Six Sigma- Define & Measure_Sudhanshu.pdf

Six Sigma- Define & Measure_Sudhanshu.pdf

• 1.
  SIX SIGMA –DEFINE & MEASURE Prepared By- Sudhanshu Mittal Manf. Executive ITC Foods – Chocolates, Haridwar
• 2.
  What is sixsigma ? • It is a comprehensive and flexible system for achieving, sustaining and maximising business success. • 6 sigma methodology involves - 1. Listening to the customer needs 2. Use of facts through data collection and statistical analysis 3. Managing, improving and re-engineering production and business processes. • The 2 key aspects of a six sigma organisation are – customer satisfaction and business excellence. • Bill Smith is known as the Father of Six sigma for his 1987 Motorola Six Sigma technology that stated that defect rate cannot be more than 3.4 parts per million opportunities. Business Excellence Cost reduction Increase in productivity Growth of market share Customer retention Cycle time reduction Defects reduction NPD
• 3.
  Sigma capability • Itis defined as the indicator of how well the process is performing. • Denoted as z value defined as Z= 𝑥−𝜇 𝜎 Where mu is the process mean or average and sigma is the spread / distribution about the mean. • This measures the capability of the process to produce defect free outputs. • Greater the value of z, he better the process is.
• 4.
  6 MAIN THEMES OF SIXSIGMA Focus on the customer Data and fact driven management Process focus Pro-active management Boundary less collaboration Driver for perfection SIX MAIN THEMES OF A SIX SIGMA ORGANISATION
• 5.
  ➢Focus on thecustomer : ❖Requirements of the customer are assessed. ❖Performance of the organization products is then evaluated. ❖Unmet needs are addressed through product or process change. ❖Customers get the highest priority. ➢Data & fact driven management : ❖Focus on taking measurements – what info is needed and what is the source ? ❖No room for decisions based on opinions / assumptions / feelings. ❖Data analysis using appropriate tools and info generated must be used to make decisions for improvements. ❖This is a closed loop system where measurements from the output are taken to take corrective actions to improve subsequent process. ❖Very important hallmark of six sigma system.
• 6.
  ➢Process focus : ❖Properunderstanding of actual process that takes place on shop floor by mapping it on charts or flow diagrams involving a series of steps. ❖This helps to ensure in depth quality requirements and controls and helps to make full analysis for control and improvement. ➢Pro-active management : ❖Responsible for setting goals and clear priorities ❖Frequent reviews ❖Implement changes to prevent errors from reaching the customer. ❖Top management focus and support.
• 7.
  ➢Boundary less collaboration: ❖Cross – functional teams with good communication to avoid delays, redesigns, rework, or wastage of resources. ❖Good teamwork is needed to support one another. ❖Common goal ❖Savings potential ➢Driver for perfection : ❖Diligent efforts ❖Repeated iterations ❖Only goal : not more than 3.4 defects per million opportunities (DPMO)
• 8.
  Six sigma roadmapand Important phases of a process improvement cycle DMAIC Define Measure Analyse Improve Control
• 9.
  DEFINE…. • Project leaderis responsible for setting targets, listening to the customer requirements & identifying the critical to quality (CTQ) parameters. • Gives the most important equation : y = f(x) where y are the parameters critical to quality and indicate customer expectations and x are the influencers/ variables that can influence the critical to quality y’s. • Standards need to be established • Understanding how the customer requirements change with the passage of time (VOC) • Project goals and supporting team both need to be laid. Teams involved Role Top management To establish vision/ goals, allocate resources Trained belts To provide technical support Project team Design project charter, timeline, cost estimations Project sponsors / Champions Line owners, select project and execute, provide resources, remove barriers Financial representatives Derive savings, project benefits, ROI
• 10.
  MEASURE… ANALYZE… • Mapthe complete process using flow diagrams for detailed understanding. • Identify CTQ parameters that need to be measured. • Establish sampling plan and data collection sources. • Data collection & ensure data is completely relevant and hygienic • Use statistical analysis for analysing random variables. • Determine the current process performance and capability against theVOC.  Statistical data analysis  Cause & Effect  Correlation & Regression
• 11.
  IMPROVE… CONTROL… • Toestablish and validate statistical hypothesis • Eliminate root causes of the problem • Optimize process by implementing counter measures. • Reduce process variability.  Establish monitoring and control plan  Statistical Process Control  Control charts  Standardize documentation  Employee training  Scope of Appreciation / Applause  Helps to maintain the gains over the long horizon.
• 12.
  DEFINE
• 13.
