Statistical Quality Control

Statistical Quality Control Revision 3.0 Plakshi GyanTech We are Knowledge Catalysts ! GT-0020-04 / 20-May-08

Introducing the Catalyst Vijay Kumar Saini is a practicing engineer in the Automobile Domain with rich exposure to the technology and management aspects. He is a Certified Quality Manager who has spent his valuable 18+ years in search of excellence in Quality Realm. He has worked extensively as TQM expert, Quality Engineer, Kaizen Manager, Hoshin Kanri Expert during his professional career. Apart from designing a lot many thought provoking trainings, he has inscribed a few management & engineering related papers also. GyanTech Group © 2008-09 information@gyantech.net 4

Training Codec Respect all Creature. You may criticize other’s idea logically & factually. Be a good Listener and a perfect Orator for the suitable situations. Please make notes of the discussion as record for your future references. while query, please mention slide no. and subject for clarity. Let’s stay together. Cross-talks are not allowed, unless instructed. Please Raise the point of common interest in public time. For specific issues, manage for private time. Your query shall be answered now or in near future. Please keep mobiles silent and avoid commotion during training. We can include additional breaks for convenience (If requested). The discussion shall be based on average level of intelligence. Also the training contents & examples may not suit every profile. So, please keep your minds open and ears alert for optimum learning, always. The explanation shall make all concepts & ideas clear in most generic way. All are ever learning. You are free to uphold your point of view. But arguments / contradiction in excess aren’t permitted due to time factor. Finally BEST OF LUCK for your learning with all of us around. GyanTech Group © 2008-09 information@gyantech.net 5

Statistical Plakshi Our Business Objectives Quality GyanTech Control Earn Optimum Profits for Organization. Notes Enhance product acceptability & image. Sustain the cut throat global competition. Maintain & improve current market position & reliability. Embrace advance technologies & trends faster and efficiently. Gain Brand and Corporate loyalty. Surprise Customers with latest and delighting Products. Any other : ???? GyanTech Group © 2008-09 information@gyantech.net 7

Statistical Plakshi What is Quality ? Quality GyanTech Control What makes a good quality… Notes • Car • Computer • Knife • Children’s toy • Pizza delivery • Courier Service Describe a recent time when you have experienced bad quality? So what are the common aspects of quality? GyanTech Group © 2008-09 information@gyantech.net 10

Statistical Plakshi Quality in Human History ... Quality GyanTech Control Quality :10,00,000 Years Notes Cost :10,000 Years Productivity :200 Years Technology :100 Years Scientific Management :50 Years W. E. Deming taught us … • “Productivity goes UP as Quality goes UP. This fact is well known, but only to a select few.” GyanTech Group © 2008-09 information@gyantech.net 11

Statistical Plakshi Definition of Quality 1/2 Quality GyanTech Control Here are some specific definitions of quality Notes • Quality is meeting and exceeding customer needs and expectations; • Quality is inversely proportional to variability. • Juran: Quality is fitness for use; • Crosby: Quality is conformance to clearly state requirements; • Deming: Quality should be aimed at the needs of the consumer, present and future; • Feigenbaum: Quality is the total composite product and service characteristics of marketing, engineering, manufacture and maintenance through which the product and service in use will meet the expectations of the customer; Some more general definitions of quality • Taguchi: Quality is the loss (from function variation and harmful effects) a product causes to society after being shipped, other than any losses caused by its intrinsic function; • ISO 9000: Quality is the totality of features and characteristics of a product or service that bear on its ability to satisfy stated or implied needs. GyanTech Group © 2008-09 information@gyantech.net 13

Statistical Plakshi Definition of Quality 2/2 Quality GyanTech Control • Radford: Quality, as applied to the products turned out by industry, Notes means the characteristics or group or combination of characteristics which distinguishes one article from another, or the goods of one manufacturer from those of competitors, or one grade of product from a certain factory from another grade turned out by the same factory; • Shewart: There are two common aspects of quality. One of these has to do with the consideration of the quality of a thing as an objective reality independent of the existence of humans. The other has to do with what we think, feel or sense as a result of the objective reality; this subjective side of quality is closely linked to value; • Ishikawa: The extent of quality is determined by how well the true quality characteristics (customer needs, expressed in customer language) match substitute quality characteristics (product specifications, expressed by a producer in technical language). These definitions have some aspects in common What are the keywords from these definitions? GyanTech Group © 2008-09 information@gyantech.net 14

