs is approximately 4.3295.

Panel A:

Panel B:

On these assumptions, Panel A has the lower life-cycle cost by approximately $1,506. If Panel B materially reduces arc-flash exposure, outage probability or regulatory risk, the decision may nevertheless favor Panel B. A cost model must not monetize away non-negotiable safety requirements.

7. ISO 55000-aligned asset management

ISO 55000-aligned asset management treats assets as means of achieving organizational objectives. It emphasizes value, alignment, leadership, assurance and continual improvement across the asset life cycle. The approach is broader than maintenance: it includes governance, risk, performance, expenditure, competence, information and stakeholder expectations.

An effective asset-management system commonly includes:

• an asset-management policy and measurable objectives;
• an asset register with unique identification and hierarchy;
• defined functions, performance standards and criticality;
• documented decision criteria for maintenance, renewal and disposal;
• risk-based plans linked to budgets and operational requirements;
• competent personnel and controlled work processes;
• reliable data, configuration control and records;
• performance evaluation, audit and management review;
• continual improvement based on evidence.

The asset register should contain more than make, model and location. Useful fields include duty, rated voltage and current, protection role, installation date, environmental exposure, maintenance history, failure modes, test results, spare-part status, obsolescence risk and functional criticality. Data quality should be governed: missing, duplicated or inconsistent records can produce false confidence in reliability calculations.

Asset decisions should be traceable. A renewal proposal should state the condition evidence, risk reduction, service requirement, alternatives considered, life-cycle cost, safety implications and residual risks. This supports engineering accountability and prevents replacement decisions based solely on age, anecdote or budget cycles.

8. Applied case: illustrative medium-voltage manufacturing plant

Background

A fictional manufacturing plant has a 13.8 kV incoming supply, two transformers, a medium-voltage switchboard and an emergency generator supporting life-safety and process-control loads. The plant has experienced three unexplained feeder trips in eighteen months.

Problem

The maintenance team proposes replacing all feeder breakers on a fixed ten-year schedule. Operations prefers resetting breakers and responding to failures because production interruptions are expensive. The electrical engineer must recommend a defensible strategy.

Analysis

Event records show that two trips occurred during humid weather and one followed a wash-down operation. Infrared inspection found elevated temperature at one cable termination. A review of maintenance records revealed inconsistent torque verification and no standardized post-maintenance insulation-resistance acceptance criteria. The breakers themselves passed mechanical operation tests. The initial symptom—breaker operation—therefore did not prove breaker wear-out.

A criticality assessment identifies the feeder supplying fire pumps and emergency ventilation as high criticality. A packaging feeder is medium criticality because a trip causes production loss but no direct life-safety consequence. The fire-pump feeder also has a hidden protective-function requirement: failure may not be noticed until a fire demand occurs.

Approach and solution

The plant establishes a safe investigation procedure, verifies isolation and performs termination inspection, insulation testing, humidity review and relay-event analysis. Corrective actions include re-termination by qualified personnel, controlled torque records, improved cable sealing, thermographic follow-up and documented protection testing.

For the fire-pump feeder, the plant adds periodic functional proof testing and a monitored alarm for impaired availability. For the packaging feeder, condition-based inspection and corrective maintenance are retained. Fixed replacement of every breaker is rejected because evidence does not show an age-related breaker failure mechanism. A spare breaker and critical termination materials are stocked to reduce MTTR.

The asset register is updated with feeder function, criticality, test intervals, failure history and responsible roles. The maintenance program records both hands-on repair time and total outage time, separating inherent from operational availability.

Outcome

After twelve months, no repeat trips occur on the investigated feeders. The plant reduces unnecessary breaker replacements, improves restoration readiness and obtains stronger evidence for future capital decisions. The key improvement is not a single technology but a connected process: functional definition, evidence-based failure analysis, risk-based maintenance and controlled asset information.

Learning points

1. A trip is a symptom, not a root cause.
2. Environmental and installation factors can dominate apparent equipment reliability.
3. Criticality determines the required assurance level.
4. Hidden protective functions require proof testing, not merely visual inspection.
5. Better data improves both maintenance decisions and governance.