  What is aDEFECT ?? • Defined as the occurrence at any process step when the actual outcome of the process does not match with the expected outcome (means expected outcome has been defined well in advance). • Any flaw/ error/ discrepancy. • Leads to a defective product. Impact of a defect – • Internal failure costs involved : material, labour, energy, utilities cost • Defect may reach the consumer, external failure costs involved : warranty cost, liability cost, recall cost, loss of reputation, drop in sales, loss of market. • More defect generation reduces line productivity and results in decreased capacity utilisation.This ultimately affects the market delivery of the product in time. Catering high demands at peak seasons becomes difficult in some cases. • Early detection of the defects can result in identification and rectification of the root cause more easily and on time. • Giving liberty in terms of defect %, creates culture that some % defect is OK that can be allowed to reach market. However, need to develop culture to encourage workers to bring attention to problems.
• 14.
  YIELD- • Fraction defective/ defect rate (p) = defective units produced / total units in • Yield = 1 – p with no rework/ retest / scrap • Process yield with n such steps each having a step yield of p = 1 − 𝑝 𝑛 • Process yield for 3 steps each with a step yield of a, b, c respectively = a X b X c • Example 1: 3 step process with fraction defective at each step = 1% P = 0.01 Yield = 1 – p = 0.99 Process yield = (0.99)^3 = 97.02 % • Example 2: 10 step process with p = 10% 1 – p = 0.9 Process yield = (0.9)^10 = 34.86 %
• 15.
  • Example 3:10 step process with p = 1% 1-p = 1-0.01 = 0.99 Process yield = (0.99)^10 = 90.43 % • Example 4: 10,000 step process with p = 1% Process yield = (1-0.01)^10000 = 0 • Example 5: 10,000 step process with p = 0.621% Process yield = (1-0.00621)^10000 = 0 • Example 6: 10,000 step process with p = 3.4 X 10^(-4)% 1-p = 0.9999966 Process yield = (0.9999966)^10000 = 96.65 % Which clearly justifies that low fraction defectives (p) are very necessary to ensure positive yield for complex products. Implication : Even at such low defect rate, 3.35 % sales loss to BMW manufacturer (for ex.) which is unaffordable.
• 16.
  PPM – • Partsper million is used to quantify very very small volumes. • PPM = no of defective units / million • Example 1: 99.379% yield at one step, what is the ppm ? 1-p = 0.99379 So, p = 0.00621 = 6210 ppm • Example 2: 96.65 % yield for a process with 10,000 steps, what is the ppm defective ? 1-p = (0.9665)^(1/10000) = 0.999997 P = 3.4 X 10^(-6) P = 3.4 ppm
• 17.
  What is aDEFECTIVE PRODUCT ?? • Defective product is the only one that when a decision has been made that the item is not acceptable. • The decision is based on either one / accumulation of multiple factors making the characteristics of the product unacceptable. • DPU is defined as the average number of defects per unit of product. • DPU = number of defects / number of units • DPMO is defined as defect per million opportunities • DPMO = DPU X 1 million /Total opportunities of defect in 1 unit • However, ppm speaks only in terms of defective units in a million population.
• 18.
  “It is apreconception that quality is all about testing.”
• 19.
  QUALITY • Dr. JosephM. Juran defined quality as fitness for use and product meeting / exceeding customer requirements. • Consumer needs should be in the form of some measurable characteristics with predefined limits of variability. • According to Dr. A. Blanton Godfrey, quality is relative, with consumer focus simply on value seeing it as a ratio of quality of price and only when we offer more value than the competitors. • Dimensions of quality : Product performance, reliability, durability, serviceability, sustainability • Identify theVOC • Product designer will take these needs. • Select features of the product and create design. • Select target and limits of variation. • Produce product at a reasonable cost. • Feature CTQ measurable characteristics. • Therefore, identifying theVOC and translating the voice into critical to quality parameters and evaluating/ improving the current performance of CTQs are fundamental aspects of quality management. QUALITY MANAGEMENT SYSTEM (QMS)
• 20.
  Total Quality cost(TQC) • TQC refers to how the organisation is financially performing in delivering products that satisfy its consumers. • It includes the financial losses due to not producing quality products and the economic gains due to delivery of quality products.
• 21.
  Prevention cost •Training sessions •Processcontrol •Improvement projects •Quality system development Appraisal cost •Material inspection and testing •Product inspection and testing •Equipment integrity Internal failure cost •Scrap, rework, retest •Resources and yield loss •Manpower •Energy and utilities cost •Production downtime External failure cost •Product recall •Warranty cost •Loss of market shares •Loss of reputation •Loss in sales •Price reduction
• 22.
  Understanding customer expectations: KANO model theory • Differentiate between “design quality” (identify theVOC – what the customer wants and that becomes the design specs, product features, and translateVOC to CTQ measurable parameters ) and the “conformance quality” (that matches the design specs without any discrepancies). • Understand theVOC and categorize and prioritize as all the attributes of product/ service are not equal in the eyes of the consumer.
