1 Six Sigma-Measure Phase Measure Phase-part I • Measure phase focuses on understanding the current performance of the process and collecting any necessary data needed for analysis. It also includes assessment of the measurement system to ensure validity of measurements. • Key objective: to establish a process baseline through the development of a clear and meaningful measurement system • Objectives: Evaluate measurement system Process definition Establish the process baseline Metric definition Collect process data • Process definition • Clear definition of process under investigation • Detailed process mapping • Process map examples Introduction to Six Sigma – INDU 441/INDU 6321 Understand the process behavior 2 Six Sigma-Measure Phase • Metric definition • To define a unit of measurement that provides a way to objectively quantify a process • Examples of metrics: o Services: the percentage of orders filled accurately; the time taken to fill a customer’s order o Manufacturing: diameters of machined ball bearings; percentage of fixtures have surface defects • Measures and indicators refer to numerical information that results from measurement. In other words, they are numerical values associated with a metric. o Indicator is often used for measurements that are not a direct or exclusive measure of performance. For instance, the number of complaints or lost customers are indicators of customer dissatisfaction (which cannot be directly measured) • Types of metrics: o Discrete metrics: a countable metric such as: ▪ A dimension is either within or out of tolerance ▪ The number of errors in an invoice ▪ An order is complete or incomplete o Continuous metrics: numerical counts or proportions such as: ▪ Length, time, or weight Introduction to Six Sigma – INDU 441/INDU 6321 3 Six Sigma-Measure Phase • A systematic process is required in order to generate useful process performance measures as follows: o Identify all customers of the system and determine their requirements (CTQ) o Define the work process that provides the product or service (detailed process map) o Define the value-adding activities and (intermediate) outputs that compose the process o Develop specific performance measures or indicators for each key activity identified in previous step (critical point in the process) ▪ Performance is measured at intermediate checkpoints ▪ Key questions: what factors determine how well the process is producing according to customer requirements? o Evaluate the performance measures to ensure their usefulness • ▪ Are measurements taken at critical points where value-adding activities occur? ▪ Is it feasible to obtain the data needed for each measure? ▪ Have operational definitions for each measurement been established? Example of defining metrics for the “pizza ordering and filling process for home delivery”: Introduction to Six Sigma – INDU 441/INDU 6321 4 Six Sigma-Measure Phase • Process measures can be displayed as a KPI tree • Operational definitions are developed to provide clear description of each KPI o KPI name: a consistent terminology must be used throughout the project o What is the KPI supposed to represent o Process diagram o Detailed definition o Measurement scope • Without an operational definition, unreliable data will be collected in different ways. • Example-fault repair time KPI Introduction to Six Sigma – INDU 441/INDU 6321 5 Six Sigma-Measure Phase • Collect process data • The first step in any data collection effort is to develop operational definitions for all measures • Classification of measurements (data worlds in Six Sigma): o Attribute data (e.g., accept/reject) ▪ Statistic: percentage o Variable data ▪ Discrete data (counting things, e.g., number of defects in a sample) ▪ Continuous data (measuring something, e.g., the measurement of PH) ▪ Statistics: average, median, range, standard deviation Introduction to Six Sigma – INDU 441/INDU 6321 6 Six Sigma-Measure Phase • Two types of data collection o In-Process: data collection is integrated into the process and is recorded automatically o Manual: data collection system is additional to the process and recorded by text or typing (e.g., check sheets) ▪ Design the check sheet with a team of people who are going to use it ▪ Keep it clear, easy, and obvious to use ▪ Communicate with people why you are using the check sheet ▪ Record names, dates, serial numbers, etc. for traceability o Samples of check sheets: Introduction to Six Sigma – INDU 441/INDU 6321 7 Six Sigma-Measure Phase • Data collection plan and sampling o Several factors must be considered for data collection planning: ▪ What is the objective of the study? ▪ What type of sample should be used? ▪ What possible error might result from sampling? ▪ What will the study cost? o Sampling approaches: ▪ Simple random sampling: every item in the population has an equal probability of being selected ▪ Stratified sampling: the population is partitioned into groups, or strata, and a random sample