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• STATISTICAL PROCESS CONTROL Dr.K.V.Narrasimham QCFI Delhi Chapter
• The new millennium will see expanded use of Quality Control Measures and increased attention to the customers needs. The customer will reign supreme as the determiner of acceptable levels of quality. Industry will adjust to this or inevitably lose market share.”
• Overview of Workshop
• A short introduction and historical summary
• The principles of SPC:
• How SPC increases the quality of manufactured goods
• How SPC effectively monitors the production line and aids in production control
• Variables Control Charts
• Attributes Control Charts
• How to set up a new SPC program:
• Initial Data collection
• Making the Control Chart
• How to interpret SPC Control Charts:
• Standard Chart Patterns
• Chart Pattern Interpretation
• Do you know What Statistics means ? The branch of mathematics that deals with the collection, organization, analysis and interpretation of data . a set of concepts, rules, and procedures that help us to: organize numerical information in the form of tables, graphs, and charts; understand statistical techniques underlying decisions that affect our lives and well-being; and make informed decisions
• Do you know What Process means ?
• deal with in a routine way; &quot;I'll handle that one&quot;; &quot;process a loan&quot;; &quot;process the applicants&quot;
• procedure: a particular course of action intended to achieve a result; &quot;the procedure of obtaining a driver's license&quot;; &quot;it was a process of trial and error&quot;
• perform mathematical and logical operations on (data) according to programmed instructions in order to obtain the required information ;
• Do you know What Control means ?
• A condition in which specific quality criteria have been achieved in a laboratory analysis.
• A type of sample used to assess the quality of an analytical process ;
• Do you know What S P C /S Q C means ? SPC = The application of statistical techniques to control a process, reducing variation so that performance remains within boundaries, or specification limits. SQC = The application of statistical techniques to control quality; includes acceptance sampling (inspection of a sample from a lot to decide whether to accept that lot) as well as SPC.
• Historical 1700 – 19000 Quality by Craftsmen . 1875- F.W.Taylor Scientific Management 1900- Henry Ford Assembly Line. 1901- 1 st Standards laboratories in G.B. 1907-08 AT & T Bell Lab Systematic, inspection and testing of products and materials. 1919-Technical Inspection Association-England-IQA 1920s-GE in England uses Statistical Methods to control “Q” Bulbs 1924- W.A. Shewhart introduces Control Charts-Bell Labs 1928- Dodge & Romig Acceptance Sampling methodology. Seminars Seminars, Training Courses, Lectures.
• Principles of SPC Clarity Population Is a set of all items that possess a certain characteristic of interest. Sample Is a subset of population,that which is taken from a population for certain purposes. Parameter is a characteristic of a population Something that describes it. Statistic Is a characteristic of sample. It is used to make inferences on the population parameters that are typically unknown
• Principles of SPC
• DATA COLLECTION
•   Data collection is nothing but collection of required information in figures for statistical analysis of a problem. This provides a sound basis for making decision and corrective action .
• Basis or guide for decisions is facts.
• Experience and sixth sense may be necessary;liable to invite error in judgement due to the decision being too personal or out of erroneous memory.
• To avoid this, it is important to get the facts in terms of numbers or quantity. These numbers are called data . They are expression of any activity or feature in numerical terms.
•
• Examples: Fuel efficiency of a scooter, percentage defectives in incoming material, volume of customer complaints, pouring temperature of steel, hardness of casting etc.
• Principles of SPC OBJECTIVE OF DATA COLLECTION   Controlling and monitoring the production process. Controlling and Monitoring the process Analyses of Non-Conformance Inspection
• Principles of SPC
• PURPOSE OF DATA COLLECTION
•
• Quality Evaluation - Raw materials, semi finished products and finished products.
• Process Control - To assure that products turned out meet specified requirements of customer/design.
• Improvement Trials - To improve product quality, reduce costs and increase productivity.
• Problem Solving - By Quality Circles.
• Compare Performance - From time to time measure improvement in production, profit,quality, competitiveness etc.
•
• Principles of SPC   TYPES OF DATA   Generally data are of two types:   Measurement Data or Variable Data:   Weight, diameter, tensile strength, % carbon, reaction time etc. Basic observation obtained by using an instrument or measuring process. These data are continuous; they are also called continuous variables. A variable is one which varies i.e. takes different values.   Attribute Data:   Data obtained by classification into two or more categories. Fot example number rejected, number passed, data obtained by count of defects, count of occurrences (number of accidents) etc.   'These data are in whole numbers and are called discontinuous or discrete variables.   TYPES OF DATA   Generally data are of two types :   Measurement Data or Variable Data or Continuous Data:     Attribute Data : .
• Measurement Data or Variable Data or Continuous Data:
•
• Weight, diameter, tensile strength, % carbon, reaction time etc. Basic observation obtained by using an instrument or measuring process. These data are continuous; they are also called continuous variables. A variable is one which varies i.e. takes different values.
Principles of SPC
• Principles of SPC
• Attribute Data or Discontinuous or Discrete variables :
• Data obtained by classification into two or more categories.
• For example number rejected,number passed, data obtained by count of defects, count of occurrences (number of accidents) etc.
