Understanding 6 Sigma

nullnullUnderstanding 6s (Six Sigma)nullWhat is 6s activity? Why should we do 6s? How to Launch 6s ? Common termContents6snull 1. What are the statistics ? 2. Solution of the Practical Problem 3. What is the 6sconcept ? 4. 6s as the Business Strategy 5. 6s Application 6. 6s Activity Process 7. Comparing other tools 8. 6s Philosophy 6sWhat is Six Sigma Activity ?null1. What are the statistics ?◆ Population & Sample SamplePopulation N ＝ 1,000Measure 10 samples (Spec. : 100±4)○ You may say “ This Population is Good because all the sample’s data are located between LSL & USL. BUT, If you estimate the defect rate using statistical analysis, this population has the probability of 2.8% defects per unit. Then this is - we call - “An epidemic” quality defect level. ○ Measuring defect rate on process through an expanding statistical concept, we can use measuring process capability.ⅩⅩⅩⅩⅩⅩⅩⅩⅩⅩUSL (Upper Spec Limit)LSL (Lower Spec Limit)96979899100104101102103Total inspection is impossible !Statistical variables (mean, variance) estimate population 6sWhat is Six Sigma Activity ?nullBasic Statistics - IContents1. Sample & Population. 2. Types of data 3. Measures of central tendency. - Mean, Median, Mode. 4. Measures of dispersion - Standard dev, Variance, Range 5. Graphs - Histogram, Boxplot, Dotplot 6. Correlationnull1. Population & samplePopulationSampleCharacteristic of population : ParameterCharacteristic of sample : StatisticsLet us consider a example: Suppose we want to find out average height of males of Delhi. Since we can not measure the height of each male of Delhi, we will have to select a sample (say 1000 nos) of males to predict the average height of entire male population (1crore) of Delhi.From the given example, we conclude the following: Population : Nos of entire males of Delhi. Parameter : Average height of males of Delhi. Sample : 1000 males of Delhi Statistics : Average height of 1000 males of Delhi. Thus statistics is used to predict parameter of population. null1. Shake it well2. Take one spoon3. Make Decision4. Action☞ No bias☞ Sampling☞ Based on StatisticsHow to collect data ?The origin of a sampling surveyIn the picture shown over here , a woman is preparing tea. Before serving tea, she is testing the taste of tea. For this purpose, she has to shake the tea well . For sample, she is tasting one spoon. Based on the taste of this spoon she is going to make decision, whether tea is good for serving or not. The above example shows that since we cannot measure the whole population, the sample must be selected at random, so that statistic reflects or predicts parameter exactly. null2. Data TypesData in any form can be of two types : 1) Discrete types 2) Continuous types Discrete data : A data which is based on information such as pass / fail . In discrete data you cannot be more specific.Tolerance : Infinity Ex1. Do you love me ? The answer can only be yes or no . ie the data is discrete Ex2. AC Gas leakage can be either OK or NOK type. Continous data - The data which uses a measurement scale of length, time or any scale. The continous data contains more information than discrete data. Defined Tolerance Ex1. How much do you love me? The answer can be anything , for eg on a scale of 1-10 you can say 1 if you don’t love me much, but you can give 10 if you are deeply in love with me . This is an example of continuous data. Ex2. Height, Length , weight, diameter etc. . null3.1 MEAN The mean (also called the average) is a measure of where the center of your distribution lies. It is simply the sum of all observations divided by the number of observations. Eg For the rainfall data in 11 major cities of the country, the mean is: (2 + 3 + 10 + 5 + 4 + 4 + 3 + 3 + 1 + 2 + 3) / 11 = 3.636. The mean is strongly influenced by extreme values. Even though most cities (7 out of 11) had 3 mm or less of rainfall, the mean is close to 4. The extreme value of 10 mm with rainfall for Mumbai is affecting the mean quite a bit. Without this observation, the mean would be exactly 3. On the other hand, if you include Mumbai with 30 mm of rain instead of 10 in the calculations, the mean would be 5.455, a value that is greater than all but one observation! .3. Measures of Central Tendency 3.2 MEDIAN The median (also called the 2nd quartile or 50th percentile) is the middle observation in the data set. It is determined by ranking the data and finding observation number [N + 1] / 2. In the rainfall data set, there are11 (non-missing) observations. Thus, the median is the value of the 6th highest (or 6th lowest) observation, which is 3: 1 2 2 3 3 3 3 4 4 5 10 If there are an even number of observations, the median is extrapolated as the value midway between that of observation numbers N / 2 and [N / 2] + 