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Chapter 2: Maintenance Forecasting and Capacity Planning

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Title: Chapter 2: Maintenance Forecasting and Capacity Planning


1
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

2
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)

3
Role of Maintenance Load Forecasting in a
Maintenance System
4
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

5
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6
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

7
Quantitative Forecasting Techniques
  • Simple Moving Average
  • Weighted Moving Average
  • Exponential Smoothing
  • Seasonal Forecasting
  • Regression Analysis

8
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

9
Weighted Moving Average
Where w1w2wn 1
10
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

11
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

12
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

13
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

14
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)

15
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

16
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.

17
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

18
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

19
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)

20
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)

21
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.

22
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

23
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

24
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,

25
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
26
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

27
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

28
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)
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