Process Capability 3 Sigma Process Capability 93 32

Process Capability 3 Sigma Process Capability 93. 32% Historical Standard 4 Sigma Process Capability 99. 38% Current Standard 6 Sigma Process Capability 99. 99966% World-Class

Process Capability What We're Going To Talk About Concept of Process Capability (Short-Term and Long-Term) Improvement Process Types Methodology Variation of Limits Capability Index Process Capability Indices (Normal Distribution Data) Process Performance Indices (Normal Distribution Data) MINITAB Five Software capability data analysis out-put key assumptions Steps to study process capability & Process Controls

Process Understanding Quality planning & analysis Mc. Graw-Hill 4 th edition

Process Capability What is process? Process consists of a combination of Machine, Method, Material, Man, Environment and Gauge measurement (optional) engaged in production. (i. e. 4 Ms and 1 E) There is a need to separately identify the related variables and quantify the effect of them into the measurement. (e. g, temp. setting 40 -50 C, work instructions, material tensile strength, calipers) Capability of the process refers to an ability, based on test performance results , to achieve the desired specification of the process. (e. g. Specs =4± 0. 3 mm) Quality planning & analysis Mc. Graw-Hill 4 th edition

Improvement Methodology Quality planning & analysis Mc. Graw-Hill 4 th edition

Improvement methodology Controllable Inputs ( machine setting, flow rate, feed quantity, cutting speed, feed rate) X 1 X 2 X 3 Output Input Variables: Characteristics: Raw materials, Output Variables (mm , psi, colouring) components, The Process Y 1, Y 2, etc. equipment, tooling, Operation N 1 N 2 N 3 methods, etc. Uncontrollable Inputs ( humidity, temperature , skills, wear & tear) [KPIV] Centering –The Process Is On Target Key Process Input Variables On target, minimum process variation Spread Variation Reduce

Process Capability Concept of Process Capability! In quality planning, it is ensured that the process should be stable and capable to produce parts that meets the specifications, customer’s requirements. Process capability is a concept that provides a quantified prediction of process effectiveness and adequacy Quantitative prediction ability resulted in a widespread adoption of the concept as a major element of quality planning. It is the measurement of variation on the product turned out by a process. This a machine accuracy study.

Process Capability Overview Key point : Every process has inputs: Man, Method, Material, Machine, Measurement (i. e. 5 Ms) and Environment (1 E) These variables combined to give an output (i. e. Customer’s requirement. ) By controlling the key inputs the output can achieve a more stable process with lesser variation and that is what the customers demand every time.

Why Process Capability Study Process capability provides a basic understanding for the production personnel on how the process behaves in relative to the process specifications. This gives an initial feel on how variability can affect the process and gives us some measurement metrics for quantifying that variability. Such studies provide information on what the process could do under its best operating conditions, by making improvement to the process to aim for its desired target.

Process Variation Process variation is the differences among individual measurement or units produced by a process Types of variation in a manufacturing process (1) Within the unit-(Positional variation) e. g. readings taken on the diameter at various positions along the shaft. (2) Between units-(Cyclical variation) e. g. readings taken on different shafts diameters. (3) Time to time- (Temporal variation) e. g. readings taken by operators working on different shifts (i. e. Day, afternoon and night shifts) (4) Measurement error- readings taken on some characteristics by different operators (i. e reproducibility) with the same measuring equipment (i. e. repeatability) on the same identified parts.

Understanding of Process Variation l l l Variation exists in everywhere even the best machine cannot make every unit exactly the same. In many processes, nonconforming product can be produced due to excessive variability cause by human errors. (e. g. missing parts, wrong information , processing errors, inaccurate gauges, tool wear) measuring instruments). Improved process capability becomes a necessity due to; • Design changes for improvement. • Costs reduction on material. • Customers demand on better quality products All of this leads to the need for tighter control of tolerances with lower variation. This means the ability to operate within tight specification limits, without producing defects becomes a competitive advantage.