• 23.
  • A –is the basic quality required to ensure the market of the product.This is not generally mentioned by the customers but they do mention it only when such attributes are absent from the product. Absent : unhappy Fully implemented : OK, not happy • B – Here the satisfaction is directly proportional to the performance. Linear relationship • C – Delighters, Excitements, WOW – creation of excitement which is different from expectations. Helps in building brands. Characteristic Satisfaction Unhappy Absent Fully implemented Satisfied Basic/ expected quality Performance OR 1- D quality Excitement A B C
• 24.
  • D –Indifferent quality Those attributes to which no importance is attached by the consumer. No satisfaction & No dis-satisfaction • E – Reverse quality Those resulting in dis-satisfaction and is mainly due to the fact that not all customers are alike. **It is through this theory that a Kano questionnaire is prepared to listen to the consumer needs. An evaluation table is prepared and the attributes are then classified after the survey.
• 25.
  EVALUATION TABLE
• 26.
  Define a problem….. •It is an undesirable deviation of the required attribute in the output of a process (product/ service). • This attribute may be any – quality characteristic, availability (quantity/ time) , consumption of resources. • It is a gap between the current and desirable state. • Ex : Burnt cookie produced is the problem of the process. However, its actual cause may be high baking temperature which is a part of process input. • Therefore, problem is always in the output while the cause of the problem lies in the process input. • We need to “define” the problem so that it can be improved well in time and we exceed customer expectations.
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  MEASURE
• 28.
  Probability & Statistics ▪Probability is the chance of an event happening when an experiment is carried out. ▪ It is used to infer what we observe if we take the measurement of our population. ▪ Statistics is used to infer what the model of the population is as it provides a means of describing the population with variability and methods of estimating the population quality from samples. ▪ Measurements are done on samples and the statistical data generated is used to infer the population characteristics / parameters. ▪ Population : system under study ▪ Sample: a subset of population which has been chosen in such a way that each item has an equal chance of being included (random sample)
• 29.
  Qualitative/ Attribute based Normal OR Differential Ex.Colour, nationality, religion Ordinal Ex. Ranking scale (poor, average, good, excellent) Quantitative/ Measurement based Measure-able Ex. Length, width, diameter, purity, temperature Types Of Sample Data
• 30.
  Descriptive & InferentialStatistics • Descriptive statistics : - Using empirical methods to describe the population. - Taking data from a population, arranging it and summarizing it to get useful information. - Does not allow to make conclusions beyond the data we have analysed. - Tools used: ❖Frequency distributionOR Histogram ❖Cumulative frequency distribution ❖Box &Whisker Plot ❖Calculated parameters to measure location and dispersion • Inferential Statistics : When the model of the population is not known, statistics can be used to infer what the model of the population is.This is called inferential statistics which is just the estimation of parameters and testing a statistical hypothesis.We use samples that are representative of the population (not completely may be) and make estimations/ generalizations about the population with the help of estimators. Minimum variance unbiased estimators (MVUB) such as x bar and s square are generally used to estimate mu and sigma square.
• 31.
  1. Histogram • Toolto describe the variability in the population within the possible range of values. • Conclusions from a histogram – 1. Where on x-axis is the centre point located around which the population is distributed. 2. Variation in the data 3. Variability is in acceptable level or not in case specification limits are laid 4. To identify problems in case the graph depicts a bimodal distribution. • Cumulative frequency distribution helps to estimate what part of the population is less than or equal to the given value of x.
• 32.
  2. Box &Whiskerplot • A graph that gives us a good indication of how the values in data are spread out. • A box and a whisker diagram is a standard way of displaying distribution of data based on a five number summary – Min, First quartile, Median,Third quartile, Max. • Indication of data symmetry and skewness • Helps to identify outliers
• 33.
  3. Calculated parameters •To measure location : 1. Mean / Average : centre point 2. Median : 50th percentile 3. Mode : most frequent data point • To measure dispersion : 1. SD : to measure the process variability from mean 2. Range : Max – Min 3. Variance
• 34.
  Sample Statistics -Terminology ❑Average/Mean (x bar) : Centre point around which the population is distributed. ҧ 𝑥 = ෌𝑥𝑖 𝑛 ❑Standard deviation (s) : amount of variability/ dispersion about the mean 𝑠 = ෌ ҧ 𝑥−𝑥𝑖 2 𝑛−1 = sq. root of variance ❑Variance (s2) : weighted average of squared deviations of variable data points from mean. Indicates dispersion around the mean. ❑x bar & s are sample statistical data while mu and sigma are known as population parameters.
• 35.