1. The median is less sensitive to extreme values than the mean.For example, the median of this data set would be 3 even if there were 30 mm with rainfall in Mumbai instead of 10. Therefore, the median is often used instead of the mean when data contain outliers, or are skewed. NB: Always arrange the given data in ascending or descending ordernull 3.4 MODE: The mode is the value in an array of data that is repeated the most. The mode is also a measure of central tendency but is rarely used,as in some cases , chances are there that a single unrepresentative value is also the one that is repeated most often. For eg in the data of the rainfall in the 11 cities here the most repeated value is 3 so the mode is 3, but if our data had been 0, 2 ,5 ,7 ,15 ,1 ,4 ,6 ,8 ,15 Then our mode would have been 15.null4.1 STANDARD DEVIATION (STDEV): The standard deviation (StDev) is a measure of how far the observations in a sample deviate from the mean. It is analogous to an average distance (independent of direction) from the mean. The standard deviation is the most commonly reported measure of dispersion. It also serves as an estimate of the dispersion in the broader population from which a sample is taken.4. Measures of DispersionLike the mean, the standard deviation is very sensitive to extreme values. The large value of 10 mm of rainfall for Mumbai increases the standard deviation quite a bit. Without this value, the standard deviation would be 1.155 instead of 2.378. Conversely, if Mumbai had 30 mm of rain, the standard deviation would be 8.210The standard deviation for the rainfall data is 2.378mm . This tells you that on average, the values in the data set tend to differ from the mean by ± 2.378. If the data are normally distributed, then the standard deviation and mean can be used to determine what proportion of the observations fall within any given range of values. For example, 95% of the values in a normal distribution fall within ± 1.96 standard deviations of the mean. 2 =  (x-x) /( n) 2= Standard deviation = item or observation = population mean = total no. of items in the populationnxxConsider example of rainfall given on page 1.2In given case we have, n=11 2222222222  (x-x) =56.54 2So  = 56.54/11 = 2.378null4.2 STANDARD ERROR OF THE MEAN (SE MEAN): The standard error of the mean (SE Mean) is not often used as a descriptive statistic, but it is important in hypothesis testing. It is an estimate of the dispersion that you would observe in the distribution of sample means, if you continued to take samples of the same size from the population. The standard error of the mean is the standard deviation divided by N4.3 RANGE: The range is defined as the difference between the highest and the lowest observed values, in a given array of data. It is very easy to understand but has very limited usefulness as a measure of dispersion. For eg: for the given rain data - the highest value is 10 & the lowest value is 1, so the range is 10-1 =9 4.4 VARIANCE : The variance of a population signifies the deviation of the data values from the mean value, it is symbolized by . To calculate the population variance we have the following formula: = (x-) / N 2= population variance = item or observation = population mean = total no. of items in the populationx 2null4.5 FIRST AND THIRD QUARTILES (Q1 AND Q3) The first quartile (Q1, also called the 25th percentile) is the highest value for the lowest 25% of the observations. For the rainfall data, Q1 is 2. The third quartile (Q3, also called the 75th percentile) is the lowest value for the highest 25% of the observations. For the rainfall data, Q3 is 4. Q1 and Q3 are often used to calculate the inter quartile range (IQR), which is another statistic used to describe dispersion. The IQR is the range of the middle 50% of the values and is calculated by the formula Q3 - Q1. The IQR for the rainfall data set is 4 - 2 = 2. The IQR is relatively insensitive to extreme values. For example, the IQR would remain the same even if there were 30 mm with rain in Mumbai instead of 10. null5. GraphsIn the histogram of the rainfall data, notice the single extreme value in the interval from 9.5 to 10.5. If not for this outlier, the distribution would be perfectly symmetric and fairly normal.5.1 HISTOGRAM OF DATA A histogram displays data that have been summarized into intervals. It can be used to assess the symmetry or skewness of the data. To construct a histogram, the horizontal axis is divided into equal intervals as shown below , and a vertical bar is drawn at each interval to represent its frequency (the number of values that fall within the interval). 