Causes of Variation 1. Natural cause/ Common Cause of variation Due to the cumulative effect of some unavoidable causes. e. g. wear and tear of a cutting tool due to long usage A process operating within natural or chance variation is said to be “in statistical control”. (i. e. all measurement readings are within the control limits of the control chart). Assignable causes have been eliminated. Y axis= shows the quality characteristic X axis= shows the number of samples

Examples on natural causes Natural causes * Vibration in the machine during running * Ambient temperature and humidity of the working environment * Normal wear and tear of machine parts due to prolong usage * Shifting of machine settings in a process * Computer response time. * Different human response to a traffic light system Reduction of common causes * Change in process technology by the owner of the process. * Introduce Poka Yoke ( Error avoidance) system in the processes. to prevent operator mistakes.

Types of Variation 2. Special or Assignable causes Examples (a) Incorrect setting adjustment on machine (b) Operators not following instructions (c) Defective or substandard raw material (d) Broken part due to fatique (e) Equipment malfunction (f) Wrong procedures adopted by operators (g) Poor product design (h) No maintenance on machines (i) Lack of understanding on operating procedures (j) Poor working conditions, e. g. poor lighting, noisy, dirty and non ventilation

Types of Variation An upward trend with the presence of assignable causes of variation look as follows.

Types of Variation Figure below shows both common cause and special cause variation A: Points dispersed away from target with some lying beyond control limits C: Points shifting away from target out of UCL B: Points located beyong UCL

Process Capability Process capability is the natural reproducibility of a process’s output. It measures how well the process is currently behaving with respect to the output specifications. It refers to the uniformity of the process Capability is often thought of in terms of the proportion of output that will be within product specification tolerances. The frequencies of defectives produced can be measured: percentage (%) (b) parts per million (ppm) (c) parts per billion (ppb) (a)

Process Capability Process capability studies can: 1) Indicate the consistency of the process output in terms of indices i. e. Cp , Cpk 2) Indicate the degree to which the output meets specification i. e. ppm , % rejection 3) Comparison with other process for improvement Specification Limits vs Process capability: 1) Process is highly capable i. e Cpk > 1. 33 2) Process is marginally capable i. e Cpk 1. 00 (Just meet specifications). 3) Process is not capable i. e Cpk < 1. 00 Refer note book…for diagram…

Process Capability Stable vs Unstable Processes A stable (i. e. “in control”) process is one in which the key process output and finished product properties show no signs of assignable causes. An unstable (i. e. “out of control”) process has assignable (i. e special) causes present.

Process Capability Control Chart and Control Limits The control chart is the tool used to evaluate whether a process is or is not in a state of statistical control. The control limits (i. e. UCL & LCL) represent the variation due to common cause. No points are beyond the control limits. Control Chart COMMON CAUSE UCL CL LCL 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Run Order Control Limits - often called “voice of the process” and used to identify special causes of variation.

Process Capability Specification Limits and Capable Processes Specification Limits – provided by the customer (referred to “voice of the customer”) are used to determine if the product meets a customer requirement. Usually given as LSL and/or USL. (e. g 4. 00± 0. 05 mm). A capable process is a stable process that demonstrates the ability to meet customer requirements. The process has to be reviewed from time to check for changes in stability and capability. When we refer to capability indices, we're comparing the process spread against the specification tolerance. Cp = ( USL-LSL) / ( 6 ) For stability, we were comparing the process average drifting towards the control limits in the average chart.

Process Capability Abnormal variation due to assignable sources Out of control Mean Normal variation due to chance LCL Abnormal variation due to assignable sources 0 1 2 3 4 5 6 UCL 7 8 9 10 11 12 13 14 15 Sample number If sample readings remained within the control limits, the process is considered as acceptable otherwise the process is “OUT OF CONTROL”

Three types of limits 1. Specification limits (LSL and USL) These limits are created by design engineering in response to customer requirements to specify the manufacturing tolerance for a product’s characteristics. e. g. 4. 2 mm (LSL) to 4. 8 mm (USL) 2. Process limits (LPL and UPL) These limits are used to measure the variation of a process. These are the 6 sigma limits of the measured characteristics. i. e. ± 3

Three types of limits 3. Control limits (LCL and UCL) These limits are computed from the measurements of the samples taken from the process. It measures the ± 3 from the center of the process. Refer note book…for diagram…

Process capability computation This requires knowledge of the process average and standard deviation. These values are usually calculated based on the data collected from manufacturing process. using a statistical software or a calculator.