•
• 'These data are in whole numbers and are called discontinuous or discrete variables
• Principles of SPC HOW TO COLLECT DATA Data can be collected in the following ways:   .1) Formulate good questions that relate to specific information needs of the project. 2) Consider appropriate data-analysis tools and be certain the data needed for the analysis are being collected Wherever possible, collect continuous variable data.   3) Define comprehensive data-collection points. 4) Select an Unbiased collector. 5) Understand data collectors and their environment.
• Principles of SPC HOW TO COLLECT DATA Data can be collected in the following ways: ( contd…)   6) Design data collection forms.   7) Prepare thc instructions. 8) Test forms and instructions. '   9) Train data collectors.. 10) Audit the collection process and validate- . &quot;the resul ts”. '
• Principles of SPC USEFUL POINTS FOR DATA COLLECTION 1) Be clear in mind about objective . 2) Prepare the question which will make it clear and precise. 3) Collect data relevant to that. 4) Use data sheet, check sheet and/or check list as per the requirement. 5) Keep them simple and easy.
• Principles of SPC 9) Analyze the collected data for its credibility and relevance (for whom, when or who collected the data are important ). 10) Present data in a way that clearly answers the question . 8) Form should be self explanatory . 7) Capture data for analysis reference and trace ability. 6) Reduce opportunities for error. USEFUL POINTS FOR DATA COLLECTION
• Principles of SPC BENEFITS OF DATA COLLECTION Right decision can be made Errors due to subjective feeling or personal bias are avoided Agreement on decisions necessary rather than different or subjective opinions. Measurements understandable to all   Assessments of magnitude of improvements Discovery of causes affecting Quality & Productivity.
• Principles of SPC CAPTURING THE DATA HOW CHECKSHEETS GRAPHS / PICTORIAL DIAGRAMS .
• Principles of SPC CHECKSHEETS A check sheet is a simple data recording form specially designed so that data can be interpreted readily from the sheet itself. Items to be checked are pre-printed so that recording becomes very easy.
• Principles of SPC TYPES OF CHECKSHEETS.
• Process control information checks
• Product quality assurance checks
• Defective item checks
• Defect location checks
• Defective cause checks
• f) Process variation distribution checks
• g) Others
• Principles of SPC PROCESS CONTROL INFORMATION CHECK Solder Bath Temperature Checkcd hy: Date:   Take reading of temperature nearest to degree.    Time Temp(deg cen) Time Temp (deg cen)   Notes:
• Principles of SPC Product Quality Assurance Check Actual Obs Spec Parameter No ddd nnnnnnn 10 … .. ……… out cccc zzzzzzz 3 Not ok bbb yyyyyyyy 2 ok aaaa xxxxxxxx 1 5 4 3 2 1
• Principles of SPC Defective item checks 18 229 IIII IIII IIII III LLLLLLL TOTAL 15 35 IIII IIII IIII IIII IIII IIII IIII nnnnnnnn 10 87 IIII IIII IIII IIII IIII IIII IIII IIII IIII IIII IIII IIII IIII IIII IIII IIII IIII II zzzzzzzz 3 52 IIII IIII IIII IIII IIII IIII IIII IIII IIII IIII II yyyyyyy 2 37 IIII IIII IIII IIII IIII IIII IIII II xxxxxxx 1 No Tally Defect Sl No IIII IIII IIII
• Principles of SPC Defect location checks Check Sheet (in picture) Defect in Chips Functional Reject Parametric Reject
• Principles of SPC Defective cause check sheets 0 00 xx 000 Xx 000 ^ ^ 00x * . 2 Symbols are various types of defects. 00 #x 000 #xx # 0 000 xx ** ** X x 000 000 Xxx 0x * ** 000 #xx 00x 0x * x . 1 A B 00 #x 000 #xx # 0 000 xx ** ** X x 000 000 Xxx 0x * ** 000 #xx 00x 0x * x . 1 A Sat am pm Fr am pm Th am pm We am pm Tu am pm Mo am pm Operator M/c
• Principles of SPC Process variation distribution checks
• Principles of SPC What is Graph Graph is pictorial representation of data which when presented is easily understandable. It helps to represent large amount of information comprehensively in a commpact manner.
• Principles of SPC Types of Graphs Line Graph x y Bar Graph Pie
• Principles of SPC Composite Bar Graph Radar Chart Area Graphs Floating Type Pictorial
• Principles of SPC Benefits of Graphs Numerical data are expressed in visual form Helps in comparison. Easy to understand No strain of going through large volume of info Creates interest. Quick to understand Useful to express data clearly and strikingly No need to have special skill to make them Helps in accurate analysis of cause.
• Principles of SPC Do's & Dont's for Drawing a Graph
• Be clear on the purpose of making the graph.
• Arrange the information in order.
• Decide on the type of graph.
• Decide on the title.
• Show the data.
• Avoid distorting the information.
• Make it easier for eyes to compare.
• Large amount of data should be depicted in
• summary form and then into finer details.
• Let graph serve a clear purpose of exploration, tabulation
• or decoration.
• Should be closely integrated with statistical and verbal
• descriptions of a data set.