5.2 DOTPLOT OF DATA Use the dotplot to examine the dispersion and concentration of the data. Each circle represents one or more observations. In the dotplot of the rainfall data set, notice that several of the dots represent more than one observation.null5.3 BOXPLOT OF DATA Boxplots summarize information about the shape, dispersion, and center of your data. They can also help you spot outliers. Box plot is as shown below : . A. The left edge of the box represents first quartile (Q1), while the right edge represents third quartile (Q3). Thus the box portion of the plot represents the interquartile range (IQR), or the middle 50% of the obs . B. The line drawn through the box represents the median of the data. C The lines extending from the box are called whiskers. The whiskers extend outward to indicate the lowest and highest values in the data set (excluding outliers). D Extreme values, or outliers, are represented by asterisks (*). A value is considered an outlier if it is outside of the box (greater than Q3 or less than Q1) by more than 1.5 times the IQR. .Q1Q3MediannullUse the boxplot to assess the symmetry of the data: If the data are fairly symmetric, the median line will be roughly in the middle of the IQR box and the whiskers will be similar in length. If the data are skewed, the median may not fall in the middle of the IQR box, and one whisker will likely be noticeably longer than the other. In the boxplot of the rainfall data the median is centered in the IQR box,and the whiskers are the same length. This indicates that except for the outlier (asterisk), the data are symmetric. This is a good indication that the outlier may not be from the same population as the rest of the sample data.null6.1 CORRELATION A Pearson correlation coefficient measures the extent to which two continuous variables are linearly related. Suppose you have a sample of candies and you want to know if the temperature of your production facility is associated with changes in the thickness of the chocolate coating. Or, you may have a sample of golf balls and want to determine if differences in their diameter are associated with differences in elasticity. There are a few points to keep in mind when performing or interpreting a correctional analysis: Correlation coefficients only measure linear relationships. A meaningful nonlinear relationship can exist even if the correlation coefficient is 0. It is never appropriate to conclude that changes in one variable cause changes in another based on a correlation. Only properly controlled experiments allow you to determine if a relationship is causal. The correlation coefficient is very sensitive to extreme values. A single value that is very different from the others in a data set can change the value of the coefficient a great deal. 6. CORRELATIONThe correlation coefficient can range in value from -1 to +1, and tells you two things about the linear relationships between two variables: Strength — The larger the absolute value of the coefficient, the stronger the linear relationship between the variables. An absolute value of one indicates a perfect linear relationship, and a value of zero indicates the absence of a linear relationship. Whether an intermediate value is interpreted as a weak, moderate,or strong correlation depends on your objectives and requirements. Direction — The sign of the coefficient indicates the direction of the relationship. If both variables tend to increase or decrease together, the coefficient is positive. If one variable tends to increase as the other decreases, the coefficient is negative.nullFollowing graphs tell about the strength & direction of relationship between 2 variables r > 0.8 means a correlation exists between the 2 variables.For the two variables x and y, r = where and Sx are the sample mean and standard deviation for the first sample, and and sy are the sample mean and standard deviation for the second sample. ( X - X ) (Y - Y) Sx S y (n -1 )Formula for rnullSuppose , we want to find out , whether any correlation exists between height(ht) & weight(wt) of individuals .We measure ht & wt of 7 individuals & get data as shown below :Pearson correlation of Height and Weight = 0.979 (as derived from the formula for ‘r’ given on the previous page P-Value = 0.000The correlation coefficient value of 0.979 indicates that there exists a strong correlation between height & wt of individual. The p-value tells you if the correlation coefficient is significantly different from 0. (A coefficient of 0 indicates there is no linear relationship): ·If the p-value is less than or equal to your  level, then you can conclude that the correlation is different from zero, which means there exists a correlation between 2 variables. If the p-value is greater than your  level, then you can not conclude that the correlation is different from zero, which means there does not exist a correlation between 2 variables. Generally , value of  is chosen as 0.05 , therefore in the given case, since p value is 0, we can conclude that there definitely exists a correlation between ht & wt.nullμUSLLSLTμUSLLSLTUSLLSLTμPrecise but not AccurateAccurate but not PreciseShifting to Target & Reducing VariationShift to TargetReducing Variation2. Solution of the Practical ProblemObject of 6s is Shift to Target Reducing variation6sWhat is Six Sigma Activity ?null6s Quality means that area of the estimated normal distribution is located between USL&LSL with 6 s. In that case area of the outlier spec. (In other words estimated defects) is just 3.4 PPM.