  Lets give athought… Q1. How are quality and variability inter-related ? The answer is simple !!All industrial processes have some variability and no process is an ideal process. Higher SD value implies a more variable process which leads to a poor quality product and more waste generation. Q2. Enlist some commonly used statistical methods in quality engineering. 1) Control charts 2) Sampling plans 3) Designed experiments 4) Regression and correlation analysis 5) Reliability engineering 6) Tolerancing
• 36.
  Probability Distribution • Randomvariable (X) : variable that assumes values from the outcomes of a random experiment. It assumes only real values & set of all possible values is known as the range space. • 2 types: 1. Discrete random variable : that assumes finite no of values Ex. Number of heads in 3 tosses of a fair coin, number when a die is thrown. Described using a probability mass function (pmf) 2. Continuous random variable : that assumes infinitely many values OR values in an interval Ex.Amount of snowfall, weight of sugar bags Described using a probability density function (pdf)
• 37.
  Discrete and Non-Continuous Distribution ▪Case : a fair coin is tossed 3 times and random variable may be defined as the number of tails that we get. ▪ p(x) >= 0 for all values of x ▪ 𝛴𝑝 𝑥 = 1 ▪ P(t) = p(X = t) X 0 1 2 3 P(X) 1/8 3/8 3/8 1/8 0 0 0 1/7 1/5 1/4 2/7 1/3 2/5 0 1 2 3 Probability distribution for no. of tails in 3 tosses Binomial Distribution Poisson Distribution
• 38.
  1. Binomial Distribution •Random variable X has a Binomial distribution with parameters n & p if probability distribution is given by P(x) = 𝑛𝐶𝑥 𝑝𝑥 1 − 𝑝 𝑛−𝑥 where x = 0,1,2……n And 𝑛𝐶𝑥 = 𝑛! 𝑥! 𝑛−𝑥 ! where x <= n • We use Bi(n , p) notation to indicate x has a binomial distribution. • x is the number of successes in ‘n’ different independent trials with p being the probability of success and 1-p is the failure probability in one trial 0<= p <= 1 • Such a trial is called as a Bernoulli trial where a random experiment is carried out with exactly 2 possible outcomes either a success or a failure and probability of success is the same every-time the experiment is conducted.
• 39.
  Ex. Getting 9heads when a fair coin is tossed 10 times • When a fair coin is tossed (random experiment), only 2 possible outcomes – H &T. • In our case, success is defined as getting a head. p(H) = 0.5 and this is same every- time. So, this is an example of Bernoulli trial = Bi (10,0.5) • N = 10, x = 9, p = 0.5, So, P (9 successes out of 10 trials ) = p(9) = 10C9 (0.5)^9 (1-0.5)^(10-9) = 10 X (0.5)^10 = 0.0098 = 0.98% < 1% that we get 9 heads while tossing a fair coin 10 times.
• 40.
  Points to remember… •Binomial distribution curve has a bell shape. • Binomial distribution never goes below zero. • As the number of trials (n) increase, the distribution moves away from zero. • As p increases, there is a shift away from zero in the curve. • Bernoulli distribution is valid only for independent trials which means that the lot size >> sample size . Independence of the trials will be lost if the sample is picked from a small lot without replacement. • Weighted average (𝜇) = 𝛴 x ∗ 𝑛𝐶𝑥 𝑝𝑥 1 − 𝑝 𝑛−𝑥 = np • Variance (𝜎2) = 𝛴 𝑥 − 𝜇 2 𝑛𝐶𝑥 𝑝𝑥 1 − 𝑝 𝑛−𝑥 = np(1-p)
• 41.
  2. Poisson Distribution •If we have an exact probability of an event happening (x out of n times), then random variable is expressed using a Binomial distribution. • However, in case we have an “average/ mean probability” of an event happening per unit time, then the random variable is said to have Poisson distribution given by the mass function p(x) = ⅇ−𝜆𝜆𝑥 𝑥! here x = 0,1,2,3….. • We use Po (𝜆) notation to indicate x has a poisson distribution. • Ex : 1. no of pinholes in a galvanised sheet 2. no of blemishes in a fabricated shirt 3. no of accidents per month in a factory • Poisson distribution has a bell curve that moves away from zero and becomes more symmetric as the value of lambda increases. • Poisson distribution never goes below zero. • Poisson approaches to binomial distribution when n approaches infinity and p approaches zero. • Weighted average (𝜇) =Variance (𝜎2) = 𝜆
• 42.
  Example on PoissonDistribution • Statement :Typist makes an average 3 mistakes per page.What is the probability that the page he types now will have not more than one mistake ? • Because of average 3 number of mistakes, the above statement symbolizes poisson distribution for the random variable. • X = no of mistakes per page, X = Po (3) with 𝜆 = 3 • Required probability p(X<= 1) = p(0)+ p(1) = ⅇ−𝜆𝜆𝑥 𝑥! = ⅇ−3 30 0! + 31 1! = (2.718)^(-3) * (4) = 0.1992 = 19.92 %
• 43.