is selected from each stratum ▪ Systematic sampling: every nth (4th, 5th, etc.) item is selected ▪ Cluster sampling: a typical group (e.g., a division of the company) is selected and a random sample is taken from within the group ▪ Judgment sampling: expert opinion is used to determine the location and characteristics of a sample group o The time framework of the study, the size and cost limitation of the sampling method, accessibility of the population, and the desired accuracy must be taken into consideration while choosing the sampling approach. Introduction to Six Sigma – INDU 441/INDU 6321 8 Six Sigma-Measure Phase o Sampling error occurs naturally and results from the fact that a sample may not always be representative of the population. o Sampling error is determined based on the sample size and the confidence level of sampling. o Sample size ▪ Consider the sample size when using x to provide a point estimate of the population mean ( ) for variable data. A 100(1 − ) percent confidence interval of is given by x z /2 / n . Thus (1 − ) probability exists that the value of the sample mean will provide a sampling error of z /2 / n or less. If we denote this sampling error by E and solve E = z /2 / n for n, we obtain the required sample size for any given value of sampling error (E) at a confidence level of 100(1 − ) precept as follows: n = ( z /2 )2 2 / E 2 ▪ A similar task is to determine the sample size for estimating a population proportion for attribute data. A point estimate of the population proportion (p) is given by the sample proportion ( p ). The standard error of the proportion is p = p (1 − p ) / n . Thus, a 100(1 − ) percent confidence interval for the population proportion is p z /2 p (1 − p ) / n . The sampling error is given by E = z /2 p(1 − p) / n . Solving the equation for n provides the following formula for the sample size: n = ( z /2 )2 p(1 − p) / E 2 • Understand the process behavior • Process capability analysis o The relationship between the natural variation and specifications is often quantified by a measure known as the process capability index o Typical questions that are asked in a process capability study: ▪ Where is the process centered? ▪ How much variability exists in the process? ▪ Is the performance relative to specifications acceptable? ▪ What factors contribute to variability? Introduction to Six Sigma – INDU 441/INDU 6321 9 Six Sigma-Measure Phase o Process capability metrics ▪ A range of metrics that measure the ability of a process to deliver the customer’s requirements (to indicate the performance of the process relative to requirements) ▪ The assessment of how well the process delivers what the customer wants ▪ Potential capability ▪ ▪ • Cp= width of the specification/width of the histogram • Reflects the potential capability of the process • Cp must be greater than 1 so that the process is called capable Capability ratio • Cr=1/ Cp • Indicates the percentage of the specification spread that is needed to contain the process range for the production process to be capable Actual capability • The process natural variability can be smaller than the specification spread while the process is still generating defects (the case where process is not centered and only one side of the specification spread must be compared to the control limits) • Cpk=Zmin/3 Introduction to Six Sigma – INDU 441/INDU 6321 10 Six Sigma-Measure Phase • Reflects the actual capability of the process. It considers only the nearest specification limit, since this is the limit which is most likely to be failed • Measures how much of the production process really conforms to the engineered specifications • Using the variable control charts Zmin = min Z L , ZU 𝑈𝑆𝐿 − 𝑋̿ 𝜎̂ 𝑋̿ − 𝐿𝑆𝐿 𝑍𝑈 = 𝑍𝐿 = 𝜎̂ 𝑅̅ 𝜎̂ = 𝑑 2 𝑠̅ 𝜎̂ = 𝑐 4 ▪ (Range chart method) (Sigma chart method) Taguchi capability metric • Cpk and Cp take into account the variations within tolerance (the variations that occur while the process mean fails to meet the specified target) • Taguchi’s approach suggests that any variation from the engineering target is a source of defect. C pm = USL − LSL 6 ˆ 2 + ( − T )2 Introduction to Six Sigma – INDU 441/INDU 6321 11 Six Sigma-Measure Phase ▪ Part per million (PPM) metric (or dpmo) PPM = PPM L + PPM U USL − PPM U = 106 [1 − ( )] ˆ LSL − PPM L = 106 ( ) ˆ o Critical to schedule (CTS) metrics (Lean metrics) ▪ Lean metrics measure the levels of waste generated by the process ▪ The elimination of waste is done through the identification of the activities that do not add value to the customer ▪ Workers capacity • The amount of time needed for one worker to produce a unit of product • Takt time is defined as the maximum amount of time that the producer is allowed to take in order to produce and deliver customer orders on time Takt time= net available production time/units requested by customer ▪ Cycle time • Total elapsed time for the process from start to completion • It does not consider the customer current