Standard deviation The standard deviation measures the spread of the data about the mean value. It is useful for : 1. Comparison of data sets which have different quality characteristics. e. g. psi , cm, kg etc. ± 1 covers 68. 26% of the normal curve from µ ± 2 covers 95. 45% of the normal curve from µ ± 3 covers 99. 73% of the normal curve from µ 2. To check the consistency of the process e. g. (A data set) : 15, 15, 14, 16. µ = 15 , =0. 577 (B data set) : 2, 7, 14, 22, 30. µ = 15 , =9. 200 B data set has a higher value. A data set has a low value and is consistent and better.

Standard deviation equation for an entire population: There are 100 parts produced by machine. In statistical terms this means we have a population of 100.

Standard deviation Equation used to estimate the population standard deviation where data is taken from a sample set. The number of readings or the number of values can be 8, 10, 12, 18, 20……. .

Standard Deviation Calculation Case Study: (20 mins) 1. Find the standard deviation of the following data set: 4, 9, 11, 12, 17, 5, 8, 12, 14 2. Estimate the standard deviation of the population.

Understanding of the Process capability indices Definition of the capability indices It is an index which measures how close a process is running to its specification limits. (i. e. USL & LSL). The larger the index, the less likely the process will be outside the specification limits. . The capability of a process: Cp is defined as the ratio of the Specification Tolerance over the actual process spread. (6 ) Cpk is defined as the ratio of the distance from the process center to the nearest specifications limits divided by (3 )

Measurement of Process Capability Three Measures of process capability Three common types of indexes used in manufacturing processes 1. Cp and Cpk, Used for measurement of process capability, the minimum requirement is Cp & Cpk 1. 33 for the process to be capable. 2. Pp and Ppk Used as an indicator for process performance, the minimum requirement is Pp & Ppk. 1. 67 3. Cpm Used for measurement of a process where the data set has a non normal distribution with a target setting on the process.

Interpretation of Indices Process capability and process performance indices Cp = Process Capability. A simple and straightforward indicator of process capability. Cpk = Process Capability Index. Adjustment of Cp for the effect of non-centered distribution. Cpk is an index (a simple number) which measures how close a process is running to its specification limits, relative to the natural variability of the process. Example : A person may be performing with minimum variation, but he can be away from his target towards one of the specification limit, which indicates lower Cpk, whereas Cp will be high. On the other hand, a person may be on average exactly at the target, but the variation in performance is high. In such case also Cpk will be lower, but Cp will be high. Cpk will be higher only when you are meeting the target consistently with minimum variation.

Interpretation of Indices Process capability and process performance indices Cp and Cpk are capability indices which addressed both short and long term process capability. Short term implies the duration of investigation is limited. e. g. using an operator and a batch of raw material for the study. Pp and Ppk are process performance indices which addressed long-term process performance for serial production which takes longer time and resources to monitor the process. Cpm addressed the reduction of deviation by the process mean from a target value. These indices are applicable to the asymmetrical specification interval e. g 4. 00 + 0. 3 mm - 0. 2 mm

Process Capability Indices Two common measures of process capability 1) Potential Capability Cp An estimate is obtained of what the process can do under certain conditions, i. e. , variability under short run and defined conditions for a process in a state of statistical control. The Cp index estimates the potential process capability when both specification limits are available. 2) Process Capability Cpk = Min {Cpu , Cpl } An estimate of process capability provides an insight of what the process is doing over a series of production run. A state of statistical is assumed. The Cpk is applicable for computation for single and double sided specification limits. Increasing the value of Cpk requires a reset of the process average back to the center of the specification and reduction in the process variation (i. e. standard deviation ). [Additional Reading Material]

Potential Capability Calculation Potential Capability Index (Cp) The Cp index assesses whether the actual process spread (i. e. 6 ) of a manufacturing process is within the specification limits. Cp Specification Tolerance = ---------------- = Actual Process Spread USL- LSL -------6 This index is appropriate for the process cannot be centered between the specification limits e. g. tool wear off , liquid concentration depletion Refer note book…for diagram…