• Principles of SPC
• Mean is the sum of the observations divided by the total number of observations:
• Principles of SPC
• Standard deviation is the square root of the variance of distribution. An estimate of the population standard deviation based on sample is given by
Standard Deviation
• Seven Tools of Quality Improvement
• Flowchart/process map
• 2. Check sheet
• 3. Cause-effect diagram
• 4. Pareto chart
• 5. Histogram
• 6. Scatter diagrams
• 7. Control chart
• 7T >QI—FLOW CHART Graphical tools for process understanding. A flowchart creates a graphical representation of the steps in a process. A process map adds lists of inputs and outputs for each step.
• 7T >QI—FLOW CHART CONVENTIONAL SYMBOLS
• 7T >QI—FLOW CHART Types of Flow Charts. TOP-DOWN FLOW CHART MATRIX FLOW CHART FLOW DIAGRAMS GANTT CHART
• 7T >QI—FLOW CHART
• 7T >QI—FLOW CHART MATRIX FLOW CHART
• 7T >QI—FLOW CHART FLOW DIAGRAMS
• 7T >QI—FLOW CHART GANTT CHART
• 7T >QI—FLOW CHART HOW TO DRAW FLOW DIAGRAM a. Discuss the purpose of it. b. Decide on your expectation . c. Decide the boundaries.  d. Put each process in writing from the beginning.  e. When you come to a decision area follow one till you complete f. For unknown areas later on check up and complete.  g. Ensure every branch is completed h. Review it and ask other members also to review .
• 7T >QI—FLOW CHART How to make use of Flow Diagram? Problem solving Better understanding of the process Change or introduction of new process For amending, altering or replacement to improve efficiency
• 7T >QI—FLOW CHART How to improve efficiency? Dr J.M.Juran suggested 4 step approach Decision pt LOOK for redundant, Unnecessary or incomplete activity Change or elimination Cost or waste Step 1 Activity Symbol LOOK Value related to cost + customer needs Prevention of errors by improving design of activity Step2
• 7T >QI—FLOW CHART How to improve efficiency? Dr J.M.Juran suggested 4 step approach Rework loop LOOK for redundant, Unnecessary or incomplete activity Change or elimination Step 3 LOOK for outdated information. Up-date them Step 4 Database or Document Symbol
• 7T >QI—C & E DIAGRAM CAUSE AND EFFECT DIAGRAM
• A tool for analyzing process dispersion. It is also referred to as the &quot;Ishikawa diagram,&quot; because Kaoru Ishikawa developed it, and the &quot;fishbone diagram,&quot; because the complete diagram resembles a fish skeleton. The diagram illustrates the main causes and sub causes leading to an effect (symptom).
• 7T >QI—C & E DIAGRAM
• 7T >QI—C & E DIAGRAM Procedure for Making Cause-and-Effect Diagrams For Identifying Causes. 1) Procedure Step I Determine the quality characteristic.   Step 2 Choose one quality characteristic and write it on the right-hand side of a sheet of paper, draw in the backbone from left to right, and enclose the characteristic in a square. Next, write the primary causes which affect the quality characteristic as big bones also enclosed by squares.
• 7T >QI—C & E DIAGRAM Step 3 Write the causes (secondary causes) which affect the big bones (primary causes) as medium-sized bones, and write the causes (tertiary causes) which affect the medium-sized bones as small bones. Step 4 Assign an importance to each factor, and mark the particularly important factors that seem to have a significant effect on the quality characteristic. Step 5 Record any necessary information.
• 7T >QI—C & E DIAGRAM C & E DIAGRAM C & E Verbal data is used instead of Numerical data Call together everyone involved in the process Use 5 M’s ( Man, Material, Method, Machine and Measurement) AND 4 P’s People, Provision (material),Procedure and Place appropriately. Word your questions properly -- like Does it happen always? When does it happen and Why? ASK 5 TIMES WHY? AND YOU WILL REACH THE MAIN CAUSE OF A Problem.
• 7T >QI—C & E DIAGRAM Keep in mind
• C & E serves the purpose of indicating the areas
• Review—review –review with the process owner
• Check all causes, sub causes and its validity.
• A good C & E normally solves the problem.
• C & E is a problem defining tool. Use it effectively
• to get the causes in a orderly and logical manner. Gives a total analytical picture showing all possible causes
• 7T >QI—C & E DIAGRAM
• Collecting data appropriate to C&E will be effective to solve problems.
• Based on our experience, knowledge and skill , examine each factor.
• One step C& E will not be effective and useful. Make it, discuss, revise it.
• Everybody in the job will be benefitted by this tool.
• It shows the reality of the situation.
• It can be used for any problem and in any situation.
• 7T >QI—C & E DIAGRAM Sub-Sub-Sub cause Remember the logical sequence as follows. - Sub-Sub cause Sub cause Effect Main cause
• 7T >QI—PARETO DIAGRAM. A graphical tool for ranking causes from most significant to least significant. It is based on the Pareto principle, which was first defined by J. M. Juran in 1950. The principle, named after nineteenth-century economist Vilfredo Pareto, suggests that most effects come from relatively few causes; that is, 80% of the effects come from 20% of the possible causes. Dr. Juran coined the phrases vital few and useful many .
