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By L Munholand, G. Soucy, P. Quintal

This work presents early results from the first study to optimize the hydrodynamics of a Plasma Lift Reactor (PLR). The PLR is designed to break down organic contaminants in aqueous solutions. New experimental results are presented for air/water tests and for plasma degradation of organic contaminants in Bayer liquor. In addition, a multiphase Computational Fluid Dynamics (CFD) model has been developed which predicts the hydrodynamic behavior in the PLR. These results of this work suggest the PLR is effective at reducing contaminants in the Bayer liquor and that the CFD model adequately describes the hydrodynamic flow.

Jan 1, 2005

By A. Iizuka

This study was aimed at separating and recovering arsenic, antimony, and tin from refining byproducts generated in a nonferrous smelter. The target byproduct was a silicate slag containing the above elements. The silicate structure of the slag was destroyed by alkali roasting, which then enabled leaching of arsenic, antimony and tin in solution effectively. Arsenic was selectively leached out by hot water after alkali roasting of the slag, while remained antimony and tin in the residue were leached out by a hot hydrochloric acid solution. However, when the solid-liquid ratio in the leaching solution was increased, hydrous gelatinous silica (gel-like silica) was formed during the hydrochloric acid treatment and filtration became difficult. Therefore, high temperature and high pressure leaching was attempted to improve the filterability of the silica leaching residue. In the high temperature and high pressure treatment, the hydrous gel-like silica was transformed into easily filterable aggregated silica, and thus, filtration became easy. By investigating the neutralization and sulfurization treatment for the obtained hydrochloric acid leachate (second leachate), it was possible to separate antimony and tin. INTRODUCTION This study aims to separate arsenic and recover valuable metals such as antimony and tin from refining byproducts generated in a nonferrous smelter. The target smelting byproduct is antimony-containing slag in this study. In many cases, alkali roasting was adopted as pretreatment for extraction and recovering valuable metals from smelting residues and wastes (Rao, 2006). For antimony-containing slag in this study, one effective method for separating arsenic is to convert arsenic to sodium arsenate (Na3AsO4) by roasting with a sodium compound and then to remove arsenic by hot water leaching. In addition, by alkali roasting, the silicate structure of the slag is destroyed, and effectively alkalizing tin and antimony is accomplished. Then, precipitating and recovering tin and antimony leached into the acid solution are considered possible by sulfurization and neutralization treatments. In this research, we conducted basic studies on the following. 1) Destruction of silicate structure in slag by alkali roasting and leachability of arsenic. 2) Conversion of hydrous gelatinous silica to aggregated silica by hydrochloric acid treatment of residues after arsenic leaching under high temperature and high pressure, as well as leachability of antimony and tin. 3) Separation and recovery of antimony and tin by sulfurization and neutralization treatments of hydrochloric acid leachate. These topics of investigation can support to consider the separation and recovery process of arsenic, antimony, and tin from antimony containing slag.

Jan 1, 2019

By Michel Ruel

Most plants do not track how their systems perform. Optimization is the easiest way to benefit from your control systems. We suggest an approach in four phases. The first phase is to assess all equipment to determine the performances for instruments, valves, variable speed drives, and other equipment. The second phase is to remediate instrumentation problems, including the ones pertaining to valves, variable speed drives, analyzers, transmitters. When equipment is in order, loops are put back in automatic mode. If a loop oscillates, use standard default values for this type of loop. The third phase consists in validating the control strategies, properly configuring the systems (control system, programs and parameters, HMI, alarms), and then tuning the loops and control strategies. The fourth phase consists in analyzing the process and expected performances in order to optimize the control loops and control strategies. If performance is not sufficient, a decision tree will be presented to determine the right approach: advanced regulatory control, model predictive control, or fuzzy logic control. Once all steps have been completed, control performance monitoring software is used to sustain the results and pinpoint equipment or loops not performing as stated. Alarm management and rationalization could also be performed after auditing the alarm system, if needed. Examples from plants will be used to demonstrate how this step-by-step method is applied and produces results. INTRODUCTION Maximizing what you already have is the best investment to remain competitive. This article aims to show the benefits of a systematic approach using modern tools to improve plant performance. We at BBA suggest dividing the work in four phases, and a subsequent phase can begin when the previous one has progressed: Assess, Remediate, Stabilize, Optimize, or add advanced control. This approach has been successfully applied to several sites. Examples and illustrations from these plants demonstrate how this step-by-step method is applied and produces results. Under the BBA method, there are four questions to answer before proceeding to the next step. For each control strategy, you should ask the following questions: Assessment: Does it work? Remediation: Do you use it? Stabilization: Is it stable? Optimization: Does it perform? Do you need advanced control?

