In it there is a Problem illustrating muda, mura, and muri through the use of a forklift example: "How best to move 6000 kg load with a forklift having a capacity of 2000 kg." The choices are
Muda: 6 trips 1000 kg, Mura: 2 trips 2000 kg plus 2 trips at 1000kg, and Muri: 2 trips 3000 kg. Then it says: "Best: 3 trips 2000 kg."
Muda is the waste in a process; these are the seven production wastes that Taiichi Ohno references. Transportation, Inventory, Movement, Waiting, Overproduction, Over-processing, and Defects. So, in the example muda is looking at unnecessary transportation.
Mura is the unevenness or fluctuation of the schedule. Variability… So, in the example mura is looking at the imbalance in the assigned task.
Muri is the overburdening of your people or equipment. So, in the example muri is looking at demanding that a forklift carry X+ weight when it is rated to carry X weight.
In the Muda example, we are wasting time and effort because we could potentiall carry more.
In the Mura example we have an imbalance in what we are transporting (which incidentally leads to more muda).
And in the Muri example we have overburdened the equipment.
So the ideal example is to transport three loads at the maximum capacity of the forklift and accomplish the task.
Friday, September 19, 2008
Tuesday, September 16, 2008
5S in Mail Box
1 September 2008 by Sue Kozlowski | |
| 5S Your Email In-box | |
 | |
| I love to open my business email in-box in the morning, don't you? Especially if you've been practicing good work-life balance and haven't peeked at it since the end of business the day before. When I go on vacation, it's a special treat. Here's a 5S strategy that I have used to keep up with the "input." [Note: I'm using MS Office terminology since that's what I'm most familiar with - please substitute your own email application terms as you read.] SORT 1. If you've been gone a few days, or have LOTS of email to go through, sort the senders by name. Tackle your boss's emails first, then other VIPs, then go down the list in order of importance to your current task load or priority projects. 2. Be ruthless. If you don't need to know it, "red-tag" the item by dragging it over to the "Deleted Items" box. [Added action: If you hate getting those cute kitten-pictures and the latest urban rumors from your friends, take 10 seconds to reply to the sender to say tactfully: please don't send them any more. It's a worthwhile investment, and a true friend will appreciate your need to keep your business in-box for business only.] STRAIGHTEN 1. If you do need to know it, but it's an on-going progress report or something that doesn't need a response, file it immediately under a helpful heading that you will find again. 2. If you need to take action on an item, you can: a) Place it in an "action needed by date" folder. b) Leave it in your inbox as a reminder. c) See if you can drag it into your Task List - it may convert to a task to which you can add details. d) See if you can drag it into your calendar - to add it as a calendar item on the day of your choice. e) Print it and put it in a "to-do" pile. --The goal is to keep a clear picture of actions that you need to take, in a way that puts you on or ahead of deadline - not frantically searching for the original email when your boss or colleague asks you how you're coming on project X. SCRUB 1. Do you archive your emails? I don't let the computer do it automatically - there are some long-term projects that I need to keep the running history on, all in once place. When a project is finished, I move the whole folder to archive. 2. If you email inbox has a restriction on size, you have options: a) you can save everything to your hard drive or shared drive (open the email, click on FILE then SAVE AS), and then save any attachments to the same place. There are also applications you can buy or download for free that handle this action. b) or, at least in MS Office, you can create a .pst file that stores on your hard drive or shared drive, looks just like a folder in your mailbox, and you can store emails there just as you do in your regular mailbox. Click on FILE, NEW, OUTLOOK DATA FILE. (Get someone to help you if you have never used this, but after you've done it once it's easy.) It doesn't usually "count against" your regular mailbox size limitations. I use this for SENT MAIL since that's what usually kills my in-box size! For example, SENT-2006, SENT-2007. STANDARDIZE 1. There's no one way to organize your folders. I've seen success with folders by name of sender; week of the month; project name; etc. A general rule of thumb is to have no more than 3 levels of folders for any one heading - unless you have a perfect memory. But pick a system and stick with it. 2. Corollary: Most of us still use and receive paper in our jobs. It's a lot easier to find things if your paper filing system matches your email folder structure, so when you try to find your hardcopy master project list for company A in region D related to Widget X, it's under the same paper file folder headings as you would find it if it had been sent electronically. [Or, get with the new century and scan all documents into your computer, if you have access to a scanner!] SUSTAIN 1. Pick a slower-than-usual week, like a holiday week. Set aside a couple of hours to go through your emails and see what you can archive - what you can discard - what you can file more appropriately. The investment of time is well worth it. There are usually many other options in each email system, such as assigning categories to emails or flagging them with various colored flags, that you can delve into as well. However, the steps above have been helpful for me. Do any of you have equally effective methods of taming the in-box jungle? Please share! | |
Tuesday, August 5, 2008
Monday, August 4, 2008
Analysing experiments
Analyzing Experiments with Ordered Categorical Data
Six Sigma projects in various industries often deal with experiments whose outcomes are not continuous variable data, but ordered categorical data. Analysis of variables (ANOVA) is a technique used to analyze continuously experimental data, but is not adequate for analyzing categorical experimental outcomes. Fortunately, many other methods have been developed to deal with categorical experiments, such as Jeng and Guo’s weighted probability-scoring scheme (WPSS).