Statistical Plakshi The Consequences of Poor Quality Quality GyanTech Control Loss of business Notes Liability Increased Productivity loss Costs & expenses up Goodwill loss Customer Loyalty reduced Brand Image deterioration Any Other … GyanTech Group © 2008-09 information@gyantech.net 24

Statistical Plakshi Responsibility for Quality Quality GyanTech Control Top Management Notes Design Procurement Production / Operations Quality Assurance Packaging and Shipping Marketing and Sales Customer Service GyanTech Group © 2008-09 information@gyantech.net 26

Statistical Plakshi Costs of Quality Quality GyanTech Control Quality Costs are those categories of costs that are Notes associated with producing, identifying, avoiding, or repairing products that do not meet requirements. These costs are: • Prevention Costs All product and/or service inspection costs. • Appraisal Costs All TQ training, TQ planning, customer assessment, process control, and quality improvement costs to prevent defects from occurring • Internal Failure Costs Costs incurred to fix problems that are detected before the product/service is delivered to the customer. • External Failure Costs All costs incurred to fix problems that are detected after the product/service is delivered to the customer. GyanTech Group © 2008-09 information@gyantech.net 29

Statistical Plakshi Definitions of Statistics Quality GyanTech Control “Statistics is the science of gaining information from Notes numerical data.” -- Moore Statistics: “the science of data involving collecting, classifying, summarizing, organizing, analyzing, and interpreting numerical information” -- McClave, Dietrich, Sincich “Statistics is no more than qualified guess work.” – Shingo An understanding of variation An awareness of when and how variability affects quality An ability to identify variability that can be controlled A commitment to controlling and reducing variability in a never-ending striving for quality improvement -- Levine, Ramsey, Berenson GyanTech Group © 2008-09 information@gyantech.net 46

Statistical Plakshi Statistical Quality Improvement Techniques Quality GyanTech Control These are the major SQC areas: Notes • Acceptance sampling • Statistical Process Control (SPC) Statistical Distribution Control Charts Process Capability Test of Hypothesis • Failure Mode & Effect Analysis (FMEA) • Design of Experiments (DOE) GyanTech Group © 2008-09 information@gyantech.net 47

Statistical Plakshi Acceptance Sampling 1/2 Quality GyanTech Control Acceptance sampling is the inspection and classification of a Notes sample of the product selected at random from a larger batch or lot and the ultimate decision about disposition of the lot. Acceptance sampling is frequently used in a purchasing or receiving situation. Two types: • Outgoing inspection - follows production • Incoming inspection - before use in production Acceptance sampling Method • Acceptable Quality Level (AQL): In sampling, producer’s objective is to ensure that the sampling plan has a low probability of rejecting good lots. Lots are defined as high quality (good) if they contain no more than a specified percentage of defectives, termed AQL. • Lot Tolerance Percent Defective (LTPD) : The consumer’s objective is to ensure that the sampling plan has a low probability of accepting bad lots. Lots are defined as low quality (bad) if the percentage of defectives is greater than a specified amount, termed LTPD. • Producer’s Risk (α ): Probability of rejecting a high quality lot. • Consumer’s Risk ( β ): Probability of accepting low quality lot. • Choice of AQL, α, LTPD, and β depends on company policy and / or contractual requirements. GyanTech Group © 2008-09 information@gyantech.net 48

Statistical Plakshi Acceptance Sampling 2/2 Quality GyanTech Control Design of a Single Sampling Plan: A single sampling plan is defined Notes by ‘n’ and ‘c’, where • 1≤ n ≤ N n = sample size , (lot size). • c = acceptance number, maximum number of defectives permissible in the sample before rejecting the lot. ‘n’ and ‘c’ are determined from four factors α • AQL , • • LTPD, • β These four factors quantify the objectives of product’s producer and its consumer. GyanTech Group © 2008-09 information@gyantech.net 49

