STATISTICAL iETHODS Iw CHEWICAL PRODUCT101 Presented before t h e Division of Industrial a n d Engineering Ch.emistry at t h e 119th Meeting of t h e American Chemical Society, Boston, Mass.
The control of quality by statistical methods is now being applied extensively in the process industries. The genius of Walter Shewhart, the high competence of a large number of other statisticians, and the urgencies of wartime production have combined to produce sets of relatively simple tables and rules for statistical quality control. The continual need of the production engineer t o know if this pressure or that flow rate is too low or too high can often be answered by quality control methods. But we are now moving, and with considerable speed, into a new phase. In development and production divisions, we are finding that statistical methods often give the means of testing a large number of hypotheses a t the same time and with extraordinary sensitivity. It is mainly with these methods that our symposium is concerned. The analysis of variance, multiple egression, and tests for randomness, are three of these methods. These were all developed to answer questions in other fields. Their successful application to problems of the chemical industry speak well for their generality and we may expect that the peculiar attributes o f the process industries, especially those connected with continuity of flow, will generate new problems to challenge the research statisticians. CUTHBERT DANIEL
clience of Trouble w i t h the advent of statistical techniques in industry, the ark of production trouble shooting is fast becoming a science. Use of these more rational diagnostic methods on process ailments imposes the obligation to plan experiments, perform tests, and collect data so that results tell the truth. Costly wrong decisions have been traced to inadequate, ill-planned, or prejudiced experimental data. Whether or not statistical analysis is used, scientific trouble shooting must employ rational procedures, such as separation of a multistream process into unit streams, and dissection of variability into within-hatch, batch-to-
batch, and time-to-time components. In plant scale experimentation several variables can be studied simultaneously, but all extraneous variables capable of influencing the test must be standardized or randomized. In a typical problem several methods of attack are critically evaluated.
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industry. The statistical approach not only alters the form and manner of carrying out these functions, but it induces a profound metamorphosis in the brain cells of those individuals who embrace its methodology. They find in this new ideology n freshness and vigor with which t o attack the stodgy and ritualistic thinking habits t h a t exist around them. The generation of such a force inevitably leads to a re-examination of long-used methods and procedures, to the discarding 0.f some and reinforcement of others, ultimately to the achievement of a synthesis between the old and the new. It is precisely through this mechanism that many new sciences have been developed.
HE advent of statistical techniques a t the operating level in industry is fast becoming a reality. The growing use of quality control charts in manufacturing and the adoption of uniform sampling acceptance procedures in inspection attest to this fact. Add t o this the xyidening circle of engineering design, research, and development activities that have embraced the principle of statistical examination of engineering data and it is clear that the penetration is deep, indeed. What is more important than the ostensible evidences of the greater use of statistical techniques, however, is the far-reaching impact of the statistical philosdphy on the many functions of
LEONARD A. SEDER Gillette Safety Rasor Co., Boston 6, Mass.
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QUALITY CONTROL CHART
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Figure 1.
Separation of Multistream Operation into Unit Streams
Height of cross-hatched bar shows average % defective for all shifts; small bars mhow amount individual shifts vaned from average; 30,000 to 40,OOO pieaes made per machine
Among the industrial functions that are currently undergoing this amalgamation of time-tested procedures with the new insight, engendered by statistics is that of production trouble shooting, which may be described as the job of keeping the production stream flowing in a quality sense. It is the task of studying and analyzing the process behavior so that the causes of unsatisfactory quality may be ferreted out and eliminated. Seldom designated by the homely title of “trouble shooting,” the function is variously known as process engineering, laboratory control, inspection, quality analysis, quality control or just plain supervision, depending on the type of industry and the particular company organization. That this function is an extremely important one in any competitive industry is self-evident. For a long time, trouble shooting was largely an art practiced by people with long experience, short memories, and a mystical sixth iense. I n recent years, its procedures have been subjected t o greater scrutiny by persons with engineering training with the result that a kind of semi-science has emerged. At the very least, the principle of the experimental approach in the correction of production faults has been established. But it remains for the statistical philosophy t o complete the transformation into a truly scientific endeavor. By offering the first rational approach to the treatment of variation, statistics has made possible the evolution of a set of procedures for trouble shooting that can be universally applied and will be universally effective in rendering a better understanding of the phenomena of mass production. That such better understanding must lead to better performance is axiomatic. The purpose of this papea is to describe and illustrate some of these procedures and to point out some of the ways in which these procedures differ from the more commonly practiced methods.
