Methods And Philosophy Of Statistical Process Control (SPC) PDF

METHODS AND PHILOSOPHY OF STATISTICAL PROCESS CONTROL (SPC) IE 3111 - QMS General Objectives u To present the basic statistical process control (SPC) problem-solving tools, called the magnificent seven. u To describe the statistical basis for the Shewhart control chart. u To discuss and...

METHODS AND PHILOSOPHY OF STATISTICAL PROCESS CONTROL (SPC) IE 3111 - QMS General Objectives u To present the basic statistical process control (SPC) problem-solving tools, called the magnificent seven. u To describe the statistical basis for the Shewhart control chart. u To discuss and illustrate some practical issues in the implementation of SPC. What is Statistical Process Control (SPC)? u Is a powerful collection of problem-solving tools useful in achieving process stability and improving capability through reduction of variability. u Its seven major tools are: Magnificent Seven A. Histogram or stem-and-leaf plot E. Defect Concentration Diagram B. Check sheet F. Scatter Diagram C. Pareto chart G. Control Chart D. Cause-and-effect diagram Which of the 7 is the most technically sophisticated? SPC – BASIC TOOLS Chance and Assignable Causes of Quality Variation u Natural Variability or Background Noise u Is the cumulative effect of many small, essentially unavoidable causes. u Often called the “Stable system of chance causes” In statistical control u Possible sources of variation: 1. Environmental Factors (Temperature, humidity, air quality fluctuations) 2. Characteristics of Raw Materials 3. Machine equipment Precision (Machine tolerance, wear and tear) 4. Operator Influence (reaction time, force application, skills levels) Chance and Assignable Causes of Quality Variation u Possible sources of variation: 5. External Disturbances (Vibrations and Mechanical disturbances) 6. Process Aging 7. Measurement and Sampling Variability 8. Supply Chain Variability Chance and Assignable Causes of Quality Variation u Assignable Causes of Variation u Such variability is generally large when compared to the background noise u Usually represents an unacceptable level of process performance. Out-of-control process u 3 major sources of variation: 1. Improperly adjusted or controlled machines 2. Operator errors 3. Defective raw material Chance and Assignable Causes of Quality Variation u NO PROCESS IS TRULY STABLE FOREVER, so the objective shall be to quickly detect the occurrence of assignable causes of process shifts so that investigation of the process and corrective action may be undertaken before many nonconforming units are manufactured. Control Chart Ø Elimination of variability in the process. Statistical Basis of the Control Chart Quick Recap What is a quality characteristic in the context of product or service quality? A. A measurable attribute or characteristic that defines the overall performance of a product or service. B. The cost associated with producing, identifying, avoiding, or repairing non-conforming products. C. The process of evaluating and measuring the conformity of products to established standards. D. The category of costs that are incurred in efforts to prevent non-conformance. E. The analysis of financial controls and budget variances related to quality management. Basic Principles u A graphical display of a quality characteristic that has been measured or computed from a sample versus the sample number or time. u Contains CL, UCL, & LCL u In control – all control points fall between UCL &LCL. No Action is needed. u Out-of-control – point(s) plots outside any of the control limits. Action needed. Basic Principles u Scenario: All points are plotted inside the control limits, however, 18 out of 20 of these points are plotted above the center line in a systematic or non-random manner. Is the process in control or out of control? u Control Charts and Hypothesis Testing (Similarity) u Hypothesis: The process is in a state of statistical control. u A point plotted with the control limits means failure to reject the hypothesis. u A point plotted outside the control limits means the hypothesis is rejected. Basic Principles u Control Charts and Hypothesis Testing (Difference) u Hypothesis Tests: It is crucial to verify certain assumptions, e.g. distributional form of the data or the assumption of independence. These assumptions are necessary for the validity of the test results. u Control Charts: In contrast, CC is primarily used for detecting deviations. Thus, worrying about assumptions may not be necessary. The focus is more on monitoring and maintaining process stability. Basic Principles u Process Shifts Due to Assignable Causes (Types) 1. Sustained Shift – This refers to a situation where the process ‘mean ’ has shifted to a new value and remains consistently at that level. 2. Abrupt Shift – The mean could also shift suddenly, but the assignable cause might be short-lived, and the process could return to its original state. 