orders • It only considers the capabilities of available resources Cycle time=net production time/number of units produced • ▪ Process cycle efficiency • ▪ The production process must be designed in a way that the cycle time does not exceed the takt time Is calculated by dividing the value-added time associated with a process by the total lead time of the process Process lead time • Is calculated by dividing the number of items in process by the completions per hour • Example: Introduction to Six Sigma – INDU 441/INDU 6321 12 Six Sigma-Measure Phase It takes 2 hours on average to complete each purchase order, then there are 0.5 completion per hour. If there are 10 purchase orders waiting in queue, the process lead time is 20 hours. ▪ Overall equipment effectiveness (OEE) OEE = A (Availability) x P (Performance) x Q (Quality) A = actual operating time/planned time P = net operating rate x operating speed rate Operating speed rate= specified cycle time/actual cycle time Net operating rate= actual processing time/operating time Q = acceptable output / total output • The OEE availability is calculated as the actual time the process is producing product or service divided by the amount of time that is planned for production. o Planned time excludes all scheduled shutdowns when equipment is not operational (including lunches, breaks, plant shutdowns for holidays, etc.) o The remaining portion of the planned time includes the available time for production, and the downtime. o Downtime is loss in production time due to shift changeovers, part changeovers, waiting for material, equipment failures and so on • The OEE enables us to determine how efficiently the equipment is used o It accounts for process inefficiencies due to poor quality materials, operator inefficiencies, equipment shutdowns, etc. o A 100% performance implies the process is running at maximum velocity. • The OEE quality is the percent of the total output that meets the requirement without need for any repair or rework o 100% quality means the process is producing no errors Example- based on the information summarized in the following table, find the OEE. Introduction to Six Sigma – INDU 441/INDU 6321 13 Six Sigma-Measure Phase Work hours Breaks Meeting Unexpected downtime Machine’s manual spec Actual machine performance Number of units processed Quality rate 8 30 min 15 min 35 min 1 unit per min 1.05 min per unit 405 0.97 Availability= time (operating – down time)/operating time= (8 60) − (30 + 15) − 35 400 = = 0.92 (8 60) − (30 + 15) 435 Equipment performance efficiency=net operating rate x operating speed rate Net operating rate=actual processing time/operating 1.05 405 425.25 = = 0.978 (8 60) − (30 + 15) 435 Operating speed rate=specified cycle time/actual cycle time= Equipment performance efficiency= 0.978 0.952 = 0.931 OEE= 0.978 0.952 0.97 = 0.831 Introduction to Six Sigma – INDU 441/INDU 6321 1 = 0.952 1.05 time= 14 Six Sigma-Measure Phase • Process baseline must be estimated by means of meaningful statistics in order to have a credible evidence of sustainable improvements o Example of inappropriate statistics for process baselines estimation: • Enumerative statistical study (Deming, 1975): a study in which action will be taken on the universe (the sample being studied) o ANOVA, t-test, confidence intervals o Proceed from predetermined hypothesis • Analytic statistical study (Deming, 1975): a study in which action will be taken on a process or cause-system that produced the sample being studied. The aim is to improve the process in the future o Provide operational guidelines rather than precise calculation of probability o Generate new hypothesis o Statistical process control (SPC) charts • Some appropriate analytic statistics questions: o Is the process central tendency stable over time? o Is the process dispersion stable over time? o Is the process distribution consistent over time? • If the answer to any of the above questions is no, the cause of the instability must be found Introduction to Six Sigma – INDU 441/INDU 6321 15 Six Sigma-Measure Phase • Analytic methods will be needed to validate the conclusions developed with the use of enumerative methods, to ensure their relevance to the process under study • Statistical process control (SPC) charts are used in the measure phase to define the process baseline o If the process is statistically stable (evidenced by SPC charts), the process capability and Sigma level are valid o If the process is not statistically stable, then the cause of variation must be sought o SPC charts enable the producer to determine if his production process is stable and in control o If the process is yielding products that are consistent and in a manner that makes it possible for the producer to make a prediction on future trends o If the variations in the output of the process are contained within the control limits in a random manner, then the process is stable and in control. o It does not say whether the products