Relationship between Process Variability and Specification Width

• Three possible ranges for Cp – Cp = 1, as in Fig. (a), process variability just meets specifications – Cp ≤ 1, as in Fig. (b), process not capable of producing within specifications – Cp ≥ 1, as in Fig. (c), process exceeds minimal specifications • One shortcoming, Cp assumes that the process is centered on the specification range • Cp=Cpk when process is centered © Wiley 2010

Relation of Cp to Rejection Rate A Cp index of 1. 0 has indicated that a process is judged to be “capable”, i. e. if the process mean (µ) is centered within the specification tolerance, 0. 27% of parts produced shall be rejected. Cp Reject Rate 1. 00 0. 270% 1. 33 0. 007% 1. 5 6. 8 ppm 2. 00 ppb Refer note book…for diagram…

Understanding of Process Capability Index (Cpk) The Cpk index (i. e. min {cpl, cpu}) relates the deviation between process mean and the nearest specification limit. It shall be used for the process within statistical control. The data used for Cpk calculation should be obtained from the Average and range control charts. A negative Cpk indicates the quality characteristic measured is out of specification LSL USL Cpl Cpu µ Refer note book…for diagram…

Single Sided Specification Some manufacturing processes specifications are one sided. Example: 1. Purity of a product made from a chemical process requirement could be 98% concentration, i. e. LSL = 98% 2. Process specification could be stated such as “No more than 0. 3 mm runout on a shaft is allowed”. i. e. USL = 0. 3 mm. The process capability can be applied to such cases by defining the following two equations. Refer note book…for diagram…

Single Sided Specification Process with Lower Specs Limit (LSL) Cp. L = m - LSL 3 Process with Upper Specification Limits (USL) Cp. U = = USL - m 3 R-bar is obtained from range chart and d 2 is a constant taken d 2 from the constant table Refer note book…for diagram…

Double Sided Specification Process with both LSL & USL Cpk = Minimum{ Cp. U, Cp. L } Cpk = Minimum { USL-µ , ----3 µ - LSL } -----3 Process mean = µ Standard deviation = (calculated from R-bar / d 2 constant ) Upper Specs Limit = USL Lower Specs Limit = LSL

Relation of Cpk with Rejection Rate. Cpk Reject rate 1. 0 0. 13 -0. 27% 1. 1 0. 05 -0. 10% 1. 2 0. 02 -0. 03% 1. 3 48. 1 -96. 2 ppm 1. 4 13. 4 -26. 7 ppm 1. 5 3. 4 -6. 8 ppm 1. 6 794 -1589 ppb 1. 7 170 -340 ppb 1. 8 33 -67 ppb 1. 9 6 -12 ppb 2. 0 1 -2 ppb Comment: Higher Cpk values yield lower fall out/reject rates and, as a result, are preferable

Cpk Interpretation Cpk < 1 – process is not capable (not acceptable) Cpk = 1 to 1. 5 – process is capable Cpk > 1. 5 – process is highly capable For industries (e. g. Automotive ) requirement Cpk 1. 33 to be considered as process capability acceptable

Cpk Interpretation Cpk = negative number Cpk = zero Cpk = between 0 and 1 Cpk = 1 Cpk > 1 LCL Mean UCL

Process Performance Indices Process performance is usually measured by Ppk, which relates the long term capability of a process to meet process specifications. The estimated Ppk is defined as Pp Specification Tolerance = ---------------- = Total Process Spread where S = { ( x 2 ) - ( x ) 2 / n } ] [ n-1 ] USL- LSL -------6 s

Comparison between Ppk and Cpk values For Cp and Cpk computation , the standard deviation ( ) is based on the average ranges of subgroups of the data, standard deviations of moving ranges, obtained from the control charts. This “within-subgroup” process variation can be considerably smaller than the overall standard deviation (s) estimate used in Ppk computation, especially when there are long-term trends in the data.