3. Steady Drift or Trend – An assignable cause might lead to a gradual continuous change in the process mean over time. Basic Principles u Hypothesis Testing in Control Charts u Type 1 Error: This occurs when the control chart wrongly signals that the process is out of control, when in fact it is in control. FALSE Positive. u Type 2 Error: This occurs when the control chart fails to signal that the process is out of control when it is actually not in control. FALSE Negative. Basic Principle u Photolithography – an important fabrication step in semiconductor manufacturing. u Flow width of the resist – a CTQ in the hard bake process that measures how much it expands due to the baking process. Basic Principle u Given: the mean is 1.5 microns; 0.15 microns for the standard deviation. u An x-bar control chart is shown. u Subgroup size – 5 wafers per hour u Is the process in statistical control? Basic Principle u What is the statistical basis of the control limits? Basic Principle u What is the statistical basis of the control limits? Basic Principle Basic Principle u General Model for Control Chart u w sample statistic that measures a CTQ of interest u µ sub w is the mean u 𝛔 sub w is the standard deviation u L distance of the control limits from the center line, expressed in stdev Basic Principle u Generally, 1. Most processes do not operate in a state of statistical control 2. The routine and attentive use of control charts will assist in identifying assignable causes. Eliminate these causes to reduce variability and improve the process. 3. Control Chart only detects assignable causes. Management, operator, and engineering actions are necessary to eliminate causes. Out-of-Control Plan (OCAP) u a detailed set of instructions, presented in the form of a flowchart or text, that outlines the specific steps that need to be taken in response to an activating event. u Elements of OCAP u Checkpoints: These are potential assignable causes for the observed out-of-control signal. Serves as reference points for investigation. u Terminators: These are the actions taken to rectify the out-of-control condition. u OCAP is a living document. Design of Control Chart u Refers to the selection of the following: 1. Sample size 2. Control limits 3. Frequency of sampling u Economic point of view, we explicitly consider: 1. Cost of sampling 2. Losses from allowing defective products to be produced 3. Cost of investigating out-of-control signals that are false alarms  Design of Control Chart: Type of Variability u Stationary behavior – the process data vary around a fixed mean in a stable and predictable manner. u Uncorrelated – the data gives the appearance of having been drawn at random from a stable population, perhaps normal distribution. u Autocorrelated – data are dependent; that is a value above the mean tends to be followed by another such value. Control Chart’s Reason for Popularity 1) Control charts are a proven technique for improving productivity. Ø Reduces scrap and rework 2) Control charts are effective in defect prevention. Ø Consistent with the “Do it right the first time” philosophy. 3) Control charts prevent unnecessary process adjustments. Ø Consistent with the “If it isn’t broken, don’t fix it” philosophy 4) Control charts provide diagnostic information Ø Allows the implementation of a change in the process. 5) Control charts provide information about process capability. Ø Useful for product and process designers. Two Limits on Control Charts u Action Limits – the outer limits say at three sigma. A point plotted outside of these limits, a search for assignable cause is made and corrective action is taken if necessary. u Warning limits – the inner limits, usually at two sigma. Points plotted between warning and control limits shall be suspicious that the process may not be operating properly. Two Limits on Control Charts u Adaptive or variable sampling interval (or variable sample size) – Process control schemes that change the sample size and or the sampling frequency depending on the position of the current sample value.  Sample Size u Refers to the number of observations or data points collected in each sample taken from the process. u A larger sample size detects small shifts more easily. This comes with more information about process variation and, thus more precise estimate of the process parameters. u When choosing the appropriate sample size, it is essential to consider the size of the shift you want to detect. Sampling Frequency u Refers to how often samples are taken from the process. It determines the rate at which data points are collected and plotted on the control chart. u Ideally, frequent sampling, where samples are taken at short intervals, enhances the ability to detect shifts quickly. u Frequent sampling may not be economical. Average Run Length (ARL) u A key metric used to evaluate the performance of a control chart. u It represents the average number of data points that need to be plotted on the control chart before