  Continuous Distribution Model •Described by a probability density function (pdf) Ex. f(x) = {0.01 x , 0=< x <= 10 0.01x (20-x) , 10=< x <= 20 0 , otherwise } Therefore, ✓ f(x) >= 0 for all values of x ✓ 𝛴𝑓 𝑥 = 1 ✓p(a <= x <= b) = ‫׬‬ 𝑎 𝑏 𝑓 𝑥 𝑑𝑥 Normal Distribution Exponential Distribution Weibull Distribution T- Distribution Chi- squared distribution F- Distribution Types
• 44.
  Continuous Distribution Models 1.Uniform distribution : probability is same for all values of x 2. Exponential distribution : f(x) decreases exponentially with increase in value of x f(x) f(x) x x
• 45.
  3. Normal /Gaussian Distribution • pdf is given by f(x) = 1 𝜎 2𝜋 ⅇ − 1 2 𝑥−𝜇 𝜎 2 then x is said to have normal distribution written as X = Nu (𝜇, 𝜎2 ) • Characteristics of a normal distribution curve : 1. It is asymptotic wrt x-axis. 2. Symmetric wrt vertical line x = 𝜇 3. Maxima of the curve occurs at x = 𝜇 4. 2 points of inflexion occur at x =𝜎 • Area under the curve = ‫׬‬ 𝑎 𝑏 𝑓 𝑥 𝑑𝑥 = 1 • Mean of the distribution = ‫׬‬ 𝑎 𝑏 𝑥 𝑓 𝑥 𝑑𝑥 = 𝜇 • Variance of the distribution = ‫׬‬ 𝑎 𝑏 𝑥 − 𝜇 2 𝑓 𝑥 𝑑𝑥 = 𝜎2 f(x) x 𝜇 𝜎
• 46.
  Normal Probability Distribution •pdf is given by f(x) = 1 𝜎 2𝜋 ⅇ − 1 2 𝑥−𝜇 𝜎 2 and random variable X = Nu (𝜇, 𝜎2 ) where mu is the mean and sigma square is the variance. • As distance from 𝜇 increases, the probability decreases. • As a thumb rule, remember – 1. 2 points of inflexion occur at +/- 1 𝜎 2. +/- 1 𝜎 from mean implies 68.27 % of population 3. +/- 2 𝜎 from mean implies 95.44 % of population 4. +/- 3 𝜎 from mean implies 99.73 % of population f(x) x 𝜇 𝜎
• 47.
  Cumulative distribution function •CDF gives us the probability that random variable takes values starting from the lowest possible value upto and including the given value of x. • If X is a discrete random variable defined by the probability mass function p(x) then CDF = F(x) = 𝛴𝑝 𝑥 drawn as a step function. • If X is a continuous random variable defined by probability density function f(x) then CDF = F(x) = ‫׬‬ 𝑎 𝑏 𝑓 𝑥 𝑑𝑥 where a is the smallest possible value and b is the limit upto which probability estimation is required. • It is drawn as a continuous curve which is monotonically increasing in nature. 1 1 x F(x) x F(x)
• 48.
  Standard Normal Distribution •If X is any random variable that is normally distributed with 𝜇 = 0 and 𝜎2 = 1, it is called a Standard normal variable denoted by z. • Probability densify function (PDF) = Ѱ(z) = 1 2𝜋 ⅇ− 1 2 𝑧 2 • Cumulative distribution function (CDF) = F(z) = ‫׬‬ −∞ 𝑧 Ѱ(t) dt • Table for CDF for various values of z is known as the NormalTable which can be read to get the various values of z. **Relationship between Normal Distribution and Standard Normal Distribution If X is normally distributed such that X = Nu (𝜇, 𝜎2 ) then 𝑥−𝜇 𝜎 = Nu (0,1) which implies z = Nu (0,1) 0 z Ѱ(z) 1
• 49.
  Example 1.
• 50.
  Central LimitTheorem • Sincepopulation measurements are not possible, so samples that are representative of the population are taken and a parameter X is monitored.The average of X is calculated daily and all these values will have a normal distribution, a mean value and a variance. So, ҧ 𝑥 is s.t.b random variable that is normally distributed. • According to Central limit theorem, if samples of size “n” are repeatedly taken from a population that is normally distributed and the averages are computed for parameter X then the averages themselves are random variable which are normally distributed with mean equal to mean of parent population and variance smaller than population variance depending upon the sample size. • If X = Nu (𝜇, 𝜎2 ) and samples of size “n” are taken then averages of sample ҧ 𝑥𝑠 = 𝑁𝑢(𝜇, 𝜎2 /n) is also normally distributed with mean = population mean and variance = population variance/ sample size (n)
• 51.
