Chapter 2: Maintenance Forecasting and Capacity Planning

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Chapter 2 Maintenance Forecasting and Capacity
Planning

• Overview
• Maintenance load forecasting
• Qualitative Forecasting Techniques
• Quantitative Forecasting Techniques
• Error Analysis
• Forecasting Maintenance Work
• Maintenance Capacity Planning
• Deterministic Techniques for Maintenance
  Capacity Planning
• Stochastic Techniques for Maintenance Capacity
  Planning
• Contract Maintenance

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Maintenance Load Forecasting

• Definitions
• Maintenance load forecasting is the process by
  which the maintenance load is predicted
• Maintenance load f(age of equipment, rate of
  equip. use, maintenance quality, climatic
  factors, skills of maintenance workers, etc.)
  and varies randomly
• Models
• Qualitative forecasting expertise, experience
  and judgment (historical analogy, surveys, the
  Delphi method)
• Quantitative forecasting mathematical models
  uses historical data to estimate future trends (
  time series-based methods moving averages,
  exponential smoothing structure methods
  regression models)

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Role of Maintenance Load Forecasting in a
Maintenance System
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Maintenance Load Forecasting

• Quality of forecasting models
• Accuracy
• Simplicity
• Flexibility
• Factors to select the forecasting approach
• The purpose of forecast
• The time horizon for the forecast
• The availability of the data

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Qualitative Forecasting Techniques

• Extract information by questionnaires or
  interviews identify variables
• Identify the relationships among the variables
  cause-and-effect or the Delphi techniques
• Identify which variables influence the forecast
  and the impact of each one
• Estimate the magnitude of the variables reduce
  variation by interactive process

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Quantitative Forecasting Techniques

• Simple Moving Average
• Weighted Moving Average
• Exponential Smoothing
• Seasonal Forecasting
• Regression Analysis

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Simple Moving Average

• Given n observations x1,x2,,xn that xt follows
  xtb?t and equally important ?t1,2,..,n .
  Where b is expected demand in any period, ?t is a
  random error with mean 0 and variance ?2?
• Requirement estimate the parameter b for the
  future value
• Solution Use least square method to minimize the
  sum of squared error

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Weighted Moving Average
Where w1w2wn 1
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Exponential Smoothing

• Assign weights to observations of previous
  periods in an inverse proportion to their age
• Where forecast for period t and
  all future periods in the case of a constant
  model x(t-1) Actual demand at period t-1
  Forecasted value for t-1 ?
  Smoothing constant, 0lt ?lt1

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Exponential Smoothing

• The ES ? estimate the parameters for a constant
  model (simple exponential smoothing), linear
  model (double exponential smoothing), and any
  polynomial model.
• Constant model x(t)b?t where b is expected
  demand. Corresponds to
• Linear model x(t)abt?t where expected
  demand at time t is E(x(t)t)abt. We have

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Exponential Smoothing

• Apply exponential smoothing again (double
  smoothing), we have
• at each period t-1, the
  values of a and b are updated as follows
• Initial conditions to start the process are

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Regression Analysis

• A regression model expresses the relationship
  between a dependent variable (characteristic)
  with some independent variables. The mathematical
  form is yf(t,x1,x2, )
  ?(t,x1,x2,). Where coefficients of f are
  needed to determine
• A regression analysis refers to the process of
  estimating the model parameters using the least
  square method.
• Least square minimize

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Error Analysis

• Objectives
• Check the effectiveness of a forecasting mode
• Evaluate and select forecasting model
• Measurements
• Sum of errors
• Mean absolute deviation (MAD)
• Mean squared error (MSE)
• Mean absolute percentage error (MAPE)
• Mean squared percentage error (MSPE)

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Forecasting Maintenance Work

• Forecast maintenance load - Emergency
  maintenance workload( random and can be minimized
  by a well designed planned maintenance)
  historical workload forecasting techniques
  and/or management experiences. - Preventive
  maintenance workload historical records
  preventive maintenance programs routine
  inspection and lubrications - Deferred
  corrective maintenance historical records
  future plans - Forecast for
  overhaul-removed items fabrication historical
  records future plans for improvement -
  Shutdown, turnarounds, and design modifications
  historical records future maintenance schedule

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Forecasting Maintenance Work

• Backlog errors in forecasting and job standards
• Load forecasting for the coming weeks or
  months work forecasting by examining the
  maintenance backlog.