The WPSS technique is interpretable and easy to implement in a spreadsheet software program. The following case study, which involves medical devices, serves as an example of how a modified WPSS technique can be used to analyze experiments with ordered categorical data.
Determining the Best Factors
This study explores the influence of contact lens design factors on outcomes related to ease of lens insertion, meaning how easy it is to put patients’ contact lenses in their eyes. Soft contact lenses are thin pieces of plastic or glass that float on the tear film on the surface of the cornea. They are shaped to fit the user's eye and are used to correct refractive errors such as nearsightedness, farsightedness and unequal curvature of the cornea (astigmatism). For this example, only three lens design factors of a certain lens type with fixed material properties are considered: lens thickness profile (3 levels), base curve dimension (3 levels) and base curve profile (2 levels). Determining the ease of insertion is a five-step process.
Step 1: Design an Experiment
Because this is an exploratory experiment, an L9 orthogonal matrix is used. The design matrix with the three lens design factors is shown in Table 1.
| Table 1: L9 Orthogonal Matrix of Three Lens Design Factors | |||
Design Factors | |||
| Experiment Number | Thickness profile | Base curve dimension | Base curve profile |
| 1 | 1 | 1 | 1 |
| 2 | 1 | 2 | 2 |
| 3 | 1 | 3 | 1 |
| 4 | 2 | 1 | 2 |
| 5 | 2 | 2 | 1 |
| 6 | 2 | 3 | 1 |
| 7 | 3 | 1 | 1 |
| 8 | 3 | 2 | 1 |
| 9 | 3 | 3 | 2 |
Step 2: Plan Number of Samples and Data Categorization
In small clinical trials, nine trained contact lens wearers are asked to try each of the nine lens designs from the L9 matrix and give their opinion on the ease of insertion. Each time a patient inserts a lens in their eye, they are asked to rate how easy it was to do. Their responses are integer numbers from 1 to 10, with the worst condition rated 1 (the patient cannot insert the lens) to the best condition rated 10 (the patient needs only one trial and the lens immediately sits on the right location of the eye). The ratings are grouped into four categories of ease of insertion:
- Category I (very easy to insert): Ratings 9 – 10
- Category II (easy to insert): Ratings 7 – 8
- Category III (moderate to insert): Ratings 5 – 6
- Category IV (difficult to insert): Ratings 1- 4
The design matrix with the outcomes for each run is shown in Table 2.