  What if thepopulation is not normal ? Let the population have any distribution with finite mean 𝜇 and a finite variance. According to Central limit theorem, sample average will be normally distributed if the sample size is large enough with mean of 𝜇 and variance = 𝜎2/n ҧ 𝑥𝑛 = 𝑁𝑢(𝜇, 𝜎2/n) when n tends to infinity. Example 2.
• 53.
  What is abusiness process ?? • A repeatable, coherent, sequence of activities with a clearly defined input, with a certain material or non- material achievement, output, and internal/ external customers. • Flow of process consumes time and resources which is often associated with repetitive tasks. • Business process in operations typically refers to volume production of goods/services in a sequence of activities performed by a set of specialized pre-defined resources. • Advantages of process view – 1. Allows to have a view of activities as a cross –functional flow instead of individual activities done in isolated silo/ area. 2. Map the activities needed to complete a value- added step. 3. Focus on the customer to meet his expectations (the meet the value addition)
• 54.
  SIPOC • Managing thewhole process rather than the individual activities allows “end to end process improvement.” • SIPOC is a tool that lists the activities/ components that occur in a process. • It is a common tool in all 6 sigma projects. • Why SIPOC ? 1. SIPOC gives high level picture (from supplier to customer) of value added steps in the process. 2. It provides the basis for first discussion of what could be the influencing CTQ parameters. Supplier Input Process Output Customer
• 55.
  Process Mapping • Itis defined as identifying all the steps, the inputs, output, controls, resources used in each step, responsibilities for each step and then mapping them as they occur. • It is a visual tool to share knowledge and build consensus among the team members. • Why? –To understand it fully so that it can be better analysed, improved, managed and controlled. • Who is involved? – All the stakeholders who are involved in daily process execution. Start/ End Process Step Decision Transportation Storage Inspection Delay Standard symbols used in making PFD
• 56.
  ❑Work on paper ❑Scopeof the process and level of detail ❑Just get started : don’t aim for perfect accuracy from the beginning • Process should be walked and verified • Editing to be done before it is saved finally ❑Inputs from shop floor operators/ process owners are mandatory • Hidden Factory • GEMBA ❑Don’t miss inspection and measurement steps ❑Include rework loops, scrap procedures. ❑Information flow ❑Financial flow can also be included PROCESS MAPPING PRACTICE
• 58.
  • What isa Measurement System ? A scheme or system including the instruments, equipments, standards, procedures, software, operators, that are required to produce a measurement do exist. • What is Measurement System Analysis (MSA) ? MSA is the technique of ensuring that the measuring instruments of adequate capability are available for taking measurements on the product characteristics and process variables. • Why is MSA important in six sigma organisation ? Six sigma is a data driven methodology, which means that data measurement is the foundation of any decision making right from defining the problem to measuring process capability to final analyse and control (throughout DMAIC) So, the quality of data is paramount and poor quality data is not recommended as it will not yield any good results in the DMAIC process improvement cycle. • When to carry out MSA ? Before collecting data from the process. Some terms for reference – 1. Gage : any device that is used to obtain measurement specifically for devices used on shop floor 2. Standard : Known reference value with limits of uncertainty.
• 59.
  Measured value Observed variation (variability) True variability/ Inherent Short term process variation Long term process variation Measurement variation/ error Errorin sampling Measurement reliability True value So, to quantify the variability, it is important to closely look at the measurement error. Measurement should be done carefully to keep the measurement error low. With number of experiments going on, multiple measurements need to be taken using the measurement system and evaluate statistical properties to see at the data reliability. Statistical properties include average of the distribution (mu), variability (sigma square) and standard deviation (SD). Valid for small time periods or variation between the samples due to machine, operator Valid for longer time periods or variation between the samples due to special causes (shift change, weather change, machine degradation)
• 60.
  Bias • Average value –Truevalue Accuracy • It is opposite to bias • Lower is the bias, greater is the accuracy Variability • The spread in the data about the mean • Factors- Repeatability & Reproducibility Precision • It is opposite to variability. • Lower is the variability, higher is the precision Linearity • Refers to how bias remains the same over the range of possible values of measurement Stability • Refers to how precision of instrument remains consistent over time Resolution • Refers to the smallest division of unit that the instrument is designed to measure. x 𝜇 𝐵𝑖𝑎𝑠 𝜇 x Variability decreased implies high precision Properties of good instrument- 1. Near zero bias 2. No linearity problem 3. High precision 4. Stability 5. Adequate resolution
• 61.