Statistical Plakshi SPC History Quality GyanTech Control 1924: Walter Andrew Shewart Notes A physicist at Bell Telephone Laboratories (in New Jersey) recognizes that variation in manufactured products, though inevitable, could be monitored and controlled using statistical procedures. Since then SPC has evolved to cover different processes and industries Basic requirements for SPC • SPC can be said to involve: 20% Statistics 10% Common Sense 70% Effectively applied Job Knowledge • This brings out 100 % Control. • This is success mantra of SPC GyanTech Group © 2008-09 information@gyantech.net 51

Statistical Plakshi 10 Steps of Implementing SPC Quality GyanTech Control 1. Analyze the process Notes 2. Decrease obvious variability 3. Gauge capability study 4. Sampling plan 5. Implement CONTROL CHARTS 6. Put the operator in charge 7. Process capability study 8. Improve the process 9. Reduce sampling 10. Return to step 1 GyanTech Group © 2008-09 information@gyantech.net 52

Statistical Plakshi Flow chart for implementation of SPC Quality GyanTech Control ENSURE PROPER CONDITION OF EQPT., GAUGES, TOOLS, ETC. Notes COLLECT PRELIM. DATA (FOR ATLEAST 25 SUBGROUPS) CALCULATE UCL / LCLR R UCLX/ LCLX USE X-R CHART USING ABOVE CONTROL LIMITS DURING REGULAR PRODUCTION IS PROCESS IDENTIFY & ELIMINATE NO UNDER ASSIGNABLE CAUSES CONTROL ? YES A Contd… GyanTech Group © 2008-09 information@gyantech.net 53

Statistical Plakshi Flow chart for implementation of SPC Quality GyanTech Control A Notes CALCULATE PROCESS CAPABILITY, CP/CPK IS CP/ CPK > NO IMPROVE THE 1.33? PROCESS YES KEEP FOLLOWING OP. PROCEDURE & CONTROL PROCESS USING X-R CHART PLOT TREND ON CP/ CPK EVERY MONTH REVIEW CONTROL LIMITS EVERY 2/3 MONTHS GyanTech Group © 2008-09 information@gyantech.net 54

Statistical Plakshi Benefits of SPC Quality GyanTech Control A process is inherently stable over an extended time period. Notes Hence SPC make it PREDICTABLE. Constant attention is required to maintain consistently in any standard process Increased Profits Increased Job Satisfaction Guaranteed Quality SPC improves processes that even have Automatic Process Control and Compensation Mechanisms. Satisfied Customers GyanTech Group © 2008-09 information@gyantech.net 55

Statistical Plakshi Type of Data Quality GyanTech Control DATA Notes VARIABLE ATTRIBUTE (Measurements (Can take only on a continuous discrete value) scale) e.g. Weight, e.g. no defectives, Hardness, no. of defects Time, Yield GyanTech Group © 2008-09 information@gyantech.net 58

Statistical Plakshi Variable data Characteristics Quality GyanTech Control Variable data Notes Central tendency Dispersion Mode Median Range Standard Mean Deviation Variable data type has two inherent characteristics . These are • Central Tendency towards the mean • Spread of the values both side of the mean. GyanTech Group © 2008-09 information@gyantech.net 59

Statistical Plakshi Variable Data’s Central Tendency Quality GyanTech Control Mean : Central Value or Average Notes i→ n x= ∑i→1 xi n Mode : Observation with highest frequency x = Maximum Frequency x1 + x2 + ... + xt + ... + xn ] ˆ [ Median : Central value when observation are arranged in order ~ = Middle Frequency[x + x + ... + x + ... + x ] x 1 2 t n GyanTech Group © 2008-09 information@gyantech.net 60

Statistical Plakshi Variable Data’s Dispersion Quality GyanTech Control Range : Total Dispersion or spread Notes R = xmax − xmin Standard deviation : Deviation measured from mean) ( xi − x )2 σ= ∑ ( n −1) Variance ( x1 − x ) 2 + ( x 2 − x ) 2 ....( xn − x ) 2 σ = n −1 ( xi − x )2 Variance = σ = 2 ∑ ( n −1) GyanTech Group © 2008-09 information@gyantech.net 61

Statistical Plakshi Population and Sample Quality GyanTech Control Collection of data by taking measurement on each item is Notes called Population A random set of measurement from the Population is called Sample Population Sample GyanTech Group © 2008-09 information@gyantech.net 62