ORIGIN OF TROUBLE-SHOOTING PROBLEMS
The origin of most trouble-shooting problems may be succinctly set down: ( 1 ) The manufacturing process is producing too high a percentage of defective or of semidefective product; ( 2 ) The over-all product quality is not yielding full customer satisfaction. The distinction is largely a categorical one; in the first instance, realization of consumer requirements has caused the establishment of standards which result in uneconomical performance, with high internal losses. In the second, lack of realization of consumer requirements has allowed the continuance of an inferior product, with high external losses and, presumably, eventual loss of business. The symptoms are high manufacturing losses and inspection costs in the first and high complaint bills and diminishing orders in the second. Either set of circumstances is symptomatic of a disease which must command the attention of management if the enterprise is to survive in a competitive economy. In terms of the statistical concept of variation, the problem in either caRe boils down to the job of altering the average quality of the process or of reducing its variability. The solution lies in collecting the appropriate facts from the process that lead, first, to a diagnosis of the cause or causes and, secondly, to the prescription of the remedy. Let us consider some of the possible plans of attack. T h e over-all strategy depends a t the outset on whether the process may be classified as dissectable or nondissectable. This is a distinction based on whether or not the product is measurablefor the property or characteristic involved-during the process of manufacture. The disaectable process is one in which the property may be measured between manufacturing steps whereas the nondissectable may be measured only a t completion of all of the operations which contribute to the quality characteristic.
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As an example of the dissectable process, consider the dimension of a shaft diameter during a series of turning and grinding operations or the viscosity of a resinous material during polymerization, cooling, compounding, and solvent dilution as it becomes a varnish. By way of limited generalization, it might be said that most simple physical, chemical, and metallurgical properties fit into this category. In the nondissectable classification, we may consider the taste of a whisky blend, the sharpness of a razor blade, the tensile strength of a casting, or the electrical output of a vacuum tube. All these have the common attribute that the property in question does not even exist until a series of manufacturing operations have been performed. Many of these are in the nature of h a 1 or operational tests on the product and hence are of prime importance from a n over-all quality viewpoint. As has been said, recognition of the extent of dissectability of the process determines the over-all strategy. For the dissectable process, a systematic plan of dissection of the process into operations, thence into “streams,” and thence further into ‘komponents of variation” is indicated. For the nondissectable process, the plan must be one of exploring the cause and effect relationships through correlation analysis or through the execution of carefully designed plant-scale experiments.
be said to exist and the trouble shooter must logically separate the process into unit streams in order to discover whether these parallel streams are, in fact, identical in their effect on the quality characteristic being studied. More often than not, such an analysis will disclose that the “low” average is due t o thc: contribution of one particular stream or that the excessive variability is the result of the mixing of streams which differ in nvlxrage. A simple example of the breakdown of a multistream operation is shown in Figure 1. Trouble was experienced with a product being made on a battery of ten machines, evidenced by a gradual rise in over-all per cent defective. Sampling of the individual machines-Le. the multistreamsshowed that the trouble was particularly associated with certain machines and not so prevalent on others. Differences among operators-another potential multistream effect-are seen t o be of second order of importance. The dissection therefore indicated which machines needed overhauling in order to reduce the process losses. So successful has been this particular dissection technique that most alert quality cont,rol engineers are quick t o challenge the production man’s blithe assumption of equality between two “identical” pieces of equipment. Experience has shown that such a naive assumption cannot be allowed t o stand unless supported by factual evidence from the product itself.
