The Relationship Between Statistical Quality Control SQC and
The Relationship Between Statistical Quality Control (SQC) and Statistical Process Control (SPC) • Statistical Process Controls (SPC) are Activities which monitor a process in real-time to prevent defects while a lot is being manufactured. • In contrast, activities which occur after manufacture to keep defects from reaching a patient by additional inspection are known as Statistical Quality Control (SQC). 2
• What is the meaning of statistics? • 1 : a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data. 2 : a collection of quantitative data. • Statistical Measures. → Measures used in statistics, such as mean, variance and standard deviation, and the difference between sample and population. Errors, Uncertainty, and Residuals. • What are statistical calculations? • The most common calculated statistical values are mean, median, and mode. The mean, the average or arithmetic mean, is computed by adding all the values and dividing by the number of values. . The most frequent value is called the mode. In a bell curve, the median, mode, and mean are equal. • What are the different types of statistical tools? • The most well known Statistical tools are the mean, the arithmetical average of numbers, median and mode, Range, dispersion , standard deviation, inter quartile range, coefficient of variation, etc. There also software packages like SAS and SPSS which are useful in interpreting the results for large sample 3 size.
• What are two types of statistics? • The two major areas of statistics are known as descriptive statistics, which describes the properties of sample and population data, and inferential statistics, which uses those properties to test hypotheses and draw conclusions. • Do you need statistics for chemistry? • Statistics is important in chemistry, specially in Analytical chemistry because it helps in the presentation of problems in data analysis and demonstrating steps to solve them. • Why do we need statistics? • Statistical methods are required to ensure that data are interpreted correctly and that apparent relationships are meaningful (or “significant”) and not simply chance occurrences. . The linear trend is another example of a data “statistic”. Two important concepts in statistics are the “population” and the “sample”. 4
Calculations of the Mean, Standard Error of the Mean (SEM) • Standard Error Calculator • The standard error of the mean (SEM) is the standard deviation of the sample mean estimate of a population mean. It is usually calculated by the sample estimate of the population standard deviation divided by the square root of the sample size. • SEM is calculated by taking the standard deviation and dividing it by the square root of the sample size. • standard deviation = √(s²) = s = ∑(xᵢ - x )² / (N-1) for a sample, where s² is the estimate of the variance. • standard error of the mean = s/√N = ∑(xᵢ - x )² / (N*(N-1)). • Where: • SEM = standard error of the mean • s = sample standard deviation (see formula below) • n = size (number of observations) of the sample 5
• The following is the sample standard deviation formula: • Where: s = sample standard deviation x 1, . . . , x. N = the sample data set x = mean value of the sample data set N = size of the sample data set 6
• About Sum (Summation) • The Sum (Summation) Calculator is used to calculate the total summation of any set of numbers. In mathematics, summation is the addition of a sequence of any kind of numbers, called addends or summands; the result is their sum or total. • About Average Calculator • About The Average Calculator is used to calculate the average value of any set of numbers. Suppose we have sample space a 1, a 2, . . . , an. Then the average value is defined via the following equation: Average = (a 1 + a 2 +. . . + an) / n Median Calculator: What is Median value In probability theory and statistics, the median is the middle data value of a set of values when the data have been arranged into order. If there is an even number of data, then there is no single middle value; the median is then usually defined to be the mean of the two middle values. • About Median Calculator • The Median Calculator is used to calculate the median value of a set of given numbers. 7
• About Percent Off Calculator • The Percent Off Calculator is used to calculate the sale price of a discounted item after the percent off discount is applied. Updated with new simple percent off function. Input the original price once, and get all prices from 5% off up to 75% off instantly. • The percent off calculation formula is as follows: Sale price = Original price × (1 - Percent off%) • For example, if you take 20 percent off of a $100 item, the sale price will be 100 × (1– 20%) = $80. • How do you calculate SD and SEM? • How is the SEM calculated? The SEM is calculated by dividing the SD by the square root of N. This relationship is worth remembering, as it can help you interpret published data. If the SEM is presented, but you want to know the SD, multiply the SEM by the square root of N. 8