• 7T >QI—PARETO DIAGRAM Examples of vital few are:- A few customers account for the majority of sales. A few processes account for the bulk of the scrap or rework cost. A few non-conformities account for the majority of customer complaints. A few suppliers account for the majority of rejected parts. A few products account for the majority of the profits.
• 7T >QI—PARETO DIAGRAM How to Make Pareto Diagrams. Step I Decide what problems are to be investigated and how to collect the data.   1) Decide what kind of problems you want to investigate. Example: Defective items, losses in monetary terms, accidents occurring.   2) Decide what data will be necessary and how to classify them. Example: By type of defect, location, process, machine, worker, method. Note: Summarize items appearing infrequently under the heading &quot;others.&quot;   3) Determine the method of collecting the data and the period dur­ing which it is to be collected. Note: Use of an investigation form is recommended.
• 7T >QI—PARETO DIAGRAM Step 2 Design a data tally sheet listing the items, with space to record their totals (Table ). Step 3 Fill out the tally sheet and calculate the totals. Step 4 Make a Pareto diagram data sheet listing the items, their individual totals, cumulative totals, percentages of overall total, and cumulative percentages (Table ).
• 7T >QI—PARETO DIAGRAM
• 7T >QI—PARETO DIAGRAM Step 5 Arrange sheet the items in the order of quantity, and fill out the data sheet. Note: The item &quot;others&quot; should be placed in the last line, no matter how large it is. This is because it is composed of a group of items each of which is smaller than the smallest item listed individually
• 7T >QI—PARETO DIAGRAM Step 6 Draw two vertical axes and a horizontal axis. 1) Vertical axes a) Left-hand vertical axis Mark this axis with a scale from 0 to the overall total. b) Right-hand vertical axis Mark this axis with a scale from 0% to 100%. 2) Horizontal axis Divide this axis into the number of intervals to the number of items classified.
• 7T >QI—PARETO DIAGRAM Step 7 Construct a bar diagram. Step 8 Draw the cumulative curve (Pareto curve). Mark the cumulative values (cumulative total or cumulative percentage), above the right-hand intervals of each item, and connect the points by a solid line.   Step 9 Write any necessary items on the diagram. 1) Items concerning the diagram Title, significant quantities, units, name of drawer. 2) Items concerning the data Period, subject and place of investigations, total number of data.
• 7T >QI—PARETO DIAGRAM Benefits of Pareto analysis 1.Prioritizing and defining problems 2.Concentrate on Vital Few when addressed carefully, will result in maximum benefit . 3.Identify the root causes of the problems 4.Checks the effectiveness of the remedy of its implementation .
• 7T >QI—CONCEPT OF VARIATION Shewhart observed that variation occurs everywhere in our world. There is variation in each of a multiple of characteristics of human beings.No two tree leaves are the same. The same is true of Industrial & commercial processes and services- variation bounds.
• 7T >QI—CONCEPT OF VARIATION
• Fundamental phenomena of Variation :-
• Everything varies-no two items or occurrences
• are exactly alike
2. Individual observations are unpredictable 3. Groups of observations either tend to form predictable patterns or produce evidences that no predictable pattern exists without some process change. Patterns of Variation Run Chart Histogram. Control Chart.
• 7T >QI—HISTOGRAM
• A graphic summary of variation in a set of data. The pictorial nature of the histogram lets people see patterns that are difficult to detect in a simple table of numbers.
• 7T >QI—HISTOGRAM MEAN SPREAD OR DISPERSION
• 7T >QI—HISTOGRAM How to prepare a Histogram. Count the data, N=100. Arrange the data into subgroups roughly 10 grps Record the largest value Xl and smallest value Xs in each group. Record the Xl & Xs on the whole Xl=3.68, Xs=3.30
• 7T >QI—HISTOGRAM Calculate the Range R = Xl – Xs=0.038 The number of classes i.e. number of bars can be taken from table, Choose k =10, Class Interval h = R/k = 0.38/10=0.038, here the class interval is expressed as a multiple of an integer, take h= 0.05. Class boundary is demarcated started at one end of the range, to avoid actuals falling on the boundary, the boundary unit is taken as half of the actual measurement unit., here it is 0.05.
• 7T >QI—HISTOGRAM Calculate the Frequency table using Tally marks Construct the Histogram i.e a Bar Chart and write all the details.
• 7T >QI—HISTOGRAM
• 7T >QI—HISTOGRAM HOW TO READ A HISTOGRAM
• 7T >QI—HISTOGRAM Small group of data from a different lot/process conditions. It shows that mean are different and variations is different. ISOLATED PEAK Mixture of two conditions, two suppliers of same parts,two m/c’s,two operators. TWIN PEAK Mixture of several process conditions, several days output mixed together in one lot. PLATEAU Measurements like ovality , taper, defects SKEWED +VLY Traceable to errors in measurement & observations rounded off. COMB What it means? Type
• 7T >QI—HISTOGRAM It is necessary to take measures to bring the mean closer to the middle of the specification.   d) This requires action to reduce the variation.   e) The measures described in both c) and d) are required.