DISSECTABLE PROCESS
DISSECTION OF UNIT STREAM OPERATION
The two stages of dissection already discussed will solve the The f i s t step in tackling the trouble-shooting problem in the great majority of simpler troubleshooting problems. The third dissectable process ip identification of the particular operation stage is reached for those hardier perennials which still resist that is primarily responsible for the undesirable average or excesanalysis; it is the dissection of the unit-stream operation into its sive variability of the quality characteristic under investigation. Generally, this involves a stepwise sampling of the process becomponents of variation. These may be defined as the statistical measures that sort t’hetotal variability into portions attributable tween operations and a n evaluation of the statistical properties. to the several elements of the operation. The principle is analoHere the simpler techniques of statistical quality control, such as the frequency histogram and the control chart, serve admirably gous to the fractionation of a volatile liquid into its several conwell. Comparison of a set of histograms or control charts thus stituents. As in fractionation, various degrees of separation are possible, starting with the same tot,al variability or “crude oil.” obtained will normally point the finger quite clearly a t the offending operation, A variation on this technique is that of following A very common rough separation-to be further refined later if necessary-is the breakdown of the total variability of a unit a particular batch of product carefully through each operation, stream operation of a batch process into: variability within b8tch: sampling and measuring after each step, as described by Biasser variability from batch to batch; variability from time to tkfie. and Xelson (4). The pros and cons of these two techniques are many but need not be discussed here. Once the responsible operation has been isolated, the remedy may or may not be obvious. If it is not, the second stage of dissection will be necessary; it is the separation of the operation into its tributary “streams.” The distinction between a “unit stream” and “multistream” operation will be readily appreciated. I n the unit-stream operation, each item or batch of product moves through identically the same physical path, in terms of equipment and personnel. For example, a single reaction kettle, operated on one shift by a single operator, with tests performed by a single analyst using a single set of TYPE 1. EXCESSIVE TYPE II . EXCESSIVE TYPE Ia‘EXCeSSlVt U T C H TO BATCH VARIABILITY WITHIN Time - ~ ~ - ~ i m t laboratory equipment, would fit this VARIABILITY VARIABILITY. BATCWCS definition. On the other hand, a mulI tistream operation is one in which each item or batch of product may take two Figure 2. Multi-Vari Chart Technique for Fractionating Components of or more such alternative paths. The Variation use of two reaction kettles, three shifts of operators. several analvsts or sets of laboratory equipment would automatically produce a multiThe purpose of the breakdown is to a s s e s the magnitude of stream operation in the previous example. Whenever a chemieach portion as related to the whole, since the type of corrective action needed will usually be indicated by the knowledge of which cal product moves in parallel paths through two or more mixers, nozzles, hoppers, towers, or kettles or when metal of these three components of variation is the largest. Withinproducts go through multicavity dies, multistation devices, batch variability, for example, is associated with inherent error or batteries of similar machines, a multistream operation may of measurement (of chemical analytical method or electrical tests)
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with some positional or other stratification effect, such as improper mixing or stirring, or with natural variability of raw material (as in cotton, wool, or rubber). Batch-to-batch variability, similarly, is associated with a high degree of nonuniformity of raw material from lot t o lot, with inadequate control of major processing variables (such as reaction time, temperature, or pressure) or with incapability of a n “adjustment” technique which requires an operator t o make quantitative chemical additions. Finally, time-to-time variability has its roots in still other factors: long-term changes in composition or purity of raw materials or differences among several suppliers; shifts in calibration of control mechanisms; gradual or sudden introduction of contamination; gradual depletion of chemical baths or catalysts; use of insufficiently trained substitute operators; or changes in atmospheric or environmental conditions.
Figure 3.
Components of Total Variability as Shown hy Pictogram
Establishment of the relative magnitude of these components of the total variability is thus the important step in the delineation of the problem. By eliminating those groups of factors which are not relevant to the solution, it focuses attention and thought t o the relatively small area where the answer will be found. The statistical techniques for performing this “fractionation” will be found under the heading of analysis of variance ill many good tests (1-3,8, 9). However, a convenient qualitative method of portraying this breakdown visually is afforded by the Multi-Vari chart (Figure 2). This simple chart indicates the range of withinbatch measurements-for example, replicate chemical analysis on the same sample or on several samples from a batch-by a straight line connecting the maximum and minimum observations. Batch-to-batch variability is indicated by the grouping oi lines for successive batches, and time-to-time variability is noted by observing trends or erratic behavior among successive groups. Depending on whether the chart exhibits Type I, 11, or I11 s y m p t o m , or a combination of them, the most profitable line of attack is evident. Another graphical method of picturing the component breakdown.;* t h a t of the Pictogram, as shown in Figure 3. This is H. pictorial histogram in which the total variability represents the base line of the histogram of the operation and in which the magnitude of each of the components is shown by the length of line assigned to it. The within-batch and batch-to-batch variabilities are shown adding together in a right triangle relationship, since the resultant of these two independent sources is the square root of the sum of the squares of the component variabilitie,c. Time is added directly in this instance and thus indicates the range of various levels at which the process has been found to be located at different times. Further illustrqtions and more complete details of these graphical methods are given in another paper by the author (6).
