EXAKT for complex items

Abstract-Using failure and condition data for a Mill pinion bearing, EXAKT software was evaluated on how it performs prognostic modeling for complex items with multiple condition monitoring variables. It was found out that Reliability Centered Maintenance (RCM) based failure data is a pre-requisite for EXAKT, and that it requires the failure and condition data in specially formatted and structured Events and Inspection tables. Using this data EXAKT performed prognostic modeling for the bearing using Marginal analysis, modeling each significant failure mode with respect to its respective data behavior patterns, whilst incorporating all significant condition data variables. It was concluded  that good failure prediction models depend on data adequacy, and that the main challenge to using EXAKT is in getting maintenance personnel involved in work orders to adopt the language of RCM and  alter the way work orders are closed to include failure modes and event types.

1. INTRODUCTION

Numerous papers have been written on the application of mathematical maintenance optimization models. In reference [1] whilst reviewing the application of maintenance optimization models, Dekker analyzed the role of these models in maintenance and noted then that the impact on decision making within maintenance organizations was limited. In the abstract of reference [2], Philip A. Scarf added, “This paper may be taken as an appeal to maintenance modelers to work with maintenance engineers and managers on real problems. Such collaboration is essential if maintenance modeling is to be accepted within the engineering community….”.

As if heeding this call, in 1995 a project was commenced at the University of Toronto to develop a Proportional Hazard Model (PHM) based software that could be used to identify optimal replacement decisions. This software was named EXAKT. Jardine et al [3] state that the overall purpose of the software is to combine historical and condition-based information to establish lowest cost replacement decisions.

Tsang et al [5], stated that in his seminal paper, Cox (1972) reported an application of PHM in the medical field using a multivariate regression analysis procedure to analyse medical survival data. and that Since 1985, PHM applications have been extended to the analysis of failure data of physical assets.

In 2010, Wong et al [4] reviewed PHM application case studies in maintenance and noted that PHM has been used in a variety of applications to determine optimal policy, for example to model aircraft engine and marine gas turbine failure and condition monitoring data, to optimize times of repair to mine haul truck wheel motors, and to model vibration monitoring data for pumps at a coal wash plant. In reference [5] Tsang gives further examples of application in the maintenance field.

This being the case it makes sense to  carry out this project, not only in support of this effort which others are making in applying prognostic modeling to maintenance, but also to add value to the colossal masses of asset health data which is being amassed.

We use various condition monitoring (CM) techniques to monitor the health of roller element bearings on critical equipment such as Ball Mills. These include visual inspection, temperature, tribology and vibration monitoring. The technologies focus mainly on the acquisition of the multi-variate condition data, and its use for diagnostic purposes. However the related and yet more important question is how to add value to this mass of data. How can we use this asset health information for prognosis, to predict the remaining asset lifetime, thus optimizing our maintenance policies?

Bearing this question in mind, EXAKT was assessed on its capability to perform prognostic modeling using a Ball Mill pinion bearing as a case study. We are seeking a tool which can add value to asset  condition monitoring data, a decision making tool which can enhance the application of our Condition Based Maintenance (CBM) programmes by  forecasting the bearings’ remaining operational life, future condition, or risk to complete operation. This will not only optimize our maintenance policies, but also eliminate lost opportunity costs due to unscheduled downtime.

To this end Asset health data for the pinion bearing consisting of multiple condition monitoring variables namely vibration readings, oil analysis results, temperature readings, and work order data was used to assess how EXAKT performs the prognostic modeling. A hands-on approach on the application of the EXAKT PHM process to the reliability data was followed. The main thrust was towards understanding and carrying out the data modeling and manipulation to produce the appropriate models.

Section 2 summarizes the theory on which the EXAKT is based and the Proportional hazards modeling (PHM), process. The next section is a narration of the work carried out during the case study. Sections 4 and 5 are the results and analysis respectively, while section 6 is the conclusion.