Statistical Plakshi Symbols for various Statistical terms Quality GyanTech Control Parameter Population Sample Notes Average µ x Mode ˆ x ˆ x Median ~ x ~ x Variance σ 2 v Standard deviation σ v Range --- R Percent defective P p GyanTech Group © 2008-09 information@gyantech.net 63

Statistical Plakshi EXERCISE 1 : Time allowed 5 minutes Quality GyanTech σ Control Please Calculate these >>> ˆ ~ x x x R Notes A 01 15 15 15 10 B 01 06 11 15 19 C 24 06 03 29 24 D 21 03 08 12 15 E 06 11 24 29 11 F 15 19 29 15 19 GyanTech Group © 2008-09 information@gyantech.net 64

Statistical Plakshi One Problem With Mother Nature Quality GyanTech Control Everything is Different… Notes No two people are same… Atmosphere changes continuously… All the products or services we produce or render change continuously… Our taste changes continuously … Our physical and mental condition is under constant change Variability… • Defectives are caused by variations. • Even non-defectives have variations within the standard. • Defectives and non-defectives are produced together. • No two product or characteristics are ever alike. • Difference may be large, or they may be immeasurably small, but is always present. • Variations can be due to chance causes or assignable. GyanTech Group © 2008-09 information@gyantech.net 66

Statistical Plakshi Variation Quality GyanTech Control Variation … Notes • Is the cause of all quality problems • Is a natural phenomenon … in nature in industry Its detection depends upon • Precision of measurement • Skill of personnel It can be reduced but not eliminated Lower variation means higher possibility of conformance Examples of Variation - Dimension of a machined part would be affected by : • Machine (clearance, bearings wear) • Tool (hardness, strength, geometry) • Operator (setting, accuracy of location) • Maintenance (lubrication, temperature) • Environment (temp., voltage fluctuation) • Material Differences (size, hardness) • Equipment Differences • Human Performance Differences • Power Fluctuation GyanTech Group © 2008-09 information@gyantech.net 67

Statistical Plakshi Total Variability Quality GyanTech Control Notes Total Variability Controlled Variability Uncontrolled Variability Because of chance causes Because of Assignable Or causes or inherent causes extrinsic causes Or Or random causes special causes •Live with these causes till •Use statistical tools to up-gradation of work identify, eliminate, or standard/ design/ machine reduce these causes GyanTech Group © 2008-09 information@gyantech.net 73

Statistical Plakshi Process Control Quality GyanTech Control WHAT is Process Control ? Notes • Bringing process under the influence of common causes alone by identifying and eliminating ASSIGNABLE CAUSES ADVANTAGES • Process operates at its best when under common causes alone • Exhibits minimum variation • Predictable process • Lower level of Non- Conformance • Sampling inspection possible GyanTech Group © 2008-09 information@gyantech.net 74

Statistical Plakshi Types of Statistical Distributions Quality GyanTech Control Statistical distributions reflects the mathematical formula that relates Notes to the values of the characteristics with their probability of occurrences in the population. Following are the some popular and useful engineering / statistical distributions : • Normal Statistical Distribution for Variable Data • Exponential Statistical Distribution for Variable Data • Weibull Statistical Distribution for Variable Data • Binomial Statistical Distribution for Attribute Data • Poisson Statistical Distribution for Attribute Data. GyanTech Group © 2008-09 information@gyantech.net 77

Statistical Plakshi Normal Distribution Quality GyanTech Control For variable measurement Notes Bell-shaped curve Uniform about center Uni-peak curve GyanTech Group © 2008-09 information@gyantech.net 78

Statistical Plakshi Area Under the Curve 1 / 2 Quality GyanTech Control Notes s -6 s s s s s 0 s s s s s s -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 68.26 Percent 95.46 Percent 99.73 Percent 99.9937 Percent 99.999943 Percent 99.9999998 Percent GyanTech Group © 2008-09 information@gyantech.net 79

Statistical Plakshi Area Under the Curve 2 / 2 Quality GyanTech Control 68% observations Notes -1s +1s − 2σ + 2σ 95% observations − 3σ + 3σ 99.73% observations GyanTech Group © 2008-09 information@gyantech.net 80