• 7T >QI—HISTOGRAM USES OF HISTOGRAM To know the pattern of variation To assess the state of control To assess the state of conformance to specifications To assess the spread or variation w.r.t specifications To assess Process capability. To get clues for bringing process under control- whether to shift mean or to reduce variation or both. To get clues for possible assignable causes for observed variation-mix of lots, suppliers.
• 7T >QI—PROCESS CAPABILITY.
• 7T >QI—PROCESS CAPABILITY.
• 7T >QI—PROCESS CAPABILITY.
• 7T >QI—PROCESS CAPABILITY.
• 7T >QI—PROCESS CAPABILITY.
• 7T >QI—PROCESS CAPABILITY.
• 7T >QI—PROCESS CAPABILITY.
• 7T >QI—PROCESS CAPABILITY.
• 7T >QI—PROCESS CAPABILITY.
• 7T >QI—PROCESS CAPABILITY.
• 7T >QI—PROCESS CAPABILITY.
• 7T >QI—PROCESS CAPABILITY.
• 7T >QI—PROCESS CAPABILITY.
• 7T >QI—PROCESS CAPABILITY.
• 7T >QI—PROCESS CAPABILITY.
• 7T >QI—SCATTER DIAGRAM A graphical technique to analyze the relationship between two variables. Two sets of data are plotted on a graph, with the y-axis being used for the variable to be predicted and the x-axis being used for the variable to make the prediction. The graph will show possible relationships among variables: those who know most about the variables must evaluate whether they are actually related or only appear to be related.
• 7T >QI—SCATTER DIAGRAM
• 7T >QI—SCATTER DIAGRAM
• 7T >QI—CONTROL CHARTS.
• A chart with upper and lower control limits on which values of some statistical measure for a series of samples or subgroups are plotted. The chart frequently shows a central line to help detect a trend of plotted values toward either control limit. Why Use a Control Chart?
• To monitor , control , and improve process performance over time by studying variation and its source.
• 7T >QI—CONTROL CHARTS. Chance cause Variation by chance cause is unavoidable and inevitably occurs in a process, even if the operation is carried out using standardized raw materials and methods. It is not practical to eliminate the chance cause technically and economically for the present. Assignable cause Variation by assignable cause means that there are meaningful factors to be investigated. It is avoidable and cannot be overlooked: there are cases caused by not following certain standards or applying improper standards. For e.g. Training , M/c repair.
• 7T >QI—CONTROL CHARTS. There are various types of control chart, according to the characteristic values or purpose. In any type of control chart the control limit is calculated by the formula:   (average value) ± = 3 x (standard deviation),   where the standard deviation is that of variation due to chance causes. This type of control chart is called a 3-sigma control chart .
• 7T >QI—CONTROL CHARTS. .  X Chart and R Chart   Procedure to Construct X Chart and R Chart 1.      Identify the process to be controlled. 2.      Select the variable of interest. 3.      Decide a suitable sample size (n) and number of samples to be collected (k) 4.      Collect the specified number of samples over a given time interval. 5.      Find the measurement of interest for each piece within the sample.       Types of Control Charts
• 7T >QI—CONTROL CHARTS. 6. Obtain the mean (  X) of each sample. (  X =[∑ x i] /n). 7. Also obtain the range R of each sample (R=Max x i - Min x i) . 8. Then obtain and { =[∑  X] /k, = [∑ R ] /k. 19.    Establish the control limits for  X and R chart.   The values for A 2, D 4 and D 3 for different sample size are given in table 33.1
• 7T >QI—CONTROL CHARTS. Table 33.1 Factors for Computing Control Chart Limits
• 7T >QI—CONTROL CHARTS. Situation: we have a beverage Co. that bottles root beer. Automatic filling machine is used and is adjusted so that the fill is as close as possible to11ounces/bottle. Every hour a random sample of 5 bottles is taken from the process and each bottle content is measured. The results for a five hour bottling run are recorded in the following slide. Test Measurement Results Readings in ounces Sample Number Bottle 1 Bottle 2 Bottle 3 Bottle 4 Bottle 5 X R 1 (hr.1) 11.09 10.95 10.82 11.06 11.23 11.03 0.41 2 (hr.2) 11.02 10.90 10.88 11.21 10.81 10.96 0.40 3 (hr.3) 10.99 10.95 11.01 11.01 10.91 10.97 0.10 4 (hr.4) 11.00 11.02 10.92 10.89 11.01 10.97 0.13 5 (hr.5) 11.06 10.91 11.01 10.86 11.00 10.97 0.20 TOTALS…………………………………………………= 54.90 1.24 GRAND AVERAGES……………………………….…X =10.98, R=0.28
• 7T >QI—CONTROL CHARTS. Calculate upper and lower control limits for both, the X – chart and the R – chart, as follows: Get the factors A2 , D3 , D4 from table. for n = 5 A2 = 0.58 , D3 = 0 , D4 =2.11 Therefore: for the X – chart: UCLx = X + A2 * R = 10.98 + 0.58 * 0.248 = 11.12 LCLx = X - A2 * R = 10.98 – 0.58 * 0.248 = 10.84 For the R – chart:UCL R = D 4 * R = 2.11 * 0.248 = 0.523 LCL R = D 3 * R = 0.0 * 0.248 = 0.000 Now we are ready to draw the charts and make the decision whether to continue bottling or to stop to adjust process.
