A THEORETICAL APPROACH TO DETERMINING SPARE PART SUPPORT FOR ANY GIVEN ORGANIZED OPERATION DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By WALTER ADOLPH BECKDAHL, M.B.A. ********** The Ohio State University 1959 Approved by t / 1 ' / /' V F / a ■ >.-• ,-y . /C/FF? U fj Advise iv ----- J- Department of Industrial Organization and Management TABLE OF CONTENTS Chapter Pa^je I INTRODUCTION .......................................... 1 II HISTORY.............................................. 15 III ..ILITARY COMPUTATION ACTIVITIES .............. 24 IV THE PROCESSES OF MILITARY REQUIREMENTS.............. 34 V THE LIFE EXPECTANCY OF PHYSICAL P R O P E R T Y ............ 42 VI INCREASES OR DECREASES IN THE EQUIPMENTUNIVERSE . 57 VII PROBABILITY THEORY AND ITS APPLICATION.............. 65 VIII ESSENTIALITY OF THE I T E M ................................ 77 IX THE EFFECTS OF TRANSPORTATION ON TOTAL REQUIREMENTS • • 83 X METHODOLOGY AND CONCLUSIONS .......................... 89 ii LIST OF FIGURES Figure Page 1 AM ILLUSTRATION OF FAILURE RATE COMPUTATION............. 44 2 FAILURE RATE CURVE FOR EQUIPMENT X ....................... 45 3 EQUIPMENT ' !i' .tEPLACE;-EFT iiATE......................... 47 h FAILURE iiATE AND liE PLACE; LENT RATE, ELECTRIC LIGHT BULBS . 48 5 SERVICE LIFE IN PERCENT OF AVERAGE L I F E ............... 52 6 SEVEN FAILURE RATE HISTOGRAMS ......................... 53 7 EQUIPMENT *!i* REPLACEMENT RATES WITH 1,000 UNITS ADDED . 59 8 HISTOGRAM OF ANNUAL PRODUCTION........................... 67 9 TABLES OF PROBABILITY................................. 69 10 POISSON CUMULATIVE DISTRIBUTION C U R V E ................. 75 11 HYPOTHETICAL CONTINGENCY KIT PROBLEM.................... 79 12 COMPUTATION OF A MAXIMUM PROTECTION L EVEL............... 80 iii CHAPTER I INTRODUCTION The study of management is relatively new and is a product of our modern times. Nevertheless management's existence can be found throughout history. Since it can be applied to every group activity it seems reasonable to assume that management has probably existed in some known or unknown form and quantity from the dawn of time.'*' Management is an activity or function which guides the technical and operational aspects of a group. It is the activity of planning, organizing, and controlling that which otherwise might be unrelated or aimless with the intention of accomplishing predetermined 2 objectives, both efficiently and effectively. Management, as defined above, is deserving of study and research. According to many of the scholars of both this and other generations, there is a genuine need for such study. It has been asserted that the need for a science of management has long existed but its creation is far from reality.-^ ^H. G. Hodges, Management. (Houghton Mifflin Co., 1956) pp 1-^. 2Louis A. Allen, Management aad Organization. (McGraw-Hill Book Company, Inc., 1958) pp. 1-29. G. Hodges, Management, (Houghton Mifflin Co., 1956) pp. 1-29* 1 The science of managing deals with concepts and abstractions ^ not easily tested or proved. These concepts are difficult to define, standardize, quantify or measure. What is being sought are funda­ mental principles which are the essential scientific foundations of all generalizations based on classified observations and which give meaning, accuracy and dependability to formulation of rules of action or policies, that, given a particular set of conditions, can K be used or applied as guides with confidence in their effectiveness. According to some of these same scholars, one cannot consider a single shop, office or a total business as something apart from the overall problem of organizing for accomplishment. They maintain that scholars of scientific management do not allow themselves to be involved in the morass of solving individual problems which arise in any pursuit of objectives and that only the development of manage­ ment principles which can be applied to guidance of all kinds of organized effort can advance the science of management.-* It is recorded that even F. W. Taylor "regretted and condemned the common practice of .»• grasping at one or another of the par­ ticular techniques that he happened to employ and looking to the technique as a solution to management problems."