| Table 2: Insertion Ratings Grouped By Category | ||||||||
Design Factors | Number of Observation By Category | |||||||
| Experiment Number | Thickness profile | Base curve dimension | Base curve profile | I | II | III | IV | Total |
| 1 | 1 | 1 | 1 | 1 | 2 | 5 | 1 | 9 |
| 2 | 1 | 2 | 2 | 3 | 3 | 3 | 0 | 9 |
| 3 | 1 | 3 | 1 | 4 | 2 | 2 | 1 | 9 |
| 4 | 2 | 1 | 2 | 2 | 2 | 3 | 2 | 9 |
| 5 | 2 | 2 | 1 | 4 | 4 | 1 | 0 | 9 |
| 6 | 2 | 3 | 1 | 1 | 3 | 1 | 4 | 9 |
| 7 | 3 | 1 | 1 | 5 | 3 | 1 | 0 | 9 |
| 8 | 3 | 2 | 1 | 2 | 5 | 1 | 1 | 9 |
| 9 | 3 | 3 | 2 | 4 | 1 | 4 | 0 | 9 |
Step 3: Calculate Probability of the Outcomes Per Category and Run
In order to estimate the location and dispersion effects of each run, the scores of each category of each run must be transformed into probability values. Let i be an experiment run, for i = 1, 2,…I (in this example, I = 9) and j be a category of experimental outcomes, for j = I, II,…J (in this example J = IV). Then it is possible to calculate the probability (proportion) that an outcome is placed in j-th category of i-th run, i.e. pij, as the following:
pij = nij/si
where nij is the number of outcomes in j-th category of i-th run and si is the total outcomes of all categories in the i-th run.
For example, the probability of an outcome being placed in the III-th category of the 1st run is p1III = n1III/s1 = 5/9 = 0.56. The probability of the outcome in each category of each run is shown in Table 3.
| Table 3: Probability of Outcomes | |||||||||
Number of Observation | Probabilities for Each Category | ||||||||
| Experiment Number | I | II | III | IV | Total | (I) | (II) | (III) | (IV) |
| 1 | 1 | 2 | 5 | 1 | 9 | 0.11 | 0.22 | 0.56 | 0.11 |
| 2 | 3 | 3 | 3 | 0 | 9 | 0.33 | 0.33 | 0.33 | 0.00 |
| 3 | 4 | 2 | 2 | 1 | 9 | 0.44 | 0.22 | 0.22 | 0.11 |
| 4 | 2 | 2 | 3 | 2 | 9 | 0.22 | 0.22 | 0.33 | 0.22 |
| 5 | 4 | 4 | 1 | 0 | 9 | 0.44 | 0.44 | 0.11 | 0.00 |
| 6 | 1 | 3 | 1 | 4 | 9 | 0.11 | 0.33 | 0.11 | 0.44 |
| 7 | 5 | 3 | 1 | 0 | 9 | 0.56 | 0.33 | 0.11 | 0.00 |
| 8 | 2 | 5 | 1 | 1 | 9 | 0.22 | 0.56 | 0.11 | 0.11 |
| 9 | 4 | 1 | 4 | 0 | 9 | 0.44 | 0.11 | 0.44 | 0.00 |
Step 4: Estimate Location and Dispersion Effects of Each Run
Given each category j has a weight wj, which is the upper limit of the j-th category rate, the location scores Wi for the i-th run is defined by
The rationale for using the upper limit of the category rate is that the weight should reflect the rating values. The dispersion score di2 is defined by
where the target values are defined as {The upper limit of the I-st category rate, 0, 0, …, 0} for categories {I, II, III, … ,J}, respectively.
The rationale of setting the target values is that only outcomes that fall in the best category are rewarded. For example, the location and dispersion scores for the 1st run are W1 = 10*0.11 + 8*0.22 + 6*0.56 + 4*0.11 = 6.7 and d12 = [10*0.11 – 10]2 + [8*0.22 – 0]2 + [6*0.56 – 0]2+ [4*0.11 – 0]2 = 93.48. The location and dispersion scores of the outcomes of each run are shown in Table 4.
| Table 4: Location, Dispersion and Mean Square Deviation Scores | ||||||
| Experiment Number | Design Factor – Thickness Profile | Design Factor – Base Curve Dimension | Design Factor – Base Curve Profile | Location Scores (Wi) | Dispersion Scores (di2) | MSD |
| 1 | 1 | 1 | 1 | 6.7 | 93.5 | 0.16 |
| 2 | 1 | 2 | 2 | 8.0 | 55.6 | 0.06 |
| 3 | 1 | 3 | 1 | 8.0 | 36.0 | 0.04 |
| 4 | 2 | 1 | 2 | 6.9 | 68.4 | 0.11 |
| 5 | 2 | 2 | 1 | 8.7 | 44.0 | 0.04 |
| 6 | 2 | 3 | 1 | 6.2 | 89.7 | 0.21 |
| 7 | 3 | 1 | 1 | 8.9 | 27.3 | 0.03 |
| 8 | 3 | 2 | 1 | 7.8 | 80.9 | 0.08 |
| 9 | 3 | 3 | 2 | 8.0 | 38.8 | 0.04 |
One performance measure to combine location and dispersion effects is mean square deviation (MSD), which allows practitioners to make judgments in one step. If any outcome is the larger-the-better characteristic, then its expected MSD can be approximately expressed in terms of location and dispersion effects as follows:
For example, the expected MSD for 1st run is E[MSD]1 = 1/(6.67)2 (1+ (3*93.5)/(6.67)2) = 0.16. The MSD scores for all runs are given in Table 4.