Jan 1, 2019

Agenda ?The Context ?The Challenge ?The Solution ?Benefits and lessons learnt from pilots ?Next Steps The Context ?Facilitate management decision making process by supporting the development of value/risk based business cases. ?Large scale investments by extractive industries are expected tobring broad-based benefits to local communities (e.g.: health, education, jobs, infrastructure) ?Investors continue to expect the demonstration of social performance?Specific interventions bring direct value to companies (e.g. skills development) ?Social Investments are key to protecting a company?s license to operate ?Quantifying the value of these investments and planning accordingly, however, has long posed a challenge for the extractive industries and community development practitioners

May 1, 2011

Real time analysis of ore quality between the mine and mill provides major benefits to copper mining and processing operations. Prompt gamma neutron activation analysis (PGNAA) is a proven technique that has been successfully applied for real time conveyed flow multi-elemental measurement. The advantage of PGNAA is that it measures through the full conveyed cross section continuously and provides representative element measurement without the need to constantly sample coarse (primary crushed) conveyed flows. High specification PGNAA analyzers enable accurate measurement over time increments as short as thirty seconds. Elements such as copper can be measured to a precision of 0.02% copper which is sufficient for high confidence in decisions for bulk flow diversion. Increments of eight tonnes are being diverted through a bulk ore sorting application to remove batches of waste from mill feed as well as divert material to different stockpiles based on ore quality. Longer measurement increments of two to five minutes are suitable for blending control of ores to reduce feed quality variability and to control average ore quality within a target range. Feed blends can be adjusted as frequently as required but typically multiple measurement increments are composited to produce a rolling average ore quality. The paper details two case studies where analyzers have been successfully used to measure conveyed flows for blending and bulk diversion applications. The real time measurements of ore composition are also used for ore reconciliation, in metal accounting and providing process operators with advance warning of ore quality changes that may affect grinding performance and cause process upsets. Real time ore quality measurement has proven beneficial in improving copper processing performance through better utilising plant capacity in a leaching operation, optimising ore feed quality, and reducing unnecessary processing of waste. INTRODUCTION Representative real time elemental analysis of conveyed ore quality using fully penetrative technologies has been available to the minerals industry since the 1990s. The Prompt Gamma Neutron Activation Analysis (PGNAA) technique was developed into a conveyed material analyser and soon adopted by the cement and coal industries which recognised the benefits in real time quality management. These commodities were ideally suited to this measurement technique as operations generally involved conveying bulk material prior to processing. Measured quality was used to divert material to different destinations or used to control blending for improved quality consistency. Uptake in the minerals industry, however, has been slow until the last ten years, and particularly until the mid-2010s.

Jan 1, 2019

By S. Parkash, A. J. Szladow

Vigorous agitation of suspensions of coking coals in water (or light mineral oils) will often result in catast rophic loss of caking properties. It is shown that this deterioration is not a consequence of oxidation of the coals (by dissolved oxygen), but that it can be qualitatively connected with internal "solid-state" reactions which appear to derive their activation energies from cavitation of the liquid.

Jan 1, 1971

By K. A. Foxford, D. A. Polya, R. P. B. Hebblethwaite

"Abstract-A variety of techniques for interpreting systems of mineralized echelon veins is discussed using examples from Panasqueira and SW England. As aids for exploration and mine planning, and as a tool for ore reserve evaluation, particular emphasis is placed upon establishing vein morphology in the third dimension, and upon understanding vein dilation and propagation histories. Special attention is also placed upon investigating vein thickness and spacing relationships, and upon understanding vein segmentation. The relevant data for these techniques are all readily obtainable from stope and core sources.The vein systems described were produced in host-rock sequences that underwent incremental dilation in response to fluid overpressures, and individual veins display evidence for mineral infilling synchronous with their propagation. Echelon vein geometries resemble those reported from igneous dikes and sills: vein walls are stepped and veins are divided into segments arranged in echelons. Changes in vein geometry, from arrays to composite structures, reflect both the evolution of the vein system with time, and the changes occurring between the margins (arrays) and core (composite structures) of the system. These characteristic morphologies can be used to infer vein propagation and fluid injection trends, proximity of neighboring veins, and the shape of the system as a whole. The techniques are applicable to systems of echelon veins produced under tensile conditions in rocks where faults were absent at the time of vein formation, and where subsequent deformation has been minimal. Further work is required to assess the application to echelon vein systems formed within more complex tectonic regimes."