• 7T >QI—CONTROL CHARTS. UCL = 11.12 X = 10.98 LCL = 10.84 X X X X X Sample Number UCL = 0.523 Ounces R = 0.248 0.00 X X X X Decision: Both charts are within limits, process is in control, continue to produce. ---------------------------------------------- 1 2 3 4 5 X X
• 7T >QI—CONTROL CHARTS-p & c
• P-Chart
• The other name for P-chart is Percent Defective Chart. The purpose of this chart is summarized below.
•
• To discover the average proportion of non- confirming articles or parts submitted for inspection over period of time
• To bring to the management attention, if there is any change in average quality level
•
• 7T >QI—CONTROL CHARTS-p & c
• 7T >QI—CONTROL CHARTS-p & c charts Example  Alpha electronic company manufactures cathode ray tubes on mass production basis. At some intermediate point of production line, 15 samples of size 50 each have been taken. Tubes within each sample were classified into good or bad. The related data are given in the following table. Construct a P-chart with 3 sigma limit and comment on the process .
• 7T >QI—CONTROL CHARTS-p & c charts Comment-- From this figure, it is clear that all points are within the control limits. But there is an upswing toward the right hand side of the figure. This means that there is predominant up-trend which may take the process out of control in future, if no corrective action is taken.
• 7T >QI—CONTROL CHARTS-p & c charts
• C-Chart
• This chart applies to the number of non-conformities in samples of constant size. C is a variable representing the number of non-conformities (defects) in each sample. Usually, the sample size is considered to be one.
• Some applications of C-chart are listed below:
•   To control the number of non-conforming rivets in an aircraft wing
• To control the number of imperfections observed in galvanized sheet
• To control the number of imperfections on a large casting like gear blank which is used to rotate kiln in cement plant
• To control the number of defects in final assemblies (like TV, radio, computer, I.C. engines etc.)
• 7T >QI—CONTROL CHARTS-p & c charts The formulas for control limits are as follows: Where is the mean number of non-conformities. Also, this is the central line in the control chart.
• 7T >QI—CONTROL CHARTS-p & c charts
• 7T >QI—CONTROL CHARTS-p & c charts
• 7T >QI—CONTROL CHARTS -np & u charts The use of attribute control charts arises when items are compared with some standard and then are classified as to whether they meet that standard or not. The np control chart is used to determine if the rate of non-conforming product is stable and will detect when a deviation from stability has occurred. np chart = size of subgroup is CONSTANT. P Chart = size of subgroup is NOT constant np Chart = NUMBER of Defectives. P Chart = Fraction Defective
• 7T >QI—CONTROL CHARTS -np & u charts Steps for Constructing an np Chart Step 1 Collect the data recording the number inspected (n) and the number of defective products (np). Divide the data into subgroups. Usually, the data is grouped by date or by lot numbers. It is strongly recommended stick with the constant sample size of 100 for subgroups . Step 2 Record the number of defectives on a chart or spreadsheet along with the subgroup size. An example of such chart is as follows:
• 7T >QI—CONTROL CHARTS -np & u charts Step 3 Use the following formula to determine Pbar, (P) and percentage defective: _ nP = number of defectives = Total Parts Inspected = np / N *100 (in % defective) =(272 / 2500 )*100=10.88%
• 7T >QI—CONTROL CHARTS -np & u charts Step 4 Compute the control limits using the following formula :
• 7T >QI—CONTROL CHARTS -np & u charts Step 5 Draw in the control limits and plot the number of defective parts listed in our chart above. Connect the dots and observe the chart to determine if there are any points out of the control limits. Out of control
• 7T >QI—CONTROL CHARTS -np & u charts U-Chart This is used when inspection unit value changes For e.g. the carpet was earlier checked for defects in one square metre. Let us say after few such checks instead 1.5 square metre was checked and again it was changed to 1.8 sq metre. In such cases control limits will change accordingly. Steps in Constructing a U-Chart
• Find the number of non-conformities, c(i), and the number of inspection units, n(i), in each sample i.
2. Compute u(i) = c(i)/n(i)
• 7T >QI—CONTROL CHARTS -np & u charts 3. Determine the centerline of the u chart: 4. The u chart has individual control limits for each subgroup i .