* s : Standard Deviation Statistic index measures how much is data apart from target value3.4ppmTargetUSLLSL+ 6 s- 6 sσ+ 3 s- 3 sσ6.68%3. What is the 6s concept ?Statistical Definition of 6s3s6s6sWhat is Six Sigma Activity ?null6 3.4 5 233 4 6,210 3 66,807 2 308,537s PPM 1 misspelled word in all of the books contained in a small library $340 indebtedness per $100 millions assets 1.8 minutes per year 1.5 misspelled words per page in a book $6.7 millions indebtedness per $100 millions assets 24 days per year6s as the Business Strategy3. What is the 6s concept ?6sWhat is Six Sigma Activity ?null In all Design, Manufacturing, and SVC processes Applying for 6s statistic Tools & Processes To find factors causing defects Acting the Analysis and Improvement Through the Defect Reduction, Increase Yield & Total Customer Satisfaction Management Innovation Tool contributes to Management OutputAchieving 3.4 PPM (3.4 Defects Per Million)What is 6s activity?PPM : Parts per Million6s as the Activity3. What is the 6s concept ?6sWhat is Six Sigma Activity ?null1. It is a statistical measurement.2. It is a improvement tool. It tells us how good our products, services, and processes really are. 6σ helps us to establish our course and gauge our pace in the race for total customer satisfaction. It’s a full packaged tool applying to design, manufacturing, sales& SVC.3. It is a business strategy. It can greatly help us gain a competitive edge As you improve the Sigma rating of a process, the product quality improves and costs go down. Naturally, the customer becomes more satisfied as a result.4. It is a philosophy. This is one of working smarter, not harder. Also it makes fewer and fewer mistakes in everything we do.4. 6s as the Business Strategy6sWhat is Six Sigma Activity ?null Ground Fruit Logic and IntuitionWall of 3s Low Hanging Fruit Seven Basic Tools Bulk of Fruit Process Characterization and Optimization Fruit-bearing 6s Sweet Fruit Design for ManufacturabilityWall of 4sWall of 5sHarvesting the Fruit of 6s4. 6s as the Business Strategy6sWhat is Six Sigma Activity ?null5. 6s Application Selecting CTQ to meet customer needs Decision reasonable Tolerance Guarantee of the CTQ’s capability analysis Improvement serious problem using S/W Real Time Monitoring system → CTQ Control system Improvement cycle time and accuracy Cost ImprovementGuarantee for the Design completion in developing stageQuality assurance in manufacturing stageMaximizing for sales & SVC6s is a tool that applies to all business systems - Design, Manufacturing, Sales and SVC R&D 6sManufacturing 6sDe- signSales &SVCMfg.6sTransaction 6sDesignMfg.Sales& SVC6sWhat is Six Sigma Activity ?nullIdentify Customer-Driven CTQ (Critical to Quality) CharacteristicsIdentify Key Processes that cause Defects in a CTQ CharacteristicsFor Each Product or Process CTQ Measure, Analyze, Improve, & Control6s is a rigorous analytical process for solving problem!!!6. 6s Activity Process1. Who are your customers? - Internal / External 2. What do you provide your customers? 3. What is critical to quality for your customers?1. What are your internal processes for providing your product or service CTQ’s to your customers? 2. Where do defects occur in these processes?D Practical Problem Measurement System Yield CalculationProcess Mapping s Calculation Benchmarking Hypothesis Testing Cause & Effect Diagram DOE Brainstorming Action Workout Techniques Piloting Control Mechanism Control Chart ProceduresMAIC6s Activity Process(manufacturing & Transaction)*** * CTQ(Critical To Quality) : Your customers feel that characteristic of product, service or process is critical. ** D : Define6sWhat is Six Sigma Activity ?nullExample of development process apply R&D 6sR&D 6sKick -OffEvaluation meeting for present conditionEvaluation meeting for basic conceptEvaluation meeting for planning confirmE/S drawing confirmCusto- mer Needs SurveyQFD S-1Spare CTQ Selec- tionSimilar process Data gatheringZ Value of CTQ값 AnalysisMeeting for CTQ Check Z Value optimize, Design improveQFD S-2Design FMEAProcess FMEADevelopment ProcessE/S makingDevelopment drawing confirmIncome PartsE/S Quality meetingP/L MakingP/L