Resolve issues with process capability indexes, business metrics

Transcription

1 3.4 Per Million BY Forrest W. Breyfogle III Insight or Folly? Resolve issues with rocess caability indexes business metrics In lean Six Sigma much training effort is sent on conveying the imortance of having a measurement system so that consistent and correct decisions are made relative to assessing art quality and rocess attributes. In this training measurement systems analysis (MSA) and associated gage reeatability and reroducibility (R&R) studies are integral. It seems MSA should be a reorting consideration for all forms of measurement including business erformance metrics. It also seems a focus should be laced on metric statements that are in a clear language. In the real world however how often are these goals achieved? Every organization s goal should be to achieve the three Rs of business: Everyone does the right things in the right way at the right time. One tool that rovides direction for the three Rs goal is rocess erformance metrics; that is a rocess erformance reort-out should lead to the most aroriate action or inaction which is indeendent of the erson comiling the information. This basic right-behavior objective is like an insection gage MSA which ensures insectors can adequately C and d determine whether a manufactured comonent should be acceted or rejected. Because of this erformance-reorting need it seems that management and ractitioners from a concetual MSA oint of view would be assessing the health of current scorecard and metric reorting systems. However this doesn t seem to occur. The question is: Why don t we examine business metrics and rocess caability indexes reorting from an MSA oint of view with the same level of intensity we do for roduct quality metrics? To quantify the magnitude of this issue consider different aroaches someone might use to reort rocess erformance. You might choose a bar chart a ie chart a red-yellow-green scorecard rocess caability indexes (that is C P and C m ) or a table of numbers. For a given rocess each of these reorting methods can rovide a very different and somewhat subjective icture of how a rocess erforms and whether any actions should be taken. To illustrate the magnitude of this issue an examle later in this column will show how reorted C P Process caability standard deviation calculations / Table 1 P X chart x and R Random samle x) 2 1 i1 R * d 2 x) 2 1 i1 /A x) 2 1 * Statistical comuter rograms will sometimes ool standard deviations for unbiasing reasons when there are m subgrous of samle size n resulting in a slightly different value for standard deviation. i1 rocess caability indexes can be sensitive to rocess samling rocedures a concetual MSA issue. In addition these reorts describe historically what haened which may not be reresentative of the future. What is really desired is a statement about what is exected in the future so changes can be made if needed. Metric reorting should lead to the most aroriate action or inaction. However rocess-metric decisions are often a function of how an individual or a grou chose its rocess samling data analysis and reorting rocedures. From a concetual MSA oint of view the reorting of rocess erformance should be indeendent of the erson doing the samling and reorting. Also it is most desirable to use a redictive measurement system in which the only difference between individual rocess reorting is from chance samling variability. Organizations benefit when managers use redictive measurement reorting throughout their business functional rocess ma. Practitioners can enhance the understanding of the benefits of this system when roviding illustrative reortouts that comare current scorecard metric reorting to redictive-erformance metric reorting system. Process caability indexes The rocess caability index C reresents the allowable tolerance interval sread in relation to the actual sread of the data when the data follow a normal distribution. This equation is: C USL LSL 6σ in which USL and LSL are the uer and 56 QP

2 lower secification limits resectively and the sread of the distribution is described as six times standard deviation; that is 6σ. C addresses only the sread of the rocess; is used to address the sread and mean (μ) shift of the rocess concurrently. Mathematically can be reresented as the minimum value of the two quantities: USL µ µ LSL 3σ 3σ min [ ] P indexes are sometimes referred to as long-term caability or erformance indexes. The relationshi between P and is similar to that between C and. The index P reresents the allowable tolerance sread relative to the actual sread of the data when the data follow a normal distribution. This equation is: P USL LSL 6σ in which again USL and LSL are the uer and lower secification limits. o quantification for data centering is described within this P relationshi. Mathematically can be reresented as the minimum value of the two quantities: USL µ µ LSL 3σ 3σ min [ ] Consider the confusion in calculating the seemingly simle statistic of standard deviation. Although standard deviation is an integral art of calculating rocess caability the method used to calculate the value rarely seems to be adequately scrutinized. In some cases it is imossible to get a secific desired result if data are not collected in the aroriate fashion. Consider the following sources of continuous data: Situation one: An x and R control chart with subgrous of samle size of 5. Situation two: An X chart with individual measurements. Samle data / Table 2 Subgrou Samle 1 Samle 2 Samle 3 Samle 4 Samle Situation three: A random samle of measurements from a oulation d For these three situations C P and P a standard deviation estimate (σˆ ) R R 0.90 is determined through the relationshis in d Table 1. In Table 1 x is the overall samle mean x i is an individual samle (i) from a total samle size R is the mean subgrou range is the mean range between adjacent subgrous is the total samle size and d 2 is a factor for constructing variables control charts; that is d for a two-observation samle and for a five-oeration samle. The data set in Table 2 illustrates the imact different data collection techniques can have on reorted rocess caability metrics. When reorting rocess caability indexes it is imortant that the data from which the metric is calculated comes from a stable rocess. In other In the second standard deviation calculation consider that samle one in Table 2 was the individual reading for each subgrou. For a secification of a statistical analysis rogram used similar standard deviations when determining the rocess caability results in Table 3. In Table 3 there is large difference between the C and values for a subgrouing samle size of one samle versus five. An examination of the standard deviation equations rovides the reason for the large difference: C and calculations which used an x and R chart had their equation s standard words the rocess is in control. 1 To quantify the caability of this rocess you could have selected only Process caability one samle instead of five for each results samle subgrou. These two scenarios would result in the following standard deviation data / Table 3 calculations: Subgrous C P x) 2 Five samles i1 n 1 One samle January 2010 QP 57