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With this type breakdown, the trouble shooter is in the position of a doctor who has made a complete collection of the symptoms of his patient, utilizing the x-ray, the electrocardiograph, and other modern medical tools. He can prescribe for the total disease instead of employing the makeshift procedure of treating each symptom as a n isolated illness. Too often in the past, troubleshooting problems have been “solved” by the blanket decision to install more precise control equipment, for example, without any knowledge as to whether the s y m p t o m of the process really indicated such a need. NONDISSECTAB LE PROCESS
The relatively straightforward approach t o the trouble-shooting problem that is possible with the dissectable process must necessarily give way to a more indirect strategy when the quality characteristic is not measurable between manufacturing steps, as in the process called nondissectable. The basic objective is still the same-to determine the responsible operation, segregate t h r multistreams, and fractionate into the components of variationbut the problem is complicated by the inability t o determinr cause and effect relationships with the same accuracy. The trouble shooter must reason from a single result-the final measurement-to a multiplicity of possible causes back in the several operations of the process. The techniques for doing this are discussed later, but it is first relevant to point out two special methods by means of which the nondissectable process may b t ~ converted into a dissectable process for trouble-shooting purposes. The first of these might be called conversion through substitution of related property. Although the desired quality characteristic may not be measurable until the manufacture is complete, some other property which is directly related to i t may be easily determinable at the several stages of processing. The use of viscosity as a measure of degree of polymerization, specific gravity as a measure of solids content in chemical processing, or the use of nondestructive hardness testing in place of destructive tensile strength measurement are cases in point. A second method of changing a nondissectable process into a dissectable one might be called conversion through parallel pilot plant operation. Here, samples from the production stream arc shunted off at various stages of the process and t h e remaining steps completed in a laboratory-controlled pilot plant. Control charts of these samples are then plotted so t h a t when trouble OCCUTS in the production process, the operation responsible ma!. be pin pointed by simply noting a t which stage the trouble first appears in the pilot plant samples. Evidently the manufacturing step just previous to the drawing of these samples is the culprit. The same technique may be employed to discover the esistencqe of multistreams by separate sampling of such suspects. A variation on this technique is t o short-circuit individual operations through the pilot plant, then back into the production stream. The pilot plant idea was employed on a continuous day-to-da!. basis by the author for trouble shooting during the early stages of development of the selenium rectifiei,. This device consists of :t metallic base plate, coated with several layers of selenium, a ver). thin layer of selenium dioside, and a sprayed-metal electrode. In all, some ten separate operations are performed in sequence, and the rectifier is entirely complete before any measurement of thc important “forward” and “reverse” electrical resistivities can be made. Initially, yields were very low, since each of the t,en operations had a large number of variables associated with it, many of which are imperfectly understood. The pilot plant technique was applied by selecting samples from each batch of product at each stage of the production operations, completing the operations in the laboratory plant, and plotting the electrical test results on control charts. A glance at this set of charts usually sufficed t o locate the operation causing the low average or the excessive variability; intensive studies of these operat,ions were then made and the trouble was corrected. In the larger
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sense, the pilot plant chaxts served t o direct the engineering talent toward points in the process where it could be most profitably spent. I n the course of time, the yield of this process was more than doubled, with the pilot plant technique contributing handsomely to the achievement. For many nondissectable processes, the t x o simplifications discussed are inapplicable for one reason or another and the trouble shooter must attempt to establish cause and effect relationships by (1) performing correlation analyses on existing process data or ( 2 ) by resorting t’o plant-scale experimentation in which variat,ion is deliberately introduced. The 5rst of these techniques is especially applicable when the accumulation of data is slow or espensive and when routine production records are already available. Frequently, it is true than an abundance of such records has been cached away to gather dust because they are not susceptible to analysis by simple methods. To the trouble shooter, however, these may represent a vast