Quality Improvement. Dale Besterfield Ninth Edition

Transcription

1 Quality Improvement Dale Besterfield Ninth Edition......

2 Pearson Education Limited Edinburh Gate Harlow Essex CM20 2JE Enland and Associated Companies throuhout the world Visit us on the World Wide Web at: Pearson Education Limited 2014 All rihts reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopyin, recordin or otherwise, without either the prior written permission of the publisher or a licence permittin restricted copyin in the United Kindom issued by the Copyriht Licensin Aency Ltd, Saffron House, 6 10 Kirby Street, London EC1N 8TS. All trademarks used herein are the property of their respective owners. The use of any trademark in this text does not vest in the author or publisher any trademark ownership rihts in such trademarks, nor does the use of such trademarks imply any affiliation with or endorsement of this book by such owners. ISBN 10: ISBN 13: British Library Catalouin-in-Publication Data A cataloue record for this book is available from the British Library Printed in the United States of America

3 Before proceedin to the action step, some final comments are appropriate. First, many analysts eliminate this step in the procedure because it appears to be somewhat redundant. However, by discardin out-of-control points with assinable causes, the central line and control limits are more representative of the process. This step may be too complicated for operatin personnel. Its elimination would not affect the next step. Second, the formulas for the control limits are mathematically equal. Thus, for the upper control limit, X 0 + As 0 = X new + A 2 R new. Similar equivalences are true for the lower control limit and both control limits for the R chart. Third, the parameter s 0 is now available to obtain the initial estimate of the process capability, which is 6s 0. The true process capability is obtained in the next step (Achieve the Objective). Also, a better estimate of the standard deviation is obtained from s 0 = R 0 > d 2 and the best estimate is obtained from s 0 = s 0 >c 4 from the X, s control charts in the sample standard deviation control chart section. Fourth, the central line, X 0, for the X chart is frequently based on the specifications. In such a case, the procedure is used only to obtain R 0 and s 0. If in our example problem the nominal value of the characteristic is 6.38 mm, then X 0 is set to that value and the upper and lower control limits are UCL X = X 0 + As 0 LCL X = X 0 - As 0 = (1.500)(0.038) = (1.500)(0.038) = 6.44 = 6.32 The central line and control limits for the R chart do not chane. This modification can be taken only if the process is adjustable. If the process is not adjustable, then the oriinal calculations must be used. Fifth, it follows that adjustments to the process should be made while takin data. It is not necessary to run nonconformin material while collectin data, because we are primarily interested in obtainin R 0, which is not affected by the process settin. The independence of m and s provide the rationale for this concept. Sixth, the process determines the central line and control limits. They are not established by desin, manufacturin, marketin, or any other department, except for X 0 when the process is adjustable. Finally, when population values are known (m and s), the central lines and control limits may be calculated immediately, savin time and work. Thus X 0 = m, s 0 = s, and R 0 = d 2 s, and the limits are obtained usin the appropriate formulas. This situation would be extremely rare. Achieve the Objective When control charts are first introduced at a work center, an improvement in the process performance usually occurs. This initial improvement is especially noticeable when the process is dependent on the skill of the operator. Postin a quality control chart appears to be a psycholoical sinal to the operator to improve performance. Most workers want to produce a quality product or service; therefore, when manaement shows an interest in the quality, the operator responds. Fiure 7 illustrates the initial improvement that occurred after the introduction of the X and R charts in January. Owin to space limitations, only a representative number of subroups for each month is shown in the fiure. Durin January, the subroup averaes had less variation and tended to be centered at a slihtly hiher point. A reduction in the rane variation also occurred. Fiure 7 Continuin Use of Control Charts, Showin Improved Quality 73