Statistical Plakshi Area under the curve :Std. Normal Table Quality GyanTech Control Notes Based on N(0,1) i.e. µ =0 Convert any σ =1 N ( µ , σ ) into N (0,1) by (Standard normal variety) x−µ Z= σ Z 0.0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.500 0.504 0.508 0.512 0.516 0.519 0.523 0.527 0.531 0.5359 0.1 0.539 0.543 0.547 0.551 0.555 0.559 0.563 0.567 0.571 0.5753 … … GyanTech Group © 2008-09 information@gyantech.net 81

Statistical Plakshi EXERCISE 2 : Take 5 Minutes Quality GyanTech Control For a product manufactured from a process, its length Notes readings show normal distribution with m of 160 mm and s of 5mm. • What is the probability of products above 168.2 mm? • What is the probability of product less than 147.1 mm? • What is the probability of product between 150 and 168.2 mm? GyanTech Group © 2008-09 information@gyantech.net 82

Statistical Plakshi Example Quality GyanTech Control P = 0.5, 1- P = 0.5, N = 20 Notes Expected Value = 10, Variance = 5 P = 0.9, 1- P = 0.1 N = 20 Expected Value = 18, Variance = 1.8 P = 0.9, 1- P = 0.1 N = 100, Expected Value = 90, Variance = 9 P = 0.5, 1- P = 0.5 N = 20 Expected Value = 10, Variance = 5 P = 0.5, 1- P = 0.1 N = 20 Expected Value = 18, Variance = 1.8 GyanTech Group © 2008-09 information@gyantech.net 84

Statistical Plakshi EXERCISE 3 : Take 5 minutes Quality GyanTech Control Activity : Binomial Distribution Exercise Notes For the following scenarios calculate the expected value, variance, and the standard deviation : 1) N = 27, P = 0.11 Expected value = Variance = Standard deviation = 2) N = 65, P = 0.40 Expected value = Variance = Standard deviation = 3) N = 83, P = 0.98 Expected value = Variance = Standard deviation = GyanTech Group © 2008-09 information@gyantech.net 85

Statistical Plakshi Example Quality GyanTech Control Notes Three Sequences of Data Values from Three Poisson Distributions with Various Values of l Poisson (l =2), Expected Value = 2 5, 3, 6, 2, 0, 5, 2, 1, 2, 2, 0, 0, 6, 2, 0, 3, 4, 1, 4, 1 Sample average = 2.45 Poisson (l =5), Expected Value = 5 3, 5, 7, 9, 7, 4, 8, 4, 8, 4, 6, 5, 5, 6, 6, 9, 5, 7, 8, 5 Sample average = 6.05 Poisson (l =20), Expected Value = 20 24, 17, 14, 13, 18, 18, 23, 26, 25, 23, 12, 25, 16, 22, 17, 26, 24, 24, 25,17 Sample average = 20.45 GyanTech Group © 2008-09 information@gyantech.net 87

Statistical Plakshi EXERCISE 4 : Take 5 minutes Quality GyanTech Control Activity : Poisson Distribution Exercise Notes Calculate the mean, variance, and standard deviation of the following Poisson distributions : 1) Poisson (l =1) Mean = Variance = Standard deviation = 2) Poisson (l =7) Expected value = Variance = Standard deviation = 3) Poisson (l =18) Expected value = Variance = Standard deviation = GyanTech Group © 2008-09 information@gyantech.net 88

Statistical Plakshi What is Control Chart ? Quality GyanTech Control Mathematical and graphical method to illustrate performance Notes of a machine or process or activity over time. It has three lines parallel to x-axis One line is in the center and is called average line. It is firm line. Other two lines are at an equidistant from center line. These are called upper and lower control limits. These are broken lines. Quality Characteristics UCL CL LCL Time GyanTech Group © 2008-09 information@gyantech.net 91

Statistical Plakshi Control Chart Types Quality GyanTech Control Variable Notes • Run-chart • X-MR chart (Individual observation – Moving range chart) • X bar - R chart (Average – Range chart) • X cap - R chart (Median – Range chart) • X bar - s chart (Average – Standard deviation chart) • Sloping control chart • Group control chart • Pre-control chart Attribute • p chart (Proportion defective chart) • np chart (Number defective chart) • c chart (Number defect chart) • u chart (Number defect per unit chart) GyanTech Group © 2008-09 information@gyantech.net 92