• 7T >QI—CONTROL CHARTS -np & u charts 5. Plot the centerline, , the individual LCLs and UCLs and the process measurements, u(i). 6.Interpret the control chart. Example Number Non-conformities Day Number Non- Per Inspected Conformities Unit   1 110 120 1.0909 2 82 94 1.1463 3 96 89 0.9271 4 115 162 1.4087 5 108 150 1.3889 6 56 82 1.4643 7 120 143 1.1917 8 98 134 1.3673 9 102 97 0.9510 10 115 145 1.2609 11 88 128 1.4545 12 71 83 1.1690 13 95 120 1.2632 14 103 116 1.1262 15 113 127 1.1239 16 85 92 1.0824 17 101 140 1.3861 18 42 60 1.4286 19 97 121 1.2474 20 92 108 1.1739 21 100 131 1.3100 22 115 119 1.0348 23 99 93 0.9394 24 57 88 1.5439 25 89 107 1.2022 26 101 105 1.0396 27 122 143 1.1721 28 105 132 1.2571 29 98 100 1.0204 30 48 60 1.2500
• 7T >QI—CONTROL CHARTS -np & u charts Calculations UBAR = 1.2005 Day CL UCL LCL Non-conformities/Unit 1 1.2005 1.513900448 0.887091405 1.09 2 1.2005 1.563485937 0.837505915 1.15 3 1.2005 1.535975424 0.865016429 0.93 4 1.2005 1.507011595 0.893980258 1.41 5 1.2005 1.51678903 0.884202823 1.39 6 1.2005 1.639741695 0.761250158 1.46 7 1.2005 1.500557911 0.900433942 1.19 8 1.2005 1.532534517 0.868457335 1.37 9 1.2005 1.525958845 0.875033008 0.95 10 1.2005 1.507011595 0.893980258 1.26 11 1.2005 1.550892833 0.850099019 1.45 12 1.2005 1.59059276 0.810399092 1.17 13 1.2005 1.537736483 0.86325537 1.26 14 1.2005 1.524375074 0.876616779 1.13 15 1.2005 1.509712226 0.891279627 1.12 16 1.2005 1.55702269 0.843969162 1.08 17 1.2005 1.527566079 0.873425774 1.39 18 1.2005 1.707693252 0.693298601 1.43 19 1.2005 1.534241668 0.866750185 1.25 20 1.2005 1.543190862 0.857800991 1.17 21 1.2005 1.529197361 0.871794491 1.31 22 1.2005 1.507011595 0.893980258 1.03 23 1.2005 1.530853298 0.870138554 0.94 24 1.2005 1.635871613 0.76512024 1.54 25 1.2005 1.548918751 0.852073102 1.20 26 1.2005 1.527566079 0.873425774 1.04 27 1.2005 1.498088223 0.90290363 1.17 28 1.2005 1.521275681 0.879716172 1.26 29 1.2005 1.532534517 0.868457335 1.02 30 1.2005 1.674935581 0.726056271 1.25
• 7T >QI—CONTROL CHARTS- When should you recalculate the control limits?
• Judgement call
• Do the data display a distinctly different kind of behaviour than in the past?
• Is the reason for this change in behaviour known?
• Is the new process behaviour desirable?
• Is it intended and expected that the new process behaviour will continue?
• If yes, then revise the limits
• 7T >QI—CONTROL CHARTS -
• 7T >QI—CONTROL CHARTS -
• 7T >QI—CONTROL CHARTS -
• 7T >QI—CONTROL CHARTS -
• 7T >QI—CONTROL CHARTS - How to Read Control Charts 1) Out of control limits Run Trend
• 7T >QI—CONTROL CHARTS - inappropriate way of sub grouping / means mixing of data with a different population in sub groups., Approach to the control limits Approach to the central line.
• 7T >QI—CONTROL CHARTS - Periodicity
• What Does a Control Chart Do?
• Focuses attention on detecting and monitoring process variation over time;
• Distinguishes special from common causes of variation, as a guide to local or management action;
• Serves as a tool for ongoing control of a process;
• Helps improve a process to perform consistently and predictably for higher quality, lower cost, and higher effective capacity;
• Provides a common language for discussing process performance .
• 7T >QI—CONTROL CHARTS Defect or Nonconformity Data Defective Data Constant Sample Size Variable Sample Size Constant n > 50 Variable n > 50 c chart p or np chart u chart p chart Attributes Variables X bar and R bar chart C ontrol C hart S election:
• 7T >QI—CONTROL CHARTS
• 7T >QI—CONTROL CHARTS GUIDELINES FOR IMPLEMENTING C.C.
• Determining which process characteristic to control
• Determining where the charts should be implemented in the process
• Choosing the proper type of control charts.
• Taking action to improve processes as the result
• Of SPC / Control Chart analysis.
• Selecting data-collection systems and computer
• software
• 7T >QI—CONTROL CHARTS WHICH & WHERE OF C.C. Close to work centers / stations. Beginning >> any product or characteristic which is imp. Analyse feedback . Unnecessary CC should be removed Info on number & types … current. Separate for Variable and Attribute. First no of cc If CC used effectively, X & R bar Charts the attribute charts Beginning >> more attribute charts applied to semi finished or finished units near the end of manufacturing process. As learning process goes on more and more X & R bar charts gets applied earlier in the process Close to the work centers / station
• 7T >QI—CONTROL CHARTS Choose proper type of CC X bar and R Chart. New process or new product by existing process Process is chronically in trouble or not able to hold specs. Trouble some process,CC ….diagnostic (troubleshooting) purpose Destructive testing is required. Reduce sampling or testing procedures Tight specs, overlapping assembly tolerances, or manf problems. Adjustment of process or set-up evaluation Change in product specs. Process stability and capability is desired.
• 7T >QI—CONTROL CHARTS Choose proper type of CC Attribute Charts. When assignable causes are in control. Complex assembly operation & product quality Is measured in occurrences of nonconformities successful or unsuccessful product function Process control is necessary, but measurement data Cannot be obtained. Historical summary is necessary for management review. Remember X bar and R chart are better than attribute charts .