9. Challenges, limitations and contemporary practice

Reliability estimates are affected by small samples, changing duty cycles, incomplete failure reporting, survivorship bias and inconsistent definitions. A calculated MTBF may improve because minor failures are no longer reported, not because the equipment became better. Analysts should document inclusion rules, exposure time, censored data and uncertainty.

Condition monitoring can identify thermal, vibration, partial-discharge, oil-quality or insulation trends, but a sensor does not automatically create useful information. False alarms, sensor drift, poor placement and inadequate response procedures can create cost without reducing risk. Monitoring intervals should reflect failure physics and the available time between detectable degradation and functional failure.

Digital twins, connected sensors and machine-learning models can support anomaly detection and remaining-useful-life estimation. They should supplement—not replace—engineering judgment, protection testing and statutory inspection. Models require representative data and must be tested for false negatives, cybersecurity vulnerabilities and distribution changes. An algorithm that has not observed a rare catastrophic failure cannot demonstrate that it will detect one.

Cybersecurity is now part of electrical asset reliability. Intelligent relays, variable-speed drives and building-management systems may be affected by unauthorized configuration changes, software defects or network outages. Configuration management, access control, backups, secure updates and recovery testing should be included in asset-management plans.

Regulatory compliance remains a boundary condition. No life-cycle calculation justifies operating equipment that fails electrical safety rules, inspection requirements, protection coordination obligations or manufacturer limits. Maintenance personnel must be competent, work must be authorized, and isolation and verification procedures must control hazardous energy.

Best-practice decision process

A practical sequence is:

1. Define the required function and performance standard.
2. Establish the asset boundary, duty and operating context.
3. Collect trustworthy failure, condition and consequence data.
4. Identify failure modes and credible causes.
5. Rank criticality and risk, including hidden safety functions.
6. Select technically effective maintenance or redesign tasks.
7. Compare alternatives using life-cycle cost and risk reduction.
8. Plan spares, skills, access, permits and safe work controls.
9. Measure reliability, repair duration, availability and maintenance quality.
10. Review results and update the asset-management system.

Chapter Summary

Reliability is the probability that an item performs its required function for a specified time, while maintainability concerns restoration after failure and availability concerns readiness for service. Failure rate may decrease, remain approximately constant or increase with age; the bathtub curve is a useful model but not a universal law. MTBF, MTTR and availability are meaningful only when failure definitions, exposure time and downtime boundaries are consistent.

Criticality analysis combines likelihood, consequence, safeguards and operational context to prioritize maintenance. Root-cause analysis must move beyond symptoms and individual blame to physical, human and organizational causes. Life-cycle cost compares alternatives over time using consistent discounting, while safety and legal requirements remain non-negotiable constraints. ISO 55000-aligned asset management connects engineering evidence, risk, performance, information, governance and continual improvement across the asset life cycle.

Key Terms

Reliability: Probability that an item performs its required function for a specified time under stated conditions.

Failure rate: Conditional rate at which an item fails, given survival to a specified time.

Hazard function: Another name for the instantaneous failure rate λ(t).

MTTF: Mean time to failure for a generally nonrepairable item.

MTBF: Mean time between failures for a repairable item under defined conditions.

MTTR: Mean time to repair or restore a failed item.

Availability: Probability that an item is capable of performing its function when required.

Maintainability: Probability of restoring an item within a specified time.

Bathtub curve: Conceptual curve showing infant mortality, useful life and wear-out regions.

Weibull distribution: Flexible life distribution whose shape parameter can represent decreasing, constant or increasing failure rate.

Criticality: Relative importance of an asset based on function, consequence and risk.

Risk: Combination of likelihood and consequence.

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

Root cause: Fundamental condition whose removal prevents recurrence of a failure.

Fault-tree analysis: Deductive analysis from a top event to combinations of contributing events.

Life-cycle cost: Present value of acquisition, operation, maintenance, failure and disposal costs.

Condition-based maintenance: Maintenance initiated by evidence of deteriorating condition.

Proof test: A planned test intended to reveal hidden failures in a protective function.