4 Not all the improved performance in January was the result of operator effort. The first-line supervisor initiated a proram of tool wear control, which was a contributin factor. At the end of January, new central lines and control limits were calculated usin the data from subroups obtained durin the month. It is a ood idea, especially when a chart is bein initiated, to calculate standard values periodically to see if any chanes have occurred. This reevaluation can be done for every 25 or more subroups, and the results compared to the previous values. 7 New control limits were established for the X and R charts and central line for the R chart for the month of February. The central line for the X chart was not chaned because it is the nominal value. Durin the ensuin months the maintenance department replaced a pair of worn ears; purchasin chaned the material supplier; and toolin modified a workholdin device. All these improvements were the result of investiations that tracked down the causes for outof-control conditions or were ideas developed by a project team. The eneration of ideas by many different personnel is the most essential inredient for continuous quality improvement. Ideas by the operator, first-line supervisor, quality assurance, maintenance, manufacturin enineerin, and industrial enineerin should be evaluated. This evaluation or testin of an idea requires 25 or more subroups. The control chart will tell if the idea is ood, poor, or has no effect on the process. Quality improvement occurs when the plotted points of the X chart convere on the central line, or when the plotted points of the R chart trend downward, or when both actions occur. If a poor idea is tested, then the reverse occurs. Of course, if the idea is neutral, it will have no affect on the plotted point pattern. In order to speed up the testin of ideas, the takin of subroups can be compressed in time as lon as the data represent the process by accountin for any hourly or dayto-day fluctuations. Only one idea should be tested at a time; otherwise, the results will be confounded. At the end of June, the periodic evaluation of the past performance showed the need to revise the central lines and the control limits. The performance for the month of July and subsequent months showed a natural pattern of variation and no quality improvement. At this point no further quality improvement is possible without a substantial investment in new equipment or equipment modification. W. Edwards Demin has stated that if he were a banker, he would not lend any money to a company unless statistical methods were used to prove that the money was necessary. This is precisely what the control chart can achieve, provided that all personnel use the chart as a method of quality improvement rather than just a maintenance function. When the objective for initiatin the charts has been achieved, its use should be discontinued or the frequency of 7 These values are usually compared without the use of formal tests. An exact evaluation can be obtained by mathematically comparin the central lines to see if they are from the same population. inspection be substantially reduced to a monitorin action by the operator. Efforts should then be directed toward the improvement of some other quality characteristic. If a project team was involved, it should be conratulated for its performance and disbanded. The Sample Standard Deviation Control Chart Althouh the X and R charts are the most common charts for variables, some oranizations prefer the sample standard deviation, s, as the measure of the subroup dispersion. In comparin an R chart with an s chart, an R chart is easier to compute and easier to explain. On the other hand, the subroup sample standard deviation for the s chart is calculated usin all the data rather than just the hih and the low value, as done for the R chart. An s chart is therefore more accurate than an R chart. When subroup sizes are less than 10, both charts will raphically portray the same variation; 8 however, as subroup sizes increase to 10 or more, extreme values have an undue influence on the R chart. Therefore, at larer subroup sizes, the s chart must be used. The steps necessary to obtain the X and s trial control and revised control limits are the same as those used for the X and R chart except for different formulas. In order to illustrate the method, the same data will be used. They are reproduced in Table 3 with the addition of an s column and the elimination of the R column. The appropriate formulas used in the computation of the trial control limits are s = a s i X = a X i UCL X = X + A 3 s UCL s = B 4 s LCL X = X - A 3 s LCL s = B 3 s where s i = sample standard deviation of the subroup values s = averae of the subroup sample standard deviations A 3, B 3, B 4 = factors found in Table B of the Appendix for obtainin the 3s control limits for X and s charts from s Formulas for the computation of the revised control limits usin the standard values of X 0 and s 0 are X 0 = X new = X - X d - d s 0 = s new = s - s d - d s 0 = s 0 c 4 UCL X = X 0 + As 0 UCL s = B 6 s 0 LCL X = X 0 - As 0 LCL s = B 5 s 0 8 A proof of this statement can be observed by comparin the R chart of Fiure 5 with the s chart of Fiure 8. 74

5 where s d = sample standard deviation of the discarded subroup c 4 = factor found in Table B for computin s 0 from s A, B 5, B 6 = factors found in Table B for computin 3s process control limits for X and s charts The first step is to determine the standard deviation for each subroup from the preliminary data. For subroup 1, with values of 6.35, 6.40, 6.32, and 6.37, the standard deviation is n n 2 n a X 2 i - a a X i b s = H n1n - 12 = A 4( ) - ( ) 2 4(4-1) = mm The standard deviation for subroup 1 is posted to the s column, as shown in Table 3, and the process is repeated for the remainin 24 subroups. Continuation of the X and s charts is accomplished in the same manner as the X and R charts. Example Problem 4 Usin the data of Table 3, determine the revised central line and control limits for X and s charts. The first step is to obtain s and X, which are computed from s and X, whose values are found in Table 3. s = a s i = X = a X i = = mm = 6.41 mm From Table B the values of the factors A 3 = 1.628, B 3 = 0, and B 4 = are obtained, and the trial control limits are UCL X = X + A 3 s LCL X = X - A 3 s = (1.628)(0.039) = (1.628)(0.039) = 6.47 mm = 6.35 mm Table 3 Data on the Depth of the Keyway (mm) a Sample Standard Subroup Measurements Averae Deviation Number Date Time X 1 X 2 X 3 X 4 X s Comment 1 12/26 8: : : : New, temporary 5 4: operator 6 12/27 8: : : : : /28 8: : : : : /29 8: : : Damaed oil line 19 2: : Bad material 21 12/30 9: : : : : Sum a For simplicity in recordin, the individual measurements are coded from 6.00 mm. 75