The location, dispersion and expected MSD effects for each design factors are shown as Tmax-Tmin (Figures 1, 2, 3). Higher Tmax-Tmin values or steeper main effects curves indicate a stronger influence of that design factor on the outcomes.
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Step 5: Determine Optimal Solutions
The level of a particular design factor with the highest location value, the lowest dispersion value or the lowest expected MSD value is the optimal solution for each of those factors, respectively. The optimal solution based on the expected MSD criteria is the optimal trade-off between maximal location and minimal dispersion scores.
The predicted optimal solution based on the expected MSD criteria is thickness profile at level 3, base curve dimension at level 2 and base curve profile at level 2. But if practitioners know there are interaction effects among design factors, they cannot depend solely on the main effect values or plots to choose the settings of design factors. The interaction plot for the expected MSD effects shows that thickness profile heavily interacts with base curve level/dimension (Figure 4). A small interaction also exists between base curve dimension and base curve profile. After taking interaction effects into consideration, practitioners need to examine whether the chosen optimal design factor levels still give optimal effects to the experiment outcomes.
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In this case, thickness profile at level 3 gives almost consistently the lowest MSD scores for different levels of base curve dimension and also consistently gives the lowest MSD scores for different levels of base curve profile. Thus, it gives the optimal effect to the experiment outcomes. Base curve dimension at level 2 almost consistently gives the lowest MSD scores for different levels of thickness profile and also consistently gives the lowest MSD score for different levels of base curve profile. Thus, it too gives the optimal effect to the experiment outcomes. The Tmax-Tmin value of the base curve profile is the lowest and its curve is flat. Thus, base curve profile has insignificant influence on the outcomes, and can be set at either level 1 or 2. Therefore, the expected MSD predicts that lens design with thickness profile at level 3, base curve dimension at level 2 and base curve profile at either level 1 or 2 would give the optimal ease of insertion.
Easy to Implement Optimization Method
A modified WPSS is a simple and straightforward method for dealing with ordered categorical data. This case study shows that a single performance measure MSD derived from WPSS can provide insight to a system through experiments and can direct practitioners to the optimal solution.
About the Author: Liem Ferryanto, Ph.D., is project director and Six Sigma Champion of global research, development and engineering at CIBA Vision Corp., a Novartis company, in Duluth, Ga., USA. He can be reached at lferryanto@gmail.com.
Wednesday, July 30, 2008
Statistical Definition
Statistical Six Sigma Definition
What does it mean to be "Six Sigma"? Six Sigma at many organizations simply means a measure of quality that strives for near perfection. But the statistical implications of a Six Sigma program go well beyond the qualitative eradication of customer-perceptible defects. It's a methodology that is well rooted in mathematics and statistics.
The objective of Six Sigma Quality is to reduce process output variation so that on a long term basis, which is the customer's aggregate experience with our process over time, this will result in no more than 3.4 defect Parts Per Million (PPM) opportunities (or 3.4 Defects Per Million Opportunities – DPMO). For a process with only one specification limit (Upper or Lower), this results in six process standard deviations between the mean of the process and the customer's specification limit (hence, 6 Sigma). For a process with two specification limits (Upper and Lower), this translates to slightly more than six process standard deviations between the mean and each specification limit such that the total defect rate corresponds to equivalent of six process standard deviations.