  Gage R&R study •It is the study of measurement variability occurring due to repeatability and reproducibility. • Repeatability (𝜎𝑒) / EquipmentVariation (EV)- occurs from instrumental hardware that prevents instrument from giving identical readings when measuring same unit of product repeatedly by the same operator. • Reproducibility (𝜎o)/ AppraiserVariation (AV) – occurs when the same unit of product is measured repeatedly by different operators. • GRR/ Gage error (𝜎g) = 𝜎𝑒 2 + 𝜎0 2 • ProcessVariation (𝜎p) = PV = inherent variation of the process • Overall variation =TV (𝜎 overall) = 𝜎𝑝 2 + 𝜎𝑔 2 OR 𝑇𝑣2 = 𝐺𝑅𝑅2 + 𝑃𝑣2 • As a thumb rule, 𝜎𝑔 𝜎𝑃 < 10% is acceptable and measurement is OK. • If this is greater than 10% but less than 30%, it “can” be accepted on the basis of cost. However, value >30% is not OK.
• 62.
  How to carryout a G R&R study ? 1. Study in detail and make sure that the equipment is calibrated and in good condition and so are the samples. Appraisers should be aware of measurement criteria and inspection methods through effective training. 2. Samples should be chosen which cover the spread. 3. Data collection table should be developed with randomized samples between trials and appraisers. 4. Appraisers perform measurements including multiple trials by everyone. Measurements done should be descriptive, selective and objective. 5. Data should be shifted to tabular sheet- G R&R 6. Perform calculations to find out the average and R double bar. Use statistical formulae thereafter.
• 63.
  Sampling • To takemeasurements, it is very important to select samples that are representative of the population.This is necessary to save time and cost as measurements on entire population are not possible. • To design a sampling plan, we prioritize the input process parameters as well as the o/p to be measured. • Goal of measurement needs to be documented. • Along with the sample size, frequency, data type, hypothesis should be identified. • Sampling size regulators – 1. If effect is weak, sampling size should be larger. 2. If variability is high, sampling size should be larger. 3. If higher confidence/ precision is needed, sampling size should be larger. • Quality sampling can either be done from a population where in sample is taken from a fixed group (no time element) or from a process where in sample is chosen from a flow of items (time element exists).
• 64.
  Quality sampling Random sampling Simple random –fixed number of elements is chosen such that each element has an equal chance of being selected Stratified – population is divided into different strata and fixed amount will be randomly selected from each strata Systematic sampling Without subgroups – every nth element will be measured With subgroups- fixed no of elements (n) will be measured in regular time interval (m). POPULATION PROCESS A B C D
• 66.
  Process capability Index •Process capability Index (Cp) is a statistical tool to measure the ability of a process to produce the output in the designed specification limits. • 𝐶𝑝 = 𝑣𝑜𝑖𝑐𝑒 𝑜𝑓 𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟 𝑣𝑜𝑖𝑐𝑒 𝑜𝑓 𝑝𝑟𝑜𝑐𝑒𝑠𝑠 • Cp = 𝑈𝑆𝐿 −𝐿𝑆𝐿 6𝑠𝑖𝑔𝑚𝑎 • Cp < 1 , incapable process • Cp > 1, process is called a capable process • For a process with 6 sigma quality , Cp = 2 • As the value of Cp increases, the process variability decreases provided the designed specification limits remain constant. • Therefore, we can conclude that greater is the value of Cp, better is the quality of process or product.
• 67.
  ProcessWith Mean Shift Cpvalue speaks only of the process variability / form of the process but does not tell anything about the target value. Cp is nowhere connected with the process mean/ mean shift. Therefore, Cp does not change as the process centre changes. CONS OF USING CP…
• 68.
  Process capability Centeringindex (Cpk) • Cpk = distance between process centre and nearest specification / 3 sigma • Cpk = min 𝜇−𝐿𝑆𝐿 3𝜎 , 𝑈𝑆𝐿−𝜇 3𝜎 • Cpk speaks of the process in terms of both- form/ variability and location/ process centering. So, it is a superior index. • Cpk < 1 , implies poor centering and the process is NC • Cpk = 1, border line case • Cpk > 1, process conforms to specifications • Cpk = 0, then the mean of process lies on one specification limit. • Cp >= Cpk and both should be greater than 1. • If Cp = Cpk then process is perfectly centred.
• 70.
  CASE 1 :SW > PW CASE 2 : SW>PW Process Shift = 1𝛔
• 71.
  CASE 3 :SW = PW CASE 4 : SW = PW, Process Shift = 1𝜎
• 72.
  CASE 5 :SW < PW CASE 6: SW < PW , Process shift= 1𝛔
• 73.