generated by this process meets customer expectations o Process capabilities indices are used to determine how effective the process is at meeting customer expectations • Distributions o They show the way in which the probabilities are associated with the numbers being studied o Sampling distributions are used in Six Sigma projects involving enumerative statistics ▪ The empirical distribution assigns the probability 1/n to each Xi in the sample ▪ Some sample statistics ▪ • Sample mean • Unbiased sample standard deviation • Standard error of the mean Binomial distribution Introduction to Six Sigma – INDU 441/INDU 6321 16 Six Sigma-Measure Phase • Assume that a process is producing some proportion of nonconforming units (p) (p: the number of nonconforming units in the sample by the number of items sampled). The probability of getting x defectives in sample of n units is: ❖ Example: 1% of products in a manufacturing line do not conform to specifications. Calculate the probability that in a sample of 30 units of the product, no more than 1 defective item is detected? p( x 1) = p( x = 0) + p( x = 1) ( ) ( ) = 30 (0.01)0 (0.99)30 + 30 (0.01)1 (0.99)29 0 1 30! 30! (0.01)0 (0.99)30 + (0.01)1 (0.99)29 0!30! 1!29! = 96.38% = ▪ Poisson distribution • When we are concerned with the number of non-conformances. The probability of counts of nonconformity: ❖ Example: the number of welding defects per unit in a circuit board follows a Poisson distribution with = 4 . Calculate the probability that a circuit board has more than 2 defectives. 4x e−4 p( x 2) = 1 − p( x 2) =1 − x! x =0 = 1 − (0.238) = 0.762 2 ▪ Normal distribution • Sometimes the process itself produces an approximately normal distribution, other times a normal distribution can be obtained by using averages or other mathematical transformation on data Introduction to Six Sigma – INDU 441/INDU 6321 17 Six Sigma-Measure Phase ▪ Exponential distribution • • Useful in analyzing the system reliability Statistical process control charts o Central Limit Theorem (CLT) - The basis of statistical process control tools ▪ The distribution of average values of samples drawn from any population will tend toward a normal distribution as the sample size grows without bound ▪ By this rule, averages of small samples can be used to evaluate any process using the normal distribution o Common and special causes of variation ▪ Common (chance) cause: any unknown and unavoidable random cause of variation • ▪ If the influence of any particular chance is very small, and if the number of common causes of variation is very large and relatively constant, we have a situation where variation is predictable within limits (a controlled system) Special (assignable) causes of variation: At times, the variation is caused by a source of variation that is not part of the constant system. These sources of variation are called special causes of variation (Deming) • Example: large variations related to machines, materials, operators, etc. ▪ Statistically controlled system: any system exhibiting only commoncause variation ▪ The goal of SPC is reduction or elimination of variability in the process by identification of special causes of variation o Statistical process control ▪ The use of valid analytical statistical methods to identify the existence of special causes of variation in a process ▪ The basic rule of statistical process control: variation from commoncause systems should be left to chance, but special causes of variation should be identified and eliminated Introduction to Six Sigma – INDU 441/INDU 6321 18 Six Sigma-Measure Phase ▪ We look for long-term process improvements to address commoncauses variation ▪ Variation between “control limits” in SPC charts: variation from common cause; any variability beyond control limits: special cause of variation ▪ Out-of-control situations: • At least one point plots beyond the control charts • The points behave a systematic or non-random manner • Run tests (Similar to Western Electric Handbook rules) ▪ Control charts are used in Six Sigma to monitor mean, range, and standard deviation (Sigma) ▪ The basis of control charts is the rational subgroup • Items produced under essentially the same conditions • The average, range, and Sigma are computed for each subgroup and then plotted on the control chart ▪ All control limits are set at plus and minus three standard deviations from the center line of the chart (Shewhart charts) ▪ Control chart selection decision tree Introduction to Six Sigma – INDU 441/INDU 6321 19 Six Sigma-Measure Phase ▪ Control limit equations for ranges charts ▪ Control limit equations for averages using ranges charts ˆ = R d2 ˆ = x ▪ Control limit equations for Sigma charts Introduction to Six Sigma – INDU 441/INDU 6321 20 Six Sigma-Measure Phase ▪ Control limit equations for averages using sigma charts ˆ = s c4 ˆ = x ▪ Example of average and sigma control charts Introduction to Six Sigma – INDU 441/INDU 6321 21 Six Sigma-Measure Phase