Statistical Plakshi Data Gathering for Control Chart Quality GyanTech Control Select size, frequency and number of sub-groups Notes Record raw data Calculate control limits Interpret for process control Interpret for process capability GyanTech Group © 2008-09 information@gyantech.net 94

Statistical Plakshi Establishing Control Limits 1 / 2 Quality GyanTech Control (Preliminary Process Capability) Notes Ensure stability of Process and complete associated documentation. Take 25 sub-groups of a convenient size n (about 4 to 5). Record the values of range for each sub-group. Add all the ranges. Divide this total by the number of sub-groups to give the mean range represented by the symbol R. Read off the value of D4 from table, corresponding to the sub-group size n. Compute D4R. Compare all the sub-group ranges against this limit and consider them as forming a homogeneous group if none exceeds this limit. If condition (8) is satisfied, accept R as the standard range for the process. If condition (8) is not satisfied, remove all sub-group results which exceed the limit and compute the average range from the remaining sub-group. GyanTech Group © 2008-09 information@gyantech.net 95

Statistical Plakshi Establishing Control Limits 2 / 2 Quality GyanTech Control Repeat (7) with the new value of R. Notes Compare all the individual ranges in the remaining sub-groups against this revised limit and consider the ranges as homogeneous if none exceeds the limit. If condition (12) is satisfied, accept the revised value of R as the standard range for the process. If condition (12) is not satisfied, repeat steps (10) to (13) and repeat again as often as necessary for it to be satisfied. Compute the value of sub-group standard deviation (s or sigma) ( xi − x )2 • σ= ∑ ( n −1) n = Total number of observations) Compute preliminary process capability Pp = 6s Note : If about 20% of the values (ranges) get eliminated, don't proceed. Check for stability of the process. GyanTech Group © 2008-09 information@gyantech.net 96

Statistical Plakshi Method of Sub grouping Quality GyanTech Control Method of Sub-grouping should be : Notes Rational means minimum variation within a subgroup. Maximum possibility of variation between subgroups should be there. For example : • Items produced consecutively (4 pieces at the end of every hour) • Every 5th or 10th Item produced etc. GyanTech Group © 2008-09 information@gyantech.net 97

Statistical Plakshi Control limit vs. Spec. limit Quality GyanTech Control Control Limit Notes • Calculated from data gathered during the process • Use to judge whether a process is in 'Statistical Control‘ or not. • Specification Limit • Given on drawing, operation sheet or other spec. • To judge acceptability of individual product. GyanTech Group © 2008-09 information@gyantech.net 99

Statistical Plakshi Calculation of Control Limits Quality GyanTech Control Item Symbol LCL UCL Notes Average X − A2 R or X + A2 R or X X − A3 S X + A3 S Range ~ ~ ~ ~ R X − A2 R X + A2 R Median ~ D3 R D4 R X Std. Deviation σ /s B3S B4 S Moving Range MR --- 3.27 MR GyanTech Group © 2008-09 information@gyantech.net 100

Statistical Plakshi Interpretation of Control Chart Quality GyanTech Control Bringing process under influence of common causes alone by Notes identifying & eliminating assignable causes is called Process Control. Process is interpreted to be under control with these thumb rules: • Equal distribution on both side of center line • Most of the points are near central line • A few points are spread out and approach the control limit • None of the points exceeds the control limit Process is implied to be out of control when • One point beyond the control limits. • Seven consecutive points above or below the central line. • A run-up or down of seven consecutive points. • 02 out of three consecutive points beyond the warning (2 sigma) limits. • Hugging central line, this is indicated when 15 consecutive points are within the 1 sigma limits. • Bi-model distribution is indicated when 8 consecutive points are beyond the 1 sigma limits, regardless of which side of the central line. GyanTech Group © 2008-09 information@gyantech.net 103

Statistical Plakshi Run Chart Quality GyanTech Control Run chart is a graphical representation of quality Notes characteristic Quality characteristic is plotted in the order of production It helps to study the behavior of process over a period of time Trends if any can be easily discovered GyanTech Group © 2008-09 information@gyantech.net 106