2. EXAKT THEORY

According to Tsang et al [5], Proportional hazards modeling (PHM) refers to an approach to modeling an asset’s hazard that takes into account information provided by condition monitoring data. It is multivariate regression analysis procedure, which aims to formally blend together data about the age of equipment along with the signals arriving from condition monitoring to estimate statistically the risk of the equipment failing at the time of inspection. In reference [6] Jardine et al state that this method tries to account for the influence of both the physical condition indicators and the working age on the statistical probability of failure and summarize it as a function in reference [7] as follows:

   [1]

In Equation 1 h(t) is the (instantaneous) conditional probability of failure at time t, also known as the hazard function, given the values of Z₁(t), Z₂(t), … Z_m(t). Each Zi(t) in represents a monitored condition data item at the time of inspection. These measurements may include the parts per million of iron or the vibration amplitude at the second harmonic of shaft rotation, or any variable that reflects the accumulated stress or damage with respect to some mode of failure. These condition data are sometimes called covariates. The model consists of two parts, the first part is a baseline hazard function (Weibull) that takes into account the age of the equipment at time of inspection, . The second part, takes into account the key variables and their associated weights.

The PHM is used to find a mathematical relationship between the risk of a component failing and the condition information together with working age.

TRANSITION PROBABILITY MODEL

In reference [4], Wong assets that a transition probability model describes the changes of covariates over time, from inspection to inspection. EXAKT assumes the Markov Chain Model can be used to express this behaviour to create the Transition Probability Model (TPM). The first step to creating the TPM is to define states or covariate bands for each covariate included in the model. EXAKT automatically sets default Interval Start Points so that each covariate band contains a certain percentage of data points. Time intervals, the period during which transition probabilities are assumed to remain unchanged, are also be defined. Transition rates are calculated by EXAKT, and are the rates of changes of transition probabilities for a short period of time. It is assumed that transitions to neighbouring states (or covariate bands) in a short period are more likely than to other states. Transition probabilities are calculated from the transition rates, to produce a transition probability matrix (which shows the probability of going from one state to the next. The Transition Probability Model is needed to make predictions based on CM data. This, together with the PHM forms a complete statistical model that is used along with cost information to calculate the corresponding optimum component replacement strategy.

DATA REQUIREMENTS FOR PHM

Failure or replacement data makes it possible to construct the PHM for specific failure modes of an asset. When the logged event is an overhaul or preventive replacement of a component, it is classified as a“suspension”.It also includes the date and time of occurrence of the failure. Inspection data includes the covariates (variables), and may contain more than one element, depending on the number of indicators being tracked in the condition-monitoring program that applies to the asset. Maintenance action data include data which may range from oil change, tightening of loosened parts, preventive replacement of parts and overhaul to breakdown maintenance. Start and finish dates for maintenance action are also required.

Installation data includes the date and time when the asset was first put into service.

In reference [5], Tseng et al also points out that the accuracy of the PHM model that characterizes the risk of failure of an asset depends on the quality of the data used for modelling. The quality problems of these data that often arise in practice include non existence of working age of the equipment, missing or no records on the type of maintenance action performed, transcription mistakes. and saturated (truncated) values obtained from sensors.

USING EXAKT SOFTWARE

In reference [8] Wiseman summarizes the steps in applying EXAKT software to optimize CBM decisions as follows:

Step 1: Preparing the data

The maintenance data to be used in the decision analysis often contain missing and/or erroneous data. They must be cleaned before using them as inputs of the analysis.

Step 2: Building the PHM model

Parameters of the PHM model that fits the field data are estimated by the maximum likelihood estimation method. Covariates (zi) with statistically insignificant covariate parameters are removed to keep the model as simple as possible. The PHM model’s accuracy improves as more failure events with their associated condition data are available.

Step 3: Testing goodness of the PHM model

Residual analysis using graphical techniques and statistical tests is performed to determine how well the PHM fits the data. The larger the sample size and the more the histories ending in failure are, the more accurate the estimated model will be.

Step 4: Defining states and determining transition probabilities

Changes in the measurements of the covariates featured in the PHM model are modelled as the results of a semi-Markov process. It is then necessary to describe the state transition behaviour of the covariates through construction of the transition-probability matrix between inspection intervals. This matrix is built from the transition statistics of the condition data from one inspection to the next.

Step 5: Making the optimal decision

At each inspection, as the latest condition data are available, the results of the PHM model, the transition-probability model, as well as the relative costs of failure and planned repairs are considered collectively to find a decision that will optimize the long-run maintenance cost for the component or system in question. The optimal decision policy is to determine whether the equipment should be replaced immediately, should continue operating and be inspected at the next inspection time, or should continue operating but be replaced at a specified time before the next planned inspection time.

© 2011, Tarairwa Ndewere. All rights reserved.