3 3.4 er million Process resonse baseline demonstrated imrovement for continuous resonse / Figure 1 Individual value Individuals chart of resonse by stage Observation UCL _ X LCL For secification of 100 +/-4 : Process was stable with an aroximate nonconformance rate of 9.2%. : Process is redictable (stable) with an aroximate nonconformance rate of 0%. Percentage Probability lot of resonse ormal Resonse UCL uer control limit LCL lower control limit deviation determined by averaging within subgrous. For the individual s chart standard deviation was calculated between subgrous. Concetual MSA issues With an effective concetual MSA system rocess samling lans should have no effect on rocess erformance statements. Because of the differences noted earlier you can conclude rocess caability Statistical business erformance charting action otions / Table 4 1. Is the rocess unstable or did something out of the ordinary occur which requires action or no action? 2. Is the rocess stable and meeting internal and external customer needs? If so no action is required. 3. Is the rocess stable but does not meet internal and external customer needs? If so rocess imrovement efforts are needed. reorting can have MSA issues because a samle of five versus one did not rovide similar answers; that is the differences being only the result of luck-of-the-draw samling. In this analysis you might notice P are similar for the two samling rocedures. An x and R control chart analysis however would indicate the rocess was out of control; therefore a rocess caability analysis would not be aroriate for this form of controlcharting analysis. 2 Other concetual MSA issues with rocess caability indexes reorting include: The hysical imlication of reorted rocess caability indexes is uncertain and ossibly wrong. Without an accomanying statement of rocess stability from a control chart all rocess caability indexes are questionable in value. Any rocess caability assessment of an unstable rocess is imroer and often decetive. Process caability indexes do not rovide a redictive erformance statement. Predictive reorting alternative From a concetual MSA oint of view Table 4 describes three reasons for statistical business erformance charting (SBPC) or foot-level 3 tracking and reorting for transactional and manufacturing rocess oututs. Process erformance reorting using rocess caability indexes bar charts ie charts red-yellow-green scorecards or tables of numbers can rovide differing rocess erformance assessments a concetual MSA issue. In addition rocess erformance reorting does not structurally address the action otions in Table 4. 4 The following examle illustrates a system for describing a rocess-outut erformance from a foot-level. For this SBPC reorting an individual s control chart subgrouing frequency is made so tyical variability from inut variables occurs between subgrous. Data from regions of stability can be used to estimate the nonconformance rate of a rocess during those timeframes. If there is a recent region of stability data from this region can be considered a 58 QP