Jan 1, 1995

By Marc C. Bétournay

"Surface crown pillars, acting to safely protect underground workers and operations from surface elements, are recognized, herein, as distinct from conventional deeper underground pillars. Moreover, because of the variation in mining and geological conditions that exist from mine site to mine site, each case is viewed as unique. A review of numerous case studies and existing literature indicates that there is little general information or systematic problem-solving approach associated with them.A design process, not unlike that of other engineering disciplines, is presented to correct these deficiencies. As part of its purpose, it will inform operators of the key elements required for design and will address the problems of these appendages. The design, while taking into consideration possible surface crown pillar settings and inherent characteristics, is founded on a step-by-step procedure starting with site investigations through to monitoring or pillar recovery. The process is flexible, in that it incorporates decision making and changes in mining strategy. The purpose of each step is explained and each step is extensively described in terms of the required equipment and methods for field work, analysis and support measures. Analytical formulae and studies from several fields directly applicable to surface crown pillars are also given. Recommendations for future research studies are presented."

Jan 1, 1987

By K. A. Foxford, D. A. Polya, R. P. B. Hebblethwaite

"A variety of techniques for interpreting systems of mineralized echelon veins is discussed using examples from Panasqueira and SW England. As aids for exploration and mine planning, and as a tool for ore reserve evaluation, particular emphasis is placed upon establishing vein morphology in the third dimension, and upon understanding vein dilation and propagation histories. Special attention is also placed upon investigating vein thickness and spacing relationships, and upon understanding vein segmentation. The relevant data for these techniques are all readily obtainable from stope and core sources.The vein systems described were produced in host-rock sequences that underwent incremental dilation in response to fluid overpressures, and individual veins display evidence for mineral infilling synchronous with their propagation. Echelon vein geometries resemble those reported from igneous dikes and sills: vein walls are stepped and veins are divided into segments arranged in echelons. Changes in vein geometry, from arrays to composite structures, reflect both the evolution of the vein system with time, and the changes occurring between the margins (arrays) and core (composite structures) of the system. These characteristic morphologies can be used to infer vein propagation and fluid injection trends, proximity of neighboring veins, and the shape of the system as a whole. The techniques are applicable to systems of echelon veins produced under tensile conditions in rocks where faults were absent at the time of vein formation, and where subsequent deformation has been minimal. Further work is required to assess the application to echelon vein systems formed within more complex tectonic regimes."

Jan 1, 1995

By C. Caballero, A. Warczok, K. Itagaki, A. Moyano, J. Font

The Codelco Norte Smelter process 2,500 tpd of arsenic-bearing concentrates with an arsenic content of up to 1.5% in one of its two main smelting units, the Teniente Converter. The product, 1,100 tpd high-grade matte or white metal, is traditionally fed to the PS converters, while the 1,700 tpd of slag is fed to the slag cleaning electric furnace for copper recovery. This is achieved in a very reductive environment which reduces the viscosity of the slag and enhances the sedimentation of the high-grade matte droplets. The behavior of arsenic in this non-oxidative environment was studied at lab-scale and fundamental thermodynamic data were obtained. Based on these data a thermodynamicbase model to assess the arsenic behavior in reductive environment was developed. It is based on a mass balance for the reduction and sedimentation stages performed in an electric furnace which allows the recovery of high-grade matte droplets after decreasing the viscosity of the slag. This model can be a very suitable tool for predicting fractional distribution of arsenic in the slag cleaning electric furnace, when the distribution ratio, vapor saturation degree, temperature, y As and pO2 are given.

Jan 1, 2007

By G. J. Arseneau

ABSTRACT Mineral resource statements are reported as tonnage (volume × density) and grades. Effort is expended to accurately estimate the volume and grade, but accurately determining bulk density is often overlooked. Oversimplification of density modelling can result in potentially serious errors in tonnage estimates and over- or underestimation of metal content. A reliable bulk density model requires an adequate database and a good understanding of density variability, along with grade and geology. In this paper, the author summarizes density measuring techniques, draws on examples of simple and complex grade-variable density domains, and discusses improved approaches for minimizing density estimation errors.