Asset register: Controlled record of assets, attributes, relationships, condition and history.

Asset management: Coordinated activity that realizes value from assets across their life cycle.

Review Questions

Short Answer Questions

1. Distinguish reliability from availability.
2. What are the three regions of the bathtub curve?
3. Define MTBF and MTTR.
4. Why can a high-MTBF asset still be highly critical?
5. State two requirements for a useful root-cause investigation.

Long Answer Questions

1. Explain the exponential and Weibull reliability models, including their assumptions and engineering applications.
2. Discuss how criticality analysis can be used to select among corrective, preventive and condition-based maintenance.
3. Explain the difference between inherent and operational availability and identify factors that cause them to differ.
4. Describe a complete root-cause analysis process for a recurring electrical protection failure.
5. Explain how life-cycle cost and ISO 55000-aligned governance support asset-renewal decisions.

Analytical / Application Questions

1. A repairable switch has 12,000 operating hours and six failures. Repair times are 3, 5, 4, 6, 2 and 4 h. Calculate the estimated MTBF, MTTR and steady-state availability, then state one limitation of the calculation.
2. A transformer has increasing oil-temperature alarms but no forced outage. Propose a condition-monitoring and decision process that distinguishes immediate safety action from planned renewal.
3. A safety-related feeder has low failure frequency but severe consequences and a long spare-lead time. Develop a risk-based maintenance and spare-parts strategy, explaining why frequency alone is inadequate.

Multiple Choice Questions with Answers

Question 1

For a constant failure rate λ, which expression gives reliability at time t?

A. R(t) = 1 − λt

B. R(t) = e^(−λt)

C. R(t) = λ/t

D. R(t) = λ + t

Correct Answer: B. R(t) = e^(−λt)

Question 2

An asset has MTBF = 1,000 h and MTTR = 10 h. What is its steady-state availability?

A. 90.0%

B. 98.0%

C. 99.0%

D. 99.9%

Correct Answer: D. 99.9%

Question 3

A Weibull shape parameter β greater than 1 generally indicates:

A. A decreasing failure rate

B. A constant failure rate

C. An increasing failure rate

D. Zero probability of failure

Correct Answer: C. An increasing failure rate

Question 4

Which measure is most directly associated with the time required to restore a failed asset?

A. MTTR

B. MTBF

C. MTTF

D. Criticality

Correct Answer: A. MTTR

Question 5

Why may a low-frequency failure require the highest maintenance priority?

A. Frequency always determines priority

B. It may have severe safety or operational consequences

C. It always has a short repair time

D. It proves the asset is in its useful-life region

Correct Answer: B. It may have severe safety or operational consequences

Question 6

Which maintenance approach is generally appropriate when degradation can be detected before functional failure?

A. Condition-based maintenance

B. Uncontrolled run-to-failure

C. Immediate disposal after every inspection

D. Ignoring condition data

Correct Answer: A. Condition-based maintenance

Question 7

In a root-cause analysis, “the breaker tripped” is best classified as:

A. A verified root cause

B. A life-cycle cost

C. A symptom or event requiring further analysis

D. A maintenance strategy

Correct Answer: C. A symptom or event requiring further analysis

Question 8

In a present-value life-cycle cost calculation, future costs are discounted because:

A. Future costs have no monetary value

B. Money and costs occurring at different times are not directly equivalent

C. Discounting removes safety requirements

D. Discounting guarantees the lowest purchase price

Correct Answer: B. Money and costs occurring at different times are not directly equivalent

Question 9

Which statement best reflects ISO 55000-aligned asset management?

A. It focuses only on corrective maintenance

B. It replaces electrical safety regulations

C. It connects asset decisions with value, risk, performance and life-cycle objectives

D. It requires every asset to be replaced at the same age

Correct Answer: C. It connects asset decisions with value, risk, performance and life-cycle objectives

Question 10

For two independent components in parallel, the system reliability is:

A. R₁R₂

B. R₁ + R₂

C. 1 − (1 − R₁)(1 − R₂)

D. 1 − R₁R₂

Correct Answer: C. 1 − (1 − R₁)(1 − R₂)