4 random samle of the future from which a rediction can be made. This rediction resumes no fundamental ositive or negative changes will occur in the future relative to the rocess inuts or its execution stes. If at some oint in time the outut of a stable rocess is erforming at an undesirable nonconformance level an organization can initiate a roject to change rocess inuts or take stes to imrove a rocess erformance level. For continuous data a robability lot can rovide an estimate of the rocess nonconformance rate in either ercentage or defects er million oortunities units. For attribute data the rocess estimated nonconformance rate is simly the overall combined subgrou failure rates in the region of rocess stability. Figures 1 and 2 illustrate footlevel reorting and the results of an imrovement roject for both continuous and attribute data. 5 Integrating SBPC When reorting how a rocess is erforming using caability indexes the magnitude of the reorted metrics for a given situation can be a function of samling rocedures. For examle different conclusions could be made when rocess data are analyzed from an individuals chart reort-out (one samle er subgrou) versus a x and R chart reorting (multile samles er subgrou); that is a concetual rocess erformance MSA issue. Traditional organizational erformance measurement reorting systems can use tables of numbers stacked bar charts ie charts and red-yellow-green goal-based scorecards. For a given situation one erson may choose one reorting scheme while another uses a comletely different aroach. These differences can lead to a different conclusion about what is haening and should Process resonse baseline demonstrated imrovement for attribute resonse / Figure UCL _ 0.02 X LCL Observation For equal subgrou sizes of 1000: : Process was stable with an aroximate nonconformance rate of 5%. : Process is redictable (stable) with an aroximate nonconformance rate of 2%. Individual value UCL uer control limit LCL lower control limit Individuals chart of failure rate by stage be done as shown in Table 4. In addition these traditional reorting methods rovide only an assessment of historical data and make no redictive statements. Using this form of metric reorting to run a business is similar to driving a car by only looking at the rearview mirror a dangerous ractice. When redictive SBPC system reorting is used to track interconnected business rocess ma functions an alternative forward-looking dashboard erformance reorting system becomes available. With this foot-level metric system organizations can systematically evaluate future exected erformance and make aroriate adjustments if they don t like what they see. Organizations can benefit when SBPC techniques are integrated within a business system that analytically and innovatively determines strategies with the alignment of imrovement rojects that ositively imact the overall business. 6 QP REFERECES AD OTES 1. Forrest Breyfogle III Control Charting at the foot-level Quality Progress ovember The data used in Table 2 were also used in the 2003 article to comare traditional x and R rocess stability assessment to foot-level oerational-metric reorting. In the 2003 article a traditional control chart indicated that the rocess was out of control while foot-level reorting indicated the rocess was in control. The article also described the advantages of a foot-level assessment when comared to traditional reorting. 2. Ibid. The article also notes technical reasons why individual control charting is referred over x and R control charting. 3. Forrest Breyfogle III Integrated Enterrise Excellence Volume II Business Deloyment: A Leaders Guide for Going Beyond Lean Six Sigma and the Balanced Scorecard Bridgeway Books Ibid. 5. Forrest Breyfogle III Control Charting at the foot-level Part 2 Quality Progress ovember This article describes the advantages of attribute-failure-rate individuals charting (as shown in Figure 2) over a -chart. 6. Forrest Breyfogle III Control and Grow Your Enterrise Quality Progress February FORREST W. BREYFOGLE III is founder and CEO of Smarter Solutions Inc. in Austin TX. He earned a master s degree in mechanical engineering from the University of Texas. Breyfogle is the author of a series of books on the Integrated Enterrise Excellence System. He is an ASQ fellow and reciient of the 2004 Crosby Medal. January 2010 QP 59

5 About the Author Forrest Breyfogle III Integrated Enterrise Excellence In a rofessional career sanning over a quarter century Forrest Breyfogle has established himself as a leading edge thinker a rolific author an innovative consultant a world-class educator and a successful business executive. His work is documented in eleven books and over ninety articles on the toic of quality imrovement. A rofessional engineer Forrest is also a member of the board of advisors for the University of Texas Center for Performance Excellence. He is the founder and CEO of Smarter Solutions Inc. an Austin Texas based consulting firm offering business measurement and imrovement consultation and education to a distinguished list of clients worldwide including BAMA CIGA Dell HP IBM Oracle Packaging Sherwin Williams Cameron TIMET and TATA. He served his country on active duty in the US Army for 2 years and has layed an active leadershi role in rofessional and educational organizations. Forrest received the restigious Crosby Medal from the American Society for Quality (ASQ) in 2004 for his book Imlementing Six Sigma (second edition). This award is resented annually by the American Society for Quality to the individual who has authored a distinguished book contributing significantly to the extension of the hilosohy and alication of the rinciles methods or techniques of quality management He is a widely recognized authority in the field of management imrovement and is a frequent seaker before rofessional associations and businesses. His earlier work in the field of management science has been widely acclaimed. A revious book Imlementing Six Sigma sold over coies and still ranks among the to Amazon books in Alied Mathematics/Engineering Statistics and Industrial Engineering /Quality Control. He founded Smarter Solutions in 1992 after a 24-year career at IBM. The associates of Smarter Solutions secialize in heling comanies throughout the world imrove their bottom line and customer satisfaction through the imlementation of techniques that are beyond traditional Lean Six Sigma and the balanced scorecard methodologies. His latest and most extensive work has been in the documentation of a new system of enterrise management the Integrated Enterrise Excellence (IEE) system in a series of four books. IEE rovides a detailed roadma that builds on and integrates the best ractices of earlier discilines like Six Sigma Lean TQM PDCA DOE and TPS combined with innovative analytical tools to roduce imrovements at the highest level of an enterrise. In addition to assisting hundreds of major clients in the wise imlementation of imrovement systems worldwide Forrest has also develoed over 300 hours of classroom instruction used to train executives managers and Black Belt ractitioners to lan for imlement and manage IEE systems. He also leads formal seminars and workshos worldwide. Forrest Breyfogle forrest@smartersolutions.com x401