Jan 1, 2014

By D. R. Wright

"The modest thermal efficiency of the steam turbine cycle essentially determines the heat required and, therefore, the coal consumption and ash production of pulverized-coal-fired powerplants. This paper emphasizes how some properties of coal and its ash can crucially affect the operation of a steam generator and its flue gas cleaning equipment. A brief reference to some siting factors and economics reaffirms the all-pervasive influence of the properties of coal and ash and establishes the importance of a firm supply of cooling water. The economics of scale remains a compelling factor in selecting the size of units, despite disappointing performances by some of the larger units. Environmental considerations suggest that smaller units still have a role to play. IntroductionCoal fuelled one industrial and economic revolution, beginning two hundred year s ago . It was the precursor of competing fuels, notably natural gas, oil and uranium, which eclipsed it in terms of convenience and rate of growth.The turmoil that now exists because of rapidly dwindling supplies of no-longer-cheap oil and the concerns about nuclear energy-justified or unjustified-exacerbated by an operating incident at the Three Mile Island Nuclear Powerplant, prompt speculation for a resurgence of coal, especially where it cangenerate electricity to replace energy from imported oil.The world's reserves of coal are not inexhaustible, although they are ample for several decades. Of greater import is the fact that the world's coal reserve s are more widely distributed than its oil reserves, and they appear less convenient as instruments of economic and political persuasion by opportunist powers. The crux is whether or not the world will accept all that a massive, if temporary, return to coal implies.Combustion of pulverized coal in steam generators to pro duce electricity is a 50-year-old, well-understood technique; it is undergoing continuous refinement to meet evolving environmental and economic criteria and is not found wanting. It is certainly the only technique available and technologically advanced enough to replace oil immediately on a large scale. Although it may take a decade to bring a new coal-fired powerplant into service, this delay is a reflection on nontechnical and administrative processes. Capital and operating costs of coal-fired powerplants are significant and subject to inflation, but, because of the accumulated experience in this field, the ability to control costs is better than for those energy processes which are less mature or still in embryo form. More exotic, soft energy systems, touted as the panacea for world energy problems, have still to prove themselves on the scale they are needed and under the stringent climatic and operating conditions coal-fired powerplants have already mastered."

Jan 1, 1980

By M. Y. Levesque

The Australian Government?s Energy Efficiency Opportunities (EEO) program launched in 2006 obliges companies that use more than 0.5 PJ (petajoule) or roughly 139 GWh (gigawatt hour) per year to conduct an energy assessment in order to identify measures to improve energy efficiency. The opportunities identified by the mining sector were assembled in the Mining Significant Opportunities Register that permitted companies not yet embracing and adopting an energy management program to see what those who are, were doing and how much energy was saved, and helps disseminate best practice. The measures can be filtered by company, year, category or equipment type. The creation of a central repository of energy efficiency initiatives is valuable but this existing database could be improved; fields identifying the energy and carbon emission savings associated with a given initiative are a surprising omission. Consequently it does not permit the relative effectiveness of different measures for energy and carbon reductions to be readily assessed. A review of energy management efforts implemented in the mining industry, published in peer reviewed journals, corporate sustainability reports or industry publications during the last 40 years has revealed many examples of best practice. However, the lack of a standardized reporting framework in any of these sources has made it difficult to assess the effectiveness and compare the adopted energy management measures ? just as is the case with the Australian register. In an attempt to address these issues, an improved database structure has been created for energy management measures from the mining industry which identifies energy and financial savings arising from energy management initiatives, classifies applications to specific processes or equipment, and recognizes leaders in the mining industry with respect to energy management. The structure of the register includes the key data relevant to energy management in mining that is absent in the Australian version. The mining industry energy management database has been made available in the public domain where stakeholders can examine the best practice examples. Mining energy champions may also contribute to the register by providing case studies; a standardized entry template affords a quality assurance dimension that is absent in other reporting initiatives. Adoption of this database with its standardized reporting mechanism will enhance transparency of the mining industry in energy matters and help it maintain its social license to operate.