Statistical Plakshi Group Control Charts Quality GyanTech Control There must be several sub-group sources that contribute Notes approx. equal no. Of sub-groups at approx. Same rate. All sources aim at the same value of quality characteristics. No differences among averages and dispersion of various sub- group sources. GyanTech Group © 2008-09 information@gyantech.net 108

Statistical Plakshi Sloping Control Chart Quality GyanTech Control Production Between two successive sub-groups must be Notes more or less constant Individual item of sub-groups must be consecutive so that trend will have minimum effect on the range of sub-group GyanTech Group © 2008-09 information@gyantech.net 110

Statistical Plakshi Attribute Control Chart Quality GyanTech Control Proportion defective chart (p–Chart) is used when sub-group Notes size is varying. Number defective chart (np–Chart) is used when sub-group size is constant. Number of defects charts : • c–Chart (No. defect chart) is used when sub-group size is constant. • u-Chart (No. defects/ unit chart) is used when sub-group size is varying GyanTech Group © 2008-09 information@gyantech.net 111

Statistical Plakshi Attribute Control Chart selection Quality GyanTech Control Notes Defectives Defect Sample Size Sample Size Constant Number np c chart chart Proportion Variable p u chart chart GyanTech Group © 2008-09 information@gyantech.net 112

Statistical Plakshi Pre to installation of Attribute Charts Quality GyanTech Control Choice of Quality Characteristic Notes • Normally single defective • For no. of defect chart, all defects counted and plotted. If classified as Major/Minor, separate chart or demerit score Inspection Aspects • Somewhat subjective • Clear criteria e.g. visual aids Choice of Rational Subgroup • Subgroups in the order of production • Initially, stratify the data Sub-group size • Empirically, n = (400 to 600) / 100p • where p = average prop. defective GyanTech Group © 2008-09 information@gyantech.net 113

Statistical Plakshi Advantages of Control Charts Quality GyanTech Control Process operates at its best when under common causes alone Notes Exhibits minimum variation Predictable process Lower level of Non- Conformance Sampling inspection possible Misconceptions of Control Charts • Control chart will control the process? No. Only show what is occurring in the operation. • A process in control is capable? Not necessarily Process control and specification Limits are not the same GyanTech Group © 2008-09 information@gyantech.net 114

Statistical Plakshi Process Capability Quality GyanTech Control Process Capability is the inherent variability of the process Notes It measures potential capability assuming that process is centered and is in state of statistical control. When all assignable causes are eliminated and process is having variability due to chance causes only, it is said to be in a state of statistical control. GyanTech Group © 2008-09 information@gyantech.net 117

Statistical Plakshi Indices for on-going process capability Quality GyanTech Control Process Capability (Cp) is the measure of the spread of the Notes process. USL − LSL Cp = 6σ Process Capability Index (Cpk) is the measure of central tendency of the process. It shows how well the parts are being produced (in other words, process variability) fit into the range specified by the design limits.  X − LTL UTL − X  C pk = min  or   3σ 3σ  If process variability (usually +/- 3 standard deviations from the process mean) is within the specified design limits, the process is said to be ‘capable’. GyanTech Group © 2008-09 information@gyantech.net 118

Statistical Plakshi Population and Sampling Distribution Quality GyanTech Control Three population distributions Notes Distribution of sample means Beta Mean sample of = means x Normal Standard deviation σx of sample means = σx = n Unifor m − 3σx − 2σx − 1σx x + 1σx + 2σx + 3σx (mean) 95.5% allx fallwithin 2σx of ± 99.7% allx fallwithin 3σx of ± GyanTech Group © 2008-09 information@gyantech.net 120

Statistical Plakshi When process is capable ? Quality GyanTech Control The process is operating under only common cause and all Notes the special causes are eliminated. Process under statistical control does not necessarily means that the process is capable. When both Cp and Cpk are more than or equal to 1.33, the process is said to be in good condition. Controlled and capable. GyanTech Group © 2008-09 information@gyantech.net 124

Statistical Plakshi In Control vs. Out Of Control Quality GyanTech Control (a) In statistical Notes control and capable of producing within control limits. A process with only Frequency natural causes of variation and capable of producing within the specified control Lower control limits. Upper control limit limit (b) In statistical control, but not capable of producing within control limits. A process in control (only natural causes of variation are present) but not capable of producing within the specified control limits; and (c) Out of control. A process out of control Size having assignable Weight, length, speed, etc. causes of variation. GyanTech Group © 2008-09 information@gyantech.net 125