Examples on Process Variation in SPC

Interpretation on Process Variation Referring to Figure 18. 14 above The figure shows four stages of process variation within the specification limits and the corrective actions to be taken when situation arises. Note In all situations , the average of the process has not drifted from the midpoint of the specification limits. There is a significant reduction in variation of the process spread which shows the process has improved from each of these stages.

Computer Software Application MINITAB Software Capability Analysis

Process Capability of thickness coat (ppm)

Process Capability of thickness coat (% rej. ) Before Process Improvement

Process Capability of thickness coat (% rej. ) After process Improvement by process centering

Process Capability of coating thickness (% rej. ) After process Improvement by reducing process variation.

Five key assumptions on Capability Indices Process stability: Statistical validity of the manufacturing process requires a statistically stable process with no shift or drift. (2) Normal distribution of the quality characteristic being measured. Normality is required to draw statistical inference about the sample or population. (3) Sufficient data ( min 125) is necessary to minimize the sampling error for the capability index. (1)

Five key assumptions continue Lewis(1991) provides a table of 95 % lower confidence limits for values of Cp and Cpk (4) Representative of samples must be random (5) Independence of measurements. Successive measurements can not be correlated.

Process Stability Analysis A process is stable if the process average of the measured quality characteristic does not drift overtime. This is nomally shown in the average control chart. Stable process UCL Nominal LCL Unstable process with process average drifting away from nominal UCL Nominal LCL Refer note book…for diagram…

Process Capability Steps 1. Develop a process flow including inputs, 2. 3. process steps, and output quality characteristics Identify critical parameters which are measurable for study e. g. parameters shown on the drawing specification i. e. volume, length, width and height, etc. Data collection by defining clearly the resolution of each data to be collected. (i. e. # of sig. Decimal required. e. g. 2 or 3 decimal points). The quantity o f data required. (i. e. 125 values min. ).

Process Capability Steps 4. Ensure the measuring gauge has been calibrated and has a resolution of 10 X the parameter to be measured 5. Establish control by selecting the appropriate personnel, equipment and material to be used for the study. 6. Record analyze the data collected using a statistical software 7. Ensure the part characteristics to be measured is in the middle of the specification prior to production of parts.

Process Capability Steps 8. Process data is normally distributed with a minimum sample size of 125 pcs with data collected in sequence. 9. Analyze source of variation from the average and range charts to find the process factors that affect the process mean and spread (Std. dev. ) 10. Establish process monitoring: Average chart to evaluate the stability and range chart to evaluate capability of the process. 11. Calculate Cp, Cpk before and after process improvement

Process Controls verification 1. List all corrective actions intended to detect and eliminate the failure causes. (operator certification, prev. maintenance) 2. Implement the corrective actions required and track the effectiveness of these actions on the failures for a month of continuous production. 3. If the actions are effective, document them into a procedure for process control. e. g. control plan 4. If not effective, additional measures are required. i. e. poka yoke, design changes etc.

Some Additional Explanations

Some Additional Explanations (cont’d)

Thank you

RESOURCES OF THE PRESENTATION: Websites 1 http: //www. asq. org/ American Society for Quality 2 http: //www. asq-software. org/ Software Division of the American Society for Quality 3 http: //www. sixsigmaforum. com/ Six Sigma Forum established by the American Society for Quality (ASQ) 4 http: //www. isixsigma. com/ A Web portal devoted to Six Sigma programs. 5 http: //www. qualitydigest. com/ Quality Digest. A magazine. 6 http: //www 2. umassd. edu/SWPI/ Software Process Resource Collection 7 http: //deming. eng. clemson. edu/ A page at Clemson University for Continuous Quality Improvement, including software and tutorials. 8 http: //www. statsoftinc. com/textbook/stathome. html An online textbook in statistics and quality planning & analysis 9 The Hong Kong research institute of textile and apparel (HKRITA) 10 Quality planning & analysis Mc. Graw-Hill 4 th edition 11 Creating Quality by William J. Kolarik , Mc. Graw-Hill 12 Arved Harding Statistician Eastman Chemical Company 13 Pearson Education, Inc. Publishing as Prentice Hall.