  Six Sigma Capability •When Cp=1, USL-LSL =6𝜎 ,p = 99.73% and as sigma decreases, we can accommodate upto 12𝜎 b/w LSL and USL. • According to definition, process has a 𝟔𝝈 capability if defects produced are less than 3.4 defects per million opportunities. • P(X occurs b/w +/- 6𝜎 )= 99.9999998 % which implies 0.002 ppm fall outside the spec. • However, most processes do not have their mean exactly at the target value/ centre of specification because the process tends to drift off centre. • According to Motorola six sigma technology, process could be off as far as 1.5 𝜎 from the specification centre or target such that it has nothing out of spec on lower side and having 3.4 parts per million out of spec on higher side. • Implies 99.99966% parts within the spec. Defect rate – 3.4 ppm. Cp = 12𝜎/ 6𝜎 = 2 • Similarly, a +/- 3𝜎 process with 1.5𝜎 mean shift, 93.32 % of our product lies in the specification, corresponds to 66800 ppm out of spec, Cp = 1.
• 74.
  Six Sigma Capability usingdiscrete data Key Assessments 1. Confirm of a stable process (control charts) 2. Measurement of attribute data and record the no. of defects 3. Calculate DPU, DPMO. 4. Convert to sigma capability 5. Check if the customer requirement is met ? Example
• 75.
  Tolerancing • Is theprocess of determining the allowable variations in product characteristics around the selected target so that the product can be produced at a competitive cost while meeting the requirements of the customer. • For producer, having a tighter tolerance/ lower variability means an increased production cost. • Also, tolerancing is an economic issue for both the customer and the producer.The gain for one may result in a loss for the other. • Tolerance depends on the manufacturing process – machine, people, environment, method. • Tolerancing should be conducted after the final process is selected. • In general, tolerance is calculated as +/- 3 SD spread (ො 𝜇 + 3 ො 𝜎) where ො 𝜇 & ො 𝜎 are calculated using n > 50.This reflects the current capability of a process of meeting the current conditions.These limits are called NaturalTolerance Limits (NTLs).
• 76.
  Tolerancing Models • Traditionaltolerancing – fitness of the product is good only as long as characteristic is at target or within the LSL & USL. Losses from characteristics away from target are zero according to this model. • Taguchi Loss function – says that traditional tolerancing is not true. He says, you have zero loss when you are exactly at the target within the characteristic. Loss will increase (in parabolic fashion) as we move away from the target. LSL USL Target Taguchi Loss function
• 77.
  AssemblyTolerancing • Use RootSum of Squares (RSS) formula- Suppose L1, L2, L3 are the measurements of independent components and assembly given by L = L1 + L2+ L3 ……. Ln LetT1,T2,T3 be the tolerances of individual measurements, then tolerance of assembly T = 𝑇1 2 + 𝑇2 2 + 𝑇3 2 … 𝑇𝑛 2 • X1 – Nu (𝜇1, 𝜎1 2 ) 𝑎𝑛𝑑 X2 – Nu (𝜇2, 𝜎2 2 ) then X1 + X2 = Nu (𝜇1+ 𝜇2, 𝜎1 2 + 𝜎2 2 ) X1 – X2 = Nu (𝜇1 - 𝜇2, 𝜎1 2 + 𝜎2 2 )
• 78.
  FMEA • A techniqueto investigate all possible weakness in a product/ process design and prioritize the weakness in terms of their potential to cause the product failure. • 2 types- Design FMEA (DFMEA) and Process FMEA (PFMEA) • PFMEA should be performed for – 1. Any new process 2. Current process planned to produce a new product 3. For investigating root cause for defective produced in an existing process. • How to carry out an FMEA ? 1. Identify possible modes of failure 2. Analyse the possible causes 3. Identify the effects on consumer 4. Rank in terms of Severity, Occurrence, Detection on a scale of 1 (good) to 10 (bad). 5. Calculate Risk Priority Number, RPN = S X O X D 6. Larger the RPN, higher is the risk of failure. Effect Cause Severity : S Occurrence: O Detection: D
• 80.
  Capability index Cpm •Cpm defined by Chan, Chang & Spiring in 1988 is defined by Cpm = 𝑈𝑆𝐿 −𝐿𝑆𝐿 6𝜎′ Where 𝜎′ = ෌ 𝑥𝑖−𝑇 2 𝑛 andT is the target. • Cp/ Cpk measures the variability about the mean/ process centre. However, Cpm measures the variability about the target. • Cpm index followsTaguchi loss function philosophy. Maximising Cpm index value follows amounts to minimising the loss function. • Cpm max occurs at the target. • Cpm = 𝑐𝑝 1+𝑣2 where 𝑣 = 𝑇−𝜇 𝜎 • If process is centred, Cp = Cpk = Cpm • If process is not centred, Cp> Cpk & Cpm • Cpm will never be negative. • Cpk can be negative if process centre is outside spec • Cpk & Cp assume target is at the centre of spec. • Cpm does not use specification limits, but uses specified value of target. • When target is not at center, Cpk and Cpm behave differently. Points to Remember…..