Many processes are prone to being influenced by special and/or assignable causes that impact the overall performance of the process relative to the customer's specification. That is, the overall performance of our process as the customer views it might be 3.4 DPMO (corresponding to Long Term performance of 4.5 Sigma). However, our process could indeed be capable of producing a near perfect output (Short Term capability – also known as process entitlement – of 6 Sigma). The difference between the "best" a process can be, measured by Short Term process capability, and the customer's aggregate experience (Long Term capability) is known as Shift depicted as Zshift or sshift. For a "typical" process, the value of shift is 1.5; therefore, when one hears about "6 Sigma," inherent in that statement is that the short term capability of the process is 6, the long term capability is 4.5 (3.4 DPMO – what the customer sees) with an assumed shift of 1.5. Typically, when reference is given using DPMO, it denotes the Long Term capability of the process, which is the customer's experience. The role of the Six Sigma professional is to quantify the process performance (Short Term and Long Term capability) and based on the true process entitlement and process shift, establish the right strategy to reach the established performance objective
As the process sigma value increases from zero to six, the variation of the process around the mean value decreases. With a high enough value of process sigma, the process approaches zero variation and is known as 'zero defects.'
Statistical Take Away
Decrease your process variation (remember variance is the square of your process standard deviation) in order to increase your process sigma. The end result is greater customer satisfaction and lower costs.
Article -what is six sigman
Six Sigma - What is Six Sigma?
Six Sigma at many organizations simply means a measure of quality that strives for near perfection. Six Sigma is a disciplined, data-driven approach and methodology for eliminating defects (driving towards six standard deviations between the mean and the nearest specification limit) in any process -- from manufacturing to transactional and from product to service.
The statistical representation of Six Sigma describes quantitatively how a process is performing. To achieve Six Sigma, a process must not produce more than 3.4 defects per million opportunities. A Six Sigma defect is defined as anything outside of customer specifications. A Six Sigma opportunity is then the total quantity of chances for a defect. Process sigma can easily be calculated using a Six Sigma calculator.
The fundamental objective of the Six Sigma methodology is the implementation of a measurement-based strategy that focuses on process improvement and variation reduction through the application of Six Sigma improvement projects. This is accomplished through the use of two Six Sigma sub-methodologies: DMAIC and DMADV. The Six Sigma DMAIC process (define, measure, analyze, improve, control) is an improvement system for existing processes falling below specification and looking for incremental improvement. The Six Sigma DMADV process (define, measure, analyze, design, verify) is an improvement system used to develop new processes or products at Six Sigma quality levels. It can also be employed if a current process requires more than just incremental improvement. Both Six Sigma processes are executed by Six Sigma Green Belts and Six Sigma Black Belts, and are overseen by Six Sigma Master Black Belts.
According to the Six Sigma Academy, Black Belts save companies approximately $230,000 per project and can complete four to 6 projects per year. General Electric, one of the most successful companies implementing Six Sigma, has estimated benefits on the order of $10 billion during the first five years of implementation. GE first began Six Sigma in 1995 after Motorola and Allied Signal blazed the Six Sigma trail. Since then, thousands of companies around the world have discovered the far reaching benefits of Six Sigma.
What is Six Sigma
Six Sigma
The goal of Six Sigma is to increase profits by eliminating variability, defects and waste that undermine customer loyalty.Six Sigma can be understood/perceived at three levels:
- Metric: 3.4 Defects Per Million Opportunities. DPMO allows you to take complexity of product/process into account. Rule of thumb is to consider at least three opportunities for a physical part/component - one for form, one for fit and one for function, in absence of better considerations. Also you want to be Six Sigma in the Critical to Quality characteristics and not the whole unit/characteristics.
- Methodology: DMAIC/DFSS structured problem solving roadmap and tools.
- Philosophy: Reduce variation in your business and take customer-focused, data driven decisions.
Here's an article with more detail on defining Six Sigma: What is Six Sigma?
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Six Sigma is a rigorous and a systematic methodology that utilizes information (management by facts) and statistical analysis to measure and improve a company's operational performance, practices and systems by identifying and preventing 'defects' in manufacturing and service-related processes in order to anticipate and exceed expectations of all stakeholders to accomplish effectiveness.
Posted By: Craig Tonner
Modified By: pradeep patra
Last Modified: Sep. 3, 2003
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