untapped reservoir of valuable information, for, by means of simple and multiple regression analysis techniques, he is able to uncover the existence of relationships that have eluded the efforts of the stjatistically untrained. Usually, such routine quality data : ~ r cin t>heform of a complete processing record, batch-by-hatc*h, in Xvhich proccssipg temperatures, pressures, humidities, kettle numbers, and chemical :tnalytical data are tabulated. Attempts to correlate the pertinent quality result-purity, for example-with any one of the processing variables-tempcrature, perhaps-usually fail because purity probably depends 011 scveral variables and, in the data at hand, all other variables Jvcre varying simultaneously in the inconsiderate way that production data habitually do vary. By means of the multiple regression technique, however, it becomes possible to assess the effect of t.emperat,ure on purity, while mat.hematically holding constant all the other factors. Ji7hat is more, it is possible t o measure indr:pciidently the effects of all the factors contributing to purity, provided iniormat,ion on them has heen included in the production records. Thus, the statistical techniquc of correlation analysis has much to offer in the study of the nondissectable process. It necessarily is limited t o those rases where: (1) sufficient’ valid production data are availaiilc; ( 2 ) someone has had the foresight to include measurcmcnts on all pertinent faciors; and (3) the l’aiigc over which the variables have actrd during the normal poduetion cycle is sufficient t o produce the extent of change in t h e quality results that it is desired t.o observe. \\.hen any one of t,hese condit,ions is not met, the trouble shooter must resort to the second of the methods of plant-scale esperimentation. In so doing, he is plac,etl in the same position as the csperimcnter in biology or mdicino who seeks t o determine the effect of small dietary ohanges superimposed on the sizable natural variability in his test animals. JVithout the necessary thoughtful planning of the csperinirnt, the biologist cannot truthfully say nhethcr the tcst guinea pigs flourished well because of the spwial diet, because thcy ivere unusually healthy individuals or because thcy came from a lit,t.er of a n exceptionally htvtlthy strain. Only by disciplining himself to a regime in which all causes are deliberatc~lyhrought into the experimental plan in a kuo\vri way can thc cspei.imoliter gain reasonablt: assur:tiice that he is measuring a cause antl clffect relationship. Fortunately, t h e researchers in biology, incdicine, and agriculture have developed t,he techniqucs for c:ontluc,ting valid experiments in the presence of variation, antl the tiwuble shooter can borrow lit)erally from their cxpc.ric:nc.es. The work of Fisher (a, 3 ) , Siledecor (8),Coohran ~ n t iC o s ( I ) , and others has been the impetus and inspiration for these developmmts. It must be emphasized that it is t h e design t.echniques t h a t are of primary importancc to the trouble shooter, rather than the strictly statist.ica1 met,hodology. Too many people have the attit.ude that, statistical analysis is mcrc:ly a refined method of %wivingat conrhisions and that the statistics will somehow com-
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pensate for a shoddy experimental design. The sad truth il; t,h;tt no amount of refined analysis can overcome the handicap of an improperly designed experiment. If an experiment is coiitiuctcil in which the variable under study is confounded with one of the “extraneous” variables, and if the extraneous variable is i i i reality the dominant factor, then the experimenter is wrtaiii to be misled, regardless of whether or not statistics is employctl i n the analysis of the data. The statist>icaltest of significance will “prove” t h a t a cause and effect relationship exists or a sranning of the data will indicate the same thing, but neither met,hod will prevent the careless experimenter from associat,ing the rrlationship with the wrong variable. Moreover, the embellishment of a n improperly designctl c?spt:i,iment wit,h an elaborate statistical analysis is not only nonscnse, i t borders on quackery. It is akin to t h e “scientific tests provo that our product is preferred over all other brands” so oft.en lirartl in commcrcial advertising. It is quitc important, therrfoi,c, that the trou1)le shooter be well aware of t,he simple funclamcwt,als of ’ esperimcntal design because the entire structure of his csistcnco crumhlcs when he allows himself to be hoodwinked by t h e yesults of ill-conceived experiments. PROPOSAL FOR A N EXPERIMENT
In o d e r to consider this problem mol’(: concretely, let. u s :ittempt to design a simple experinicnt in a t ,ical manufnctui~iiig plant. To use a process that will be fami r , assume we : t w iii the business of manufacturing doughnuts. The srqucncc’ of operations is: 1. Raw materials, principally flour, shortening, and flavoring, are Tveighed out according t o formula. 2. They are mixed in a Banbury or similar mixer. 3. The plastic mixture is rolled out into sheets. 4. Annular rings are blanked out. 5. The rings are fried in deep fat,. 6. Finished doughnuts are cooled wit1 tested. ’
For the purposes of this illustration, :mume that t h r t w i .