6 UCL s = B 4 s LCL s = B 3 s = = = mm = 0 mm The next step is to plot the subroup X and s on raph paper with the central lines and control limits. This step is show in Fiure 8. Subroups 4 and 20 are out of control on the X chart and, because they have assinable causes, they are discarded. Subroup 18 is out of control on the s chart and, because it has an assinable cause, it is discarded. Computation to obtain the standard values of X 0, s 0, and s 0 are as follows: X 0 = X new = X - X d - d = s 0 = s new = s - s d - d = = 6.40 mm = mm s 0 = s 0 c 4 from Table B, c 4 = = = mm The reader should note that the standard deviation, s 0, is the same as the value obtained from the rane in the precedin section. Usin the standard values of X 0 = 6.40 and s 0 = 0.038, the revised control limits are computed. UCL X = X + As 0 LCL X = X 0 - As 0 = 6.40 = (1.500)(0.038) - (1.500)(0.038) = 6.46 mm = 6.34 mm UCL s = B 6 s 0 LCL s = B 5 s 0 = (2.088)(0.038) = (0)(0.038) = mm = 0 mm State of Control Process in Control When the assinable causes have been eliminated from the process to the extent that the points plotted on the control chart remain within the control limits, the process is in a state of control. No hiher deree of uniformity can be attained with the existin process. Greater uniformity can, however, be attained throuh a chane in the basic process throuh quality improvement ideas. When a process is in control, there occurs a natural pattern of variation, which is illustrated by the control chart in Fiure 9. This natural pattern of variation has (1) about 34% of the plotted points in an imainary band between 1 standard deviation on both sides of the central Fiure 8 X and s Chart for Preliminary Data with Trial Control Limits 76

7 Fiure 9 Natural Pattern of Variation of a Control Chart line, (2) about 13.5% of the plotted points in an imainary band between 1 and 2 standard deviations on both sides of the central line, and (3) about 2.5% of the plotted points in an imainary band between 2 and 3 standard deviations on both sides of the central line. The points are located back and forth across the central line in a random manner, with no points beyond the control limits. The natural pattern of the points or subroup averae values forms its own frequency distribution. If all of the points were stacked up at one end, they would form a normal curve (see Fiure 11). Control limits are usually established at 3 standard deviations from the central line. They are used as a basis to jude whether there is evidence of lack of control. The choice of 3s limits is an economic one with respect to two types of errors that can occur. One error, called Type I by statisticians, occurs when lookin for an assinable cause of variation, when in reality a chance cause is present. When the limits are set at 3 standard deviations, a Type I error will occur 0.27% (3 out of 1000) of the time. In other words, when a point is outside the control limits, it is assumed to be due to an assinable cause, even thouh it would be due to a chance cause 0.27% of the time. We miht think of this situation as uilty until proven innocent. The other type error, called Type II, occurs when assumin that a chance cause of variation is present, when in reality there is an assinable cause. In other words, when a point is inside the control limits, it is assumed to be due to a chance cause, even thouh it miht be due to an assinable cause. We miht think of this situation as innocent until proven uilty. Table 4 illustrates the difference between the Type I Table 4 Type I and Type II Errors Plotted Point Is Outside Control Limits Inside Control Limits Assinable cause present OK Type II Error Chance cause present Type I Error OK and Type II errors. If control limits are established at, say, ;2.5 standard deviations, Type I errors would increase and Type II decrease. Abundant experience since 1930 in all types of industry indicates that 3s limits provide an economic balance between the costs resultin from the two types of errors. Unless there are stron practical reasons for doin otherwise, the ;3 standard deviation limits should be used. 9 When a process is in control, only chance causes of variation are present. Small variations in machine performance, operator performance, and material characteristics are expected and are considered to be part of a stable process. When a process is in control, certain practical advantaes accrue to the producer and consumer. 1. Individual units of the product or service will be more uniform or, stated another way, there will be less variation and fewer rejections. 2. Because the product or service is more uniform, fewer samples are needed to jude the quality. Therefore, the cost of inspection can be reduced to a minimum. This advantae is extremely important when 100% conformance to specifications is not essential. 3. The process capability or spread of the process is easily attained from 6s. With a knowlede of process capability, a number of reliable decisions relative to specifications can be made, such as a. to decide the product or service specifications or requirements, b. to decide the amount of rework or scrap when there is insufficient tolerance, and c. to decide whether to produce the product to tiht specifications and permit interchaneability of components or to produce the product to loose specifications and use selective matchin of components. 4. Trouble can be anticipated before it occurs, thereby speedin up production by avoidin rejections and interruptions. 9 Elisabeth J. Umble and M. Michael Umble, Developin Control Charts and Illustratin Type I and Type II Errors, Quality Manaement Journal, Vol. 7, No. 4 (2000):