an out-of-control condition is detected. u Where p is the probability that any point exceeds the control limits. Average Run Length (ARL) Average Run Length (ARL) Rational Subgroup u Goal: to enhance the sensitivity of control charts in detecting meaningful changes or shifts in the process. u Maximizing Inter-Subgroup Differences u This means if an assignable cause is present it is more likely to significantly manifest. u Minimizing Intra-Subgroup Differences u Differences within a subgroup are most likely due to random or common causes. u Time Order of Production u This basis for subgrouping allows us to capture changes or trends in the process over time. Rational Subgroup: Approaches A. Snapshot Approach Ø Each sample consists of units that were produced at the same time (or as closely together as possible) Ø When to use? To detect process shifts. Ø Advantage: maximize inter-subgroup differences; minimize intra-subgroup differences. Rational Subgroup: Approaches B. Random Sample Approach Ø All subgroup is a random sample of all process output over the sampling interval. Ø When to use? To make decisions about the acceptance of all units of products produced within the interval.  Analysis of Patterns on Control Charts u Observations: u All 25 points fall within CL; the pattern is very non-random. u 19 out of 25 points plot below the CL. u Starting at the 4th point, 5 points in a row increase in magnitude. This is called a run, specifically run up. u Starting at the 18th point, an unusually long run down can be observed. u Run length of 8 or more is often taken as a signal of an out-of-control condition.  Analysis of Patterns on Control Charts u Observations: u The plotted sample averages exhibit a cyclic behavior, yet they all fall within the control limits. u Indicates a problem with the process such as operator fatigue, raw material deliveries, heat or stress buildup, and so forth. Question u The ability to interpret a particular pattern in terms of assignable causes requires: a. Experience b. Knowledge of the Process c. Know the principles of control charts d. All of the above Analysis of Patterns on Control Charts u Set of decision rules for detecting nonrandom patterns on control charts. (Suggested by Western Electric Statistical Quality Control Handbook (1956)) 1. One-point plots outside the three-sigma control limits 2. Two out of three consecutive points plot beyond the two-sigma warning limits. 3. Four out of five consecutive points plot at a distance of one sigma or beyond from the center line, or 4. Eight consecutive points are plotted on one side of the center line. u These suggest concluding that the process is out of control. Analysis of Patterns on Control Charts Sensitizing Rules for Control Charts The Rest of the Magnificent Seven Check Sheet u Purpose: Collecting historical or current operating data for process investigation. u Commonly used in the “Measure” step of DMAIC. u Key Components of a Check Sheet: u Type of data to be collected, Part or Operation Number, Date, Analyst’s Name, and Additional information for diagnosing poor performance. u Design Consideration: u Clearly specify the data to be collected. u Ensure suitability for further calculations or computer data entry. u Conduct a trial run for layout and design validation. Check Sheet Pareto Chart u A visual tool used in the Measure and Analysis steps of DMAIC. u It represents a frequency distribution of attribute data arranged by category. u Helps identify the most frequently occurring types of defects or issues. u Does not automatically prioritize by importance, only by frequency. u Consider using a weighing scheme for defects with varying consequences. Pareto Chart u A visual tool used in the Measure and Analysis steps of DMAIC. u It represents a frequency distribution of attribute data arranged by category. u Helps identify the most frequently occurring types of defects or issues. u Does not automatically prioritize by importance, only by frequency. u Consider using a weighing scheme for defects with varying consequences. Pareto Chart Cause-and-Effect Diagram u Is a formal tool frequently useful in un-layering potential causes. u This diagram is useful in the Analyze and Improve steps of DMAIC. u Constructed by a quality improvement team assigned to identify problem areas. Cause-and-Effect Diagram Defect Concentration Diagram u Defect Concentration Diagram: Used in the analyze step of DMAIC. u Provides a visual representation of the unit with all relevant views. u Defect types are drawn on the diagram to analyze their location for potential causes. Defect Concentration Diagram Scatter Diagram u A useful plot for identifying a potential relationship between two variables. u Then y is plotted against the corresponding x. u The shape of the scatter diagram often indicates what type of relationship may exist between two variables – regression modeling. u This diagram is useful in the analyze step of DMAIC. Scatter Diagram