Introduction to Six Sigma – INDU 441/INDU 6321 22 Six Sigma-Measure Phase ▪ Control limit equations for individual measurements (X charts) • When it is not feasible to use averages for process control • Expensive observations (destructive testing), output too homogeneous (chemical processes), etc. • Range charts (moving range charts) are applicable • Example: Introduction to Six Sigma – INDU 441/INDU 6321 23 Six Sigma-Measure Phase R=Largest in subgroup – Smallest in subgroup, where the subgroup is a consecutive pair of successive measurement ▪ Control charts for attribute data ▪ Control limit equations for proportion defective (p chart) • Analysis of p chart patterns between the control limits become extremely complicated if the sample size varies because the distribution of p varies with the sample size • Example Introduction to Six Sigma – INDU 441/INDU 6321 24 Six Sigma-Measure Phase Introduction to Six Sigma – INDU 441/INDU 6321 25 Six Sigma-Measure Phase ▪ Control limit equations for count of defective (np chart) ▪ Example Introduction to Six Sigma – INDU 441/INDU 6321 26 Six Sigma-Measure Phase ▪ Control limit equations for average occurrences-per-unit (u charts) • Can be applied to any variable where the appropriate performance measure is a count of how often a particular event occurs • Unlike p and np charts, u charts do not necessarily involve counting physical items. Rather, they involve counting of events Introduction to Six Sigma – INDU 441/INDU 6321 27 Six Sigma-Measure Phase where n is the subgroup size in units. If the subgroup size varies, the control limits will also vary. • Example Introduction to Six Sigma – INDU 441/INDU 6321 28 Six Sigma-Measure Phase ▪ Control limit equations for counts of occurrences-per-unit (c charts) Introduction to Six Sigma – INDU 441/INDU 6321 29 Six Sigma-Measure Phase ▪ Example Introduction to Six Sigma – INDU 441/INDU 6321 30 Six Sigma-Measure Phase ▪ Control chart interpretation • Probing the patterns in control charts to identify the underlying system of causes at work • Freak patterns o Causes that have a large effect but occur infrequently o Look at cause-and-effect diagram for items that meet this criteria o The key to identifying freak patterns are timelines in collecting and recording the data o Try sampling more frequently if you have difficulty to identify freak patterns • Drift patterns o The current process value is partly determined by the previous process state o Tool ware, plating bath Introduction to Six Sigma – INDU 441/INDU 6321 31 Six Sigma-Measure Phase o Whenever economically possible, the drift should be eliminated, e.g., by installing an automatic chemical dispenser for the plating bath, or make automatic compensating adjustments to correct the tool wear o When drift elimination is not possible, the control charts can be modified in one of the two ways: • ▪ Makes the slop of the center line and control limits match the natural process drift ▪ Plot deviations from the natural drift Cycles o Due to the nature of the process (e.g., hour of the day, day of the week, etc.) o Caused by modifying the process inputs or methods according to a regular schedule o The action to eliminate cycles ▪ The control chart can be adjusted by plotting the control measure against a variable base ▪ If a day-of-the-week cycle exists for shipping errors because of the workload, you can plot errors per 100 orders instead of error per day Introduction to Six Sigma – INDU 441/INDU 6321 32 Six Sigma-Measure Phase • Run tests (special causes) o If the process is stable, the distribution of subgroup averages will be approximately normal o We can analyze the patterns on the control charts to see if they might be attributed to a special cause of variation Introduction to Six Sigma – INDU 441/INDU 6321 33 Six Sigma-Measure Phase o The patterns on the control charts can be used as an aid in trouble shouting • Estimating process baseline using process capability analysis o Collect samples from 25 or more subgroups of consecutively produced units o Plot the results on the appropriate control chart. If all groups are in statistical control go to step 3. Otherwise, attempt to identify special cause of variation by observing the conditions or time periods under which they occur o Using the control limits from the previous step. Once you are satisfied that sufficient time has passed for most special causes to have been identified and eliminated, got to step 4. o Estimate process capability. The initial error rates estimated in the “Define” phase can then be revised by the right values. o Estimate process Sigma level based on the dpmo metric Introduction to Six Sigma – INDU 441/INDU 6321 34 Six Sigma-Measure Phase Introduction to Six Sigma – INDU 441/INDU 6321 35 Six Sigma-Measure Phase Introduction to Six Sigma – INDU 441/INDU 6321 36 Six Sigma-Measure Phase Introduction to Six Sigma – INDU 441/INDU 6321 37 Six Sigma-Measure Phase Introduction to Six Sigma – INDU 441/INDU 6321