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Maintenance Capacity Planning

• Maintenance capacity planning determines the
  optimal level of resources (workers, skills,
  spares, inventory equipment, and tools) required
  to meet the forecasted maintenance load (future
  load forecast and backlog)
• Procedure
• Determine total maintenance load
• Estimate the required spares material to meet
  the load
• Determine the equipment tools that are
  necessary for all types of maintenance work

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Maintenance Capacity Planning

• Determine the skills the number of workers from
  each skill. Special attention should be given to
  multi-skill crafts
• Provide special plans for highly computerized
  equipment, if required
• Problems use maintenance load, standard times,
  job arrival times to determine the optimal mix of
  skills of crafts from the sources available and
  the optimal capacity that meet the required load.
  Objectives cost, availability, reliability.
• Techniques - Deterministic approach
  heuristic, LP - Stochastic approach queuing
  models, simulation

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Deterministic Techniques for Maintenance
Capacity Planning

• Heuristic Tableau Method
• Problem Determine craft mix, minimize cost
• Principle use common sense guidelines and
  principles to solve
• Provide sufficient in-house workers for
  high-priority work
• Measurement ratio between overtime work and
  regular-time work, and a fixed healthy backlog
• Examples (text book)

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Linear and Integer Programming Techniques

• Decision variables the number of hours from
  different skill levels and trades made available
  through regular in-house, overtime or contract
  maintenance
• Objectives maximize resource utilization,
  minimize total cost
• Constraints overtime hours, capacity of sources,
  etc.
• Examples (text book)

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Stochastic Techniques for Maintenance Capacity
Planning

• Queuing theory has been used to determine
  maintenance staffing, to evaluate the performance
  of the system under steady-state conditions.
  However, queuing theory do not reflect the
  transient system behavior
• Simulation is applied for the complex system and
  consideration of transient situation.

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Queuing models

• Description Customer ?arrive?Server choose
  (FIFO, LIFO, etc.)?leave
• Elements of a queuing model
• Arrival distribution
• Service time distribution
• Design of service facility
• Service discipline
• Customer population (size of the queue and
  customer population
• Human behavior

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Queuing models

• Output information (under steady-state
  condition)
• Ls expected number of customers in the system
• Lq expected queuing length
• Ws expected waiting time in system
• Wq expected waiting time in the queue
• Input information (a/b/c), (d/e/f)
• a arrival distribution
• b service time distribution
• c number of parallel servers
• d service discipline
• e maximum number allowed in the system
• f size of customer population

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Example 1 of Queuing Model

• (M/M/C),(GD/?/?). If C servers have an
  exponential distribution with parameter ? and if
  we let ??? then we have
• where P0 is the probability of
  zero customers in the queue,

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Example 2 of Queuing Model

• (M/M/R),(GD/K/K), RltK find a value of R
  repairmen (servers) for K machines that minimizes
  the total expected costs, which consist of the
  cost of failure and the cost of service. If ? is
  the rate of breakdown per machine and there are n
  broken machines, given the arrival rate
• and the service rate is
• Pn is the probability of n
  machines in the system. The steady-state results

Where expected number of idle repairmen
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Simulation

• Stochastic simulation is the process of
  representing a system on the computer and then
  employing well-designed experiments (scenarios)
  to evaluate its performance. Using this process,
  systems can be analyzed, planned, and designed
• Procedure to implement a simulation for
  maintenance capacity planning
• Study company maintenance requirements to
  determine the types of maintenance workers
  crews required, the types criticality of
  equipment repaired, the failure mechanism for
  each piece of equipment, the effect of a
  failure on production or service provided by the
  organization

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Simulation

• Forecast maintenance workload and divide it
  according to priority
• Outline the existing work order system and define
  the logic of work assignments
• Setup the relevant machine servicing model after
  determining the failure rate of each machine, the
  service rate, and the cost of each machines
  being out of service
• Develop simulation software application and
  verify and validate the model
• Perform production runs and, on the basis of all
  measures of performance, find the optimal
  staffing levels

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Contract Maintenance

• Does contracting maintenance build or diminish
  the competitive advantage?
• Contracting maintenance during peak periods is
  more effective in most working environment when
  finite projects or tasks can be estimated and
  outsourced as a work package. (capital expansion,
  modification projects)