Aug 1, 2013

By S. Koppalkar

ABSTRACT: The development and evolution of the gravity recoverable gold (GrG) test procedure at McGill university is reviewed in this paper. Since the late 1980s, the research group led by the late Professor André Robert Laplante at McGill university has undertaken fundamental studies and applied research of the Knelson concentrator to develop a sustainable method of estimating GrG. Historically, a concept of “free gold” was used, and it was de?ned as the gold that could be separated and recovered from gold ore by amalgamation. Due to health and safety hazards, the practical use of amalgamation has declined. around 1994, a methodology using a 3-in Knelson concentrator to measure gravity recoverable gold was established at McGill university. as a result of more than 10 years of improvement and optimization, this technique has become a standard method of evaluating GrG for gold ores, gold plant streams and platinum group metals. By 2006, about 200 GrG tests were carried out at McGill universityon ores from all over the world. recently, a modi?ed version of the GrG test (a simpli?ed test) was developed to provide a quick and rough estimate of the GrG in a sample; this simpli?ed test has theadvantage of reduced mass, processing time and cost. to recognize and honour the contributions madeby the late Professor Laplante towards the establishment of a standard test procedure for assessing gravity recovery potential, the authors propose that the GrG test be named after Laplante.

Jan 1, 2010

By C. W. Jr. Waterman

INTRODUCTION MY SUBJECT is one which would require several speakers and many hours of time for adequate presentation in all its many facets. Because of the widely varying market requirements and coal seams mined, the coal industry of the United States bas of necessity employed many types of preparation facilities to satisfy its needs. Predominance of Baum-type jigs, however, bas marked the mechanical cleaning installations since the early thirties, and these machines continue to hold the lead. CLEANING As a matter of record we find that, at the end of 1948, we had 480 mechanical cleaning plants in operation. Of these, 19 used air cleaners only,?400 used water washers only, . and 61 used dry and wet washers in combination . Due to the increased use of spray water underground on cutting and mechanical mining equipment, there has in recent years been a marked downward trend in dry cleaning installations. In fact, the moisture in dry-cleaned fines has been increased to such an extent by spraying that recent dry cleaning installations have incorporated thermal drying ahead of the dry cleaning units in an effort to overcome the varying and increasingly higher moisture percentages in their raw coal feeds. While on the subject of dry cleaning, it might be well to bring to your attention one of our most recent developments in this art. I refer to the McNally-Brusset vacuum jig.

Jan 1, 1951

By J. G. Trowell, D. T. Magee

"IntroductionMANITOBA'S first recoverable oil was from the California Standard Daly 15-18 well in Lsd. 15, Sec. 18, Twp. 10, Range 27, W.P.M., completed early in 1951. This well also gave the first indications of commercial production in the Williston basin, which is centred in North Dakota and extends into southeastern Saskatchewan and southwestern Manitoba. Subsequent drilling in the Manitoba portion of the basin has revealed the presence of oil in more or less commercial quantities at various points in an area approximately four townships in width and eleven townships in length.Although completions are becoming fairlly widespread in the area,, the greatest activity is in the Virden district, with the focal point in the Daly field, approximately eight miles west •of Virden. This paper will deal with the various techniques used in the Daly field, where •completion problems have •been unusually troublesome. Techniques evolved there have already been used with success at other points in southwestern Manitoba.Daly FieldGeneralTo date, all production has been from the Mississippian limestone, which is encountered •at depths ranging from 2,300 to 2,500 feet. Pay thickness is •of the order of 100 feet. Core analyses indicate average porosity .of about 9 per cent but permeabilities, for the most part, are extremely low."