• 7T >QI—CONTROL CHARTS Actions taken to Improve the Process. Primary Obj of SPC is PROCESS IMPROVEMENT . Application of CC Statistical control and Capability . IS THE PROCESS CAPABLE ? IS THE PROCESS IN CONTROL Yes No Yes No SPC SPC SPC SPC Investigate Specs Change process Experimental Design Investigate Specs Change process Experimental Design ideal Excessive scrap or rework due to variability SPC good, read patterns Specs are wide ..in Control Continue SPC
• 7T >QI—CONTROL CHARTS Process Improvement using CC Process Measurement System Input Output Detect assignable cause Identify root cause of the problem Implement Corrective Action Verify and follow up
• 7T >QI—CONTROL CHARTS Process Improvement using CC Designed experiment…. Discovering the key variables influencing the quality characteristics of interest in the process. Is an approach to systematically vary the controllable input factors and determine the effect these factors have on the output product parameters. ( Factorial Design)
• 7T>QI SAMPLING INSPECTION ACCEPTANCE SAMPLING
• 7T>QI SAMPLING INSPECTION Purpose: Screening, Prevention and Reporting. Methods of Inspection: Total Inspection, Sampling Inspection, Inspection w/o testing . Types / Kinds Acceptance, Process, and Final Inspection
• 7T>QI SAMPLING INSPECTION ACCEPTANCE SAMPLING The objective of acceptance sampling is to take decision whether to accept or reject a lot based on sample’s characteristics. The lot may be incoming raw material or finished parts. An accurate method to check the quality of lots is to do 100% inspection. But 100% inspection will have the following limitations:  i)                   The cost of inspection is high. ii)                   Destructive methods of testing is not feasible. iii)                 Time taken for inspection will be to long. iv)                 When the population is large or infinite, it would be impossible or impracticable to inspect each unit. Hence, acceptance-sampling procedures has a lot of scope in practical application. Acceptance sampling can be used for attributes as well as variables.
• 7T>QI SAMPLING INSPECTION ACCEPTANCE SAMPLING For e.g. The sampling plan is as follows: Let the size of incoming lot be N and the size of the sample drawn be n (say 50) and an Acceptance number C (say 3). If the number of defective pieces is less or equal to 3, then accept the whole lot from which the sample is drawn, otherwise reject the lot. This is called single sampling plan.
• % Defective in Lot P(Accept Whole Shipment) 100% 0% Cut-Off Return whole shipment Keep whole shipment OC Curve 100% Inspection 1 2 3 4 5 6 7 8 9 10 0
• OC Curve with Less than 100% Sampling P(Accept Whole Shipment) 100% 0% % Defective in Lot Cut-Off 1 2 3 4 5 6 7 8 9 10 0 Return whole shipment Keep whole shipment Probability is not 100%: Risk of keeping bad shipment or returning good one.
• 7T>QI SAMPLING INSPECTION ACCEPTANCE SAMPLING TWO TYPES OF ERROR . Producer’s Risk or Type 1 error. Means lot good, but sampling plan rejects Consumer’s Risk or Type 2 error. Means lot bad, but sampling plan accepts.
• ACCEPTANCE SAMPLING-O.C.Curve. AOQL= Acceptable Quality Level, Customer satisfied. Probability of Acceptance= (1- ) LTPD=Lot Tolerance % defectives, Probability of Acceptance= Customer not satisfied
• Acceptable quality level (AQL)
• Quality level of a good lot
• Producer (supplier) does not want lots with fewer defects than AQL rejected
• Lot tolerance percent defective (LTPD)
• Quality level of a bad lot
• Consumer (buyer) does not want lots with more defects than LTPD accepted
AQL & LTPD
• ACCEPTANCE SAMPLING-O.C.Curve. AOQL= Acceptable Quality Level, Customer satisfied. Probability of Acceptance= (1- ) LTPD=Lot Tolerance % defectives, Probability of Acceptance= Customer not satisfied
• Acceptance Sampling O.C.Curve.
• Acceptance Sampling O.C.Curve.
• Drawing the O C Curve Steps:
• Multiply p by the sample size, n
• 2. Find the value of np in the left column of the table.
3. Move to the right until you find the column for c. 4. Record the value for the probability of acceptance, Pa. When p = AQL, the producer’s risk, α, is 1 minus the probability of acceptance. When p = LTPD, the consumer’s risk,  , equals the probability of acceptance.
• Drawing the O C Curve Example Shipment of 1000 mufflers. Sample size n = 60 Acceptance number c = 1. AQL of 1 defective muffler per 100 LTPD of 6 defective mufflers per 100. Calculate the operating characteristics curve for this plan and determine the producer and consumer’s risk for the plan.
• Drawing the O C Curve
• Drawing the O C Curve
• ACCEPTANCE SAMPLING –ATTRIBUTES. Three often-used attribute-sampling plans are as follows:           Single-sampling plan          Double-sampling plan         Sequential sampling plan
• ACCEPTANCE SAMPLING –ATTRIBUTES.
• ACCEPTANCE SAMPLING –ATTRIBUTES
• Summary
• Variation exists in every process
• Uncontrolled/Special cause
• Controlled/Common cause
• Start by plotting data over time