^ Yet Taylor is regarded as the 'father' of scientific management and his early works ^Harold F. Smiddy and Lionel Naum, "Evolution of Science of Managing in America" Management Science, Volume I, No. X, October, 195*+! PP* 1-31. ^R. C. Davis, The Fundamentals of Top Management. (Harper and Brothers, 1951) PP* 5-^* ^P. N. Leroczky, The (Quantification of Managerial Control in Industry, Ph.D. dissertation, (The Ohio State University, 1931) P* 5* in the field can hardly be categorized as other than techniques for ^ improving worker performance in a particular set of circumstances. It is not intended that this study provide a prolonged or involved discussion of whether only principles and concepts make up the substance of scientific management or whether the so-called * techniques'are included. It is, however, believed that the study portrayed here will be classified as a technique — even though it has widespread application. As such, it perhaps will not be con­ sidered a contribution to the science of management, but only a con­ tribution to the ever increasing techniques used by managers. From observing the management area it is believed that most of the experimental and fact-finding effort that has been directed toward the management area has been concentracted on the function of control. Hany techniques have been developed in work measurement, quality control, routine scheduling, time and motion analysis, etc., for controlling and improving the output of the production and clerical worker.? Inversely, it seems that comparatively little scientific effort has been directed toward the function of planning. It is true that some aspects of planning have received considerable quantitative analysis. Among the easiest to cite is marketing planning where great effort has been expended to determine potential market, customer preferences and shares of the market. In spite of these activities, scientific planning seems to be in its infancy. ?E. Scott Roscoe, Organization for Production, (R. D. Irwin Inc., 1959) PP. 179-215. For the purpose of making a contribution to the field of ^ management science this research study has been made in the function of planning. It is firmly believed that by the techniques portrayed in this paper one of the prominent tasks facing many managers can be more scientifically approached. Basic to the planning function of every organization are two economic problems: (1) that, of allocating scarce resources among several desired outputs and (2) that of determining how much of the O various scarce resources are needed for a desired output. The solu­ tions to these problems will probably differ for each organization and for every time period. Existing systems for determining the quantities of resources involved can always be improved. While the general problem of programming economic activities, such as those mentioned above, has been a subject of inquiry for years, the accom­ plishments in this field have seemed rather minute. In dealing with these and many other problems, management has taken, of late, an increasing interest in the use of quantitative analysis. With the increasing complexities of business planning it seems certain that the future will be marked by an even greater use of such analysis, .quantitative analysis may take many forms, one being the use of mathematical models. Models help to describe the situation under investigation and in some sense duplicates it. Models help in picking out those parts of the situation which appear to be most important to the analysis. An increased understanding ®E. Whittaker, Economic Analysis, (John Wiley and Sons, Inc., 1956) pp. 20-25. and facility with models, particularly mathematical models should ? be beneficial to future managers. It seems the most promising avenue toward better problem solving and decision making.^ An attempt to build a mathematical model has been made in this study. This model shows the analysis involved in reaching the decision in (2) above. The research involves the development of techniques or methodology for accurately determining the number of spare parts or spare units required to support a given program. Determining the numbers of spare parts required to support a program is a management activity for many industrial, service, and military operations. The management of a business which manu­ factures and sells automobiles or appliances must determine how many engines, fuel pumps, generators or other components will fail over the life span of their product and the rate at which failure will take place. Once this determination is made management must decide the number of components and units which should be stored at each distri­ bution point to guarantee service to the owners of their products while not overburdening the distributors with excess inventory. Management must also determine which mode of transportation will be employed to maintain inventory levels by balancing the costs of premium transportation against the costs of additional inventory at each distribution point. Many organizations which sell services are involved in similar planning. The commercial airlines and the railroads, for example, have ^E. H. Bowman and R. Fetter,