Statistical Plakshi Process Vs Specification Quality GyanTech Control Notes Voice of the Process -3 s +3 s Process Width Design Width LSL T USL Voice of the Customer GyanTech Group © 2008-09 information@gyantech.net 126

Statistical Plakshi Desired level of Cpk … Quality GyanTech Control Notes Cpk VALUE JUDGEMENT 0.67 < Cpk < 1.0 Lacking 1.0 < Cpk < 1.33 Insufficient 1.33 < Cpk < 1.67 Sufficient 1.67 < Cpk < 2.0 Good 2.0 < Cpk Excellent GyanTech Group © 2008-09 information@gyantech.net 129

Statistical Plakshi Process capability vs. specification tolerance Quality GyanTech Control P.C. < (U-L) Notes • Use of less precise process • Possibility of squeezing Tolerance • Inspection can be reduced • Process average can be set at an economic level (use of modified control limits) L U GyanTech Group © 2008-09 information@gyantech.net 130

Statistical Plakshi Process capability vs. specification tolerance Quality GyanTech Control P.C. =(U-L) Notes • Attempt to reduce variability • Greater attention (constant surveillance) to centering of the process • Set the process at most economic level • Provide for sorting the product, when the distribution changes • If possible (as a last resort), review specifications L U GyanTech Group © 2008-09 information@gyantech.net 131

Statistical Plakshi Process capability vs. specification tolerance Quality GyanTech Control P.C. > (U-L) Notes • Non- conformance inevitable • 100% Inspection strongly recommended • Attempt to reduce variability • Switch over to more precise process • Set the process at most economic level • If possible (as a last resort), review specifications L U GyanTech Group © 2008-09 information@gyantech.net 132

Statistical Plakshi EXERCISE 5: Take 10 minutes Quality GyanTech Control Draw process curves, calculate Cp / Cpk & comment on this situation Notes Situation LSL USL Mean St. Dev. One 10 20 14 1 Two 10 20 15 3 Three 0 10 7 0.5 Four 0 10 10 0.5 Five 10 15 13 2 GyanTech Group © 2008-09 information@gyantech.net 133

Statistical Plakshi EXERCISE 6 : Take 10 minutes Quality GyanTech Control Notes (Determine Cp and Cpk; Specifications : 21.50 +/- 0.50) S.No. Reading 1 Reading 2 Reading 3 1. 21.50 21.60 21.80 2. 21.45 21.50 21.75 3. 21.45 21.70 21.85 4. 21.75 21.60 22.00 5. 21.80 21.50 21.60 6. 21.45 21.60 21.80 7. 21.85 21.50 21.80 8. 21.85 21.50 21.85 9. 21.80 21.75 21.80 10. 22.00 21.60 22.00 11. 21.85 21.75 21.85 . Contd GyanTech Group © 2008-09 information@gyantech.net 134

Statistical Plakshi EXERCISE 6 – contd… Quality GyanTech Control S.No. Reading 1 Reading 2 Reading 3 Notes 12. 21.75 21.90 21.50 13. 22.10 21.50 21.85 14. 22.00 21.50 22.10 15. 22.10 21.45 21.80 16. 21.80 21.40 21.45 17. 22.00 21.30 21.45 18. 22.00 21.30 21.90 19. 22.00 21.60 21.90 20. 21.80 21.30 21.85 21. 21.90 21.60 21.85 22. 22.00 21.60 21.75 GyanTech Group © 2008-09 information@gyantech.net 135

Thank you very much for a patient listening, persuasive enthusiasm and earnest interaction ! Please refer your Comments / Queries / Questions at Vijay Kumar Saini information@gyantech.net +91 – 9810891691 We solicit your valuable feedbacks & suggestions for improvisation of this program, contents & logistics etc. Please feel free to provide us with your earnest and honest feedback . This will help us in improving our services and offerings. With Thanks. GT-0020-04 / 20-May-08

Statistical Quality Control

1 comments

Notes on slide 1

2 Favorites