Jan 1, 1953

By Balmer Neilly

FOR some reason or other, Mine Taxation has never been a popular subject for discussion in meetings of this kind, and it has never received the study and consideration its importance demanded. By way of explanation, two reasons may be suggested. In the first place, the computation, adjustment, and final payment of taxes, have been looked upon in most cases as a Head Office chore. Secondly, since taxes represent an uncontrollable cost item, they have been treated as an added rather than an inclusive factor in calculating unit costs. Perhaps because I am half Irish, and therefore resent taxation of all kinds, perhaps because I am half Scotch, and am therefore concerned with the results, I have always taken a keen interest in this subject. Moreover, by some peculiar set of circumstances, I have been a participating party in many, perhaps I can say most, of the discussions on this subject that have taken place between the Governments and the representatives of this industry during the past thirty years. Looking backward, certain very definite impressions remain. Political considerations have never had any part in these discussions. Views have been exchanged upon the frankest possible basis, and, when we disagreed on some particular detail, we agreed to disagree, and followed through in harmony and? good faith. We, as an industry, have refrained from importuning and fault finding in ways that might be considered as petty or selfish, and it is only upon occasions such as this, where conditions necessitate action, that we lay our troubles before the powers that be. The Ontario Mining Tax Act was drafted by men who were earnest and practical as to purpose, and that Act has stood the test of time. It is, in. truth, a mode! Act, for it has been copied in its general clauses by both Quebec and the Dominion of Canada. We all know that, when a machine is running smoothly, we should leave it alone. The same is true of a well designed, easily applicable, taxation measure, and our present difficulty with respect to this Act arises out of an amendment made in 1916. In that year, you will remember, the Dominion imposed a wartime Income Tax Act. It was described as a wartime necessity and it was intimated t:1 at with the end of hostilities its application would be restricted and finally cancelled. The rate of taxation was modest, and when the Ontario Government was asked that the Dominion Income Tax be allowed as a deductible item, they readily acquiesced. This was looked upon as a temporary arrangement.

Jan 1, 1943

By Ahmad Abdollahi

Many factors affect mechanical properties of hypoeutectic Al-Si alloys. As examples the presence of impurities such as Mn and Fe due to the formation of intermetallic phases, additions of small amounts of alkaline earth metals and cooling rate in consideration of Si formation, they all have an impact on mechanical properties of hypoeutectic Al-Si alloys. In this investigation, the effect of Fe content into the specification range of A357 alloy, the addition of different modifiers consisting of Na, Sr and Ca for the alloy of A356 and different mounting techniques for separately cast test coupons of hypoeutectic Al-Si alloys using the lost wax method were studied. The results showed that using material with lower Fe content and addition of modifiers improve mechanical properties. Also different mounting techniques resulted in different mechanical properties.

Jan 1, 2004

By F. Ajersch, A. R. Hekmat

Apparent viscosities of hypo-eutectic (Al-7% Al) and hyper-eutectic (Al-35% Si) binary alloys were measured in the semi-solid state using a Couette type viscometer at variable shear rates. Analysis of the microstructural evolution demonstrates the differences in the rate and degree of attrition of the primary phase particles which are characteristic of the thixotropic nature of the semi-solid alloy. It was observed that the Si primary phase in the hyper-eutectic alloy is much more difficult to fragment than the dendritic a-Al phase in the hypo-eutectic alloy. For the case of the a-Al, the dendritic structure is broken down by attrition and fracture of the dendrite arms whereas the fracture of the Si hexagonal crystals in the hypereutectic alloy occurs along the {100} and {110} cleavage planes. Results are presented for fixed solid fractions of the primary phase at isotherm condition for each type of alloy.

Jan 1, 2006

By J. L. Collins

"This paper deals with the quantitative analysis of mine maintenance records. Based on a case study of dozer engine records, the author suggests an easy method of deriving useful information for managerial decisions in a step-by-step manner.More specifically, the paper deals with the following topics:• determination of the most economical replacement time,• determination of reliability characteristics,• determination of the number of replacements, and• determination of the number of spares.IntroductionThe mining industry collects a lot of information about every aspect of its activities, an example of which appears in Table I. In Table I , the distribution describes the operating hours at failure of 56 different dozer engines used in severe applications. Besides calculating an average and possibly a standard derivation from the data, little else is derived, at least from a statistical point-of-view.More information can be obtained from these records that could help management in the decision-making process.To illustrate this point, the sample data appearing in Table I will be analyzed in detail by making use of well-known concepts in reliability engineering.Distribution of DataTable I represents a distribution obtained from the recorded hours cumulated from the operators' time cards. The operating hours have been divided into fourteen classes for each 1000 hours of engine running, e.g . all engines scoring an operating time of between 1001 and 2000 hours formed a class , those scoring between 2001 and 3000 hours another one, etc. Generally, the class interval should be a multiple of the equipment preventive maintenance check period.The minimum acceptable sample size should be large enough to ensure that the score in each class interval is at least one. Ideally, the score for each class interval should be at least five so that a chi-square test could be carried out if necessary.The average life of an engine can be found by adding the products of the frequency and the class mark (mid-point) values. Therefore:"

Jan 1, 1987