• • • • CONFIDENCE INTERVAL: A Confidence Interval is a range of values we are fairly sure our true value lies in. How do I calculate 95% confidence interval? We can use the standard deviation for the sample if we have enough observations (at least n=30, hopefully more). Using our example: number of observations n = 40. mean X = 175. Calculating the Confidence Interval Step 1: start with the number of observations n the mean X and the standard deviation s Note: we should use the standard deviation of the entire population, but in many cases we won't know it. We can use the standard deviation for the sample if we have enough observations (at least n=30, hopefully more). Using our example: number of observations n = 40 mean X = 175 standard deviation s = 20 9
• Step 2: decide what Confidence Interval we want: 95% or 99% are common choices. Then find the "Z" value for that Confidence Interval here: • • • Confidence Interval Z 80% 1. 282 85% 1. 440 90% 1. 645 95% 1. 960 99% 2. 576 99. 5% 2. 807 99. 9% 3. 291 For 95% the Z value is 1. 960 10
• Example: Average Height • We measure the heights of 40 randomly chosen men, and get a mean height of 175 cm, • We also know the standard deviation of men's heights is 20 cm. • The 95% Confidence Interval (we show to calculate it later) is: 175 cm ± 6. 2 cm • • This says the true mean of ALL men (if we could measure all their heights) is likely to be between 168. 8 cm and 181. 2 cm. • But it might not be! • The "95%" says that 95% of experiments like we just did will include the true mean, but 5% won't. • So there is a 1 -in-20 chance (5%) that our Confidence Interval does NOT include the true mean. 11
• Step 3: use that Z value in this formula for the Confidence Interval • • • X ± Zs√n Where: X is the mean Z is the chosen Z-value from the table above s is the standard deviation n is the number of observations And we have: 175 ± 1. 960 × 20√ 40 Which is: 175 cm ± 6. 20 cm In other words: from 168. 8 cm to 181. 2 cm The value after the ± is called the margin of error The margin of error in our example is 6. 20 cm 12
• What is quality tools and techniques? • There are seven basic quality tools identified as appropriate for use in both the quality management plan and control quality processes. They are known as Ishikawa's seven basic tools of quality: cause-and-effect diagrams, flowcharting, check sheets, Pareto diagrams, control charts, histograms and scatter diagrams. • What is statistical process control example? • Key tools used in SPC include run charts, control charts, a focus on continuous improvement, and the design of experiments. An example of a process where SPC is applied is manufacturing lines. . In addition to reducing waste, SPC can lead to a reduction in the time required to produce the product. 13
What is meant by Decision Theory in Statistics? • Decision theory, in statistics, a set of quantitative methods for reaching optimal decisions. A solvable decision problem must be capable of being tightly formulated in terms of initial conditions and choices or courses of action, with their consequences. In general, such consequences are not known with certainty but are expressed as a set of probabilistic outcomes. Each outcome is assigned a “utility” value based on the preferences of the decision maker. An optimal decision, following the logic of theory, is one that maximizes the expected utility. Thus, the ideal of decision theory is to make choices rational by reducing them to a kind of routine calculation. • Decision analysis, also called statistical decision theory, involves procedures for choosing optimal decision in the face of uncertainty…. 14
What are the statistical analysis tools? • The Top 7 Statistical Tools You Need to Make Your Data Shine • SPSS (IBM) SPSS, (Statistical Package for the Social Sciences) is perhaps the most widely used statistics software package within human behavior research. . • R (R Foundation for Statistical Computing). . . • MATLAB (The Mathworks). . . • Microsoft Excel. . • SAS (Statistical Analysis Software). . . • Graph. Pad Prism. . • Minitab. • What is K value in statistics? • › k is the constant dependent on the hypothesized distribution of the sample mean, the sample size and the amount of confidence desired. › • n is the number of observations in the sample. › Note that (standard deviation / √n) is the standard error of the mean and is a measure of how good our estimate of the mean is. 15
WHAT IS MEANT by statistical significance-P • What does P 0. 03 mean? • statistically significant • So, you might get a p-value such as 0. 03 (i. e. , p =. 03). This means that there is a 3% chance of finding a difference as large as (or larger than) the one in your study given that the null hypothesis is true. However, you want to know whether this is "statistically significant". • What does P 0. 05 mean? • P > 0. 05 is the probability that the null hypothesis is true. 1 minus the P value is the probability that the alternative hypothesis is true. A statistically significant test result (P ≤ 0. 05) means that the test hypothesis is false or should be rejected. A P value greater than 0. 05 means that no effect was observed. • What is the P value formula? • The p-value is calculated using the sampling distribution of the test statistic under the null hypothesis, the sample data, and the type of test being done (lower-tailed test, upper-tailed test, or two-sided test). . an upper-tailed test is specified by: p- 16
• What does P in research mean? • What is the P value? The P value means the probability, for a given statistical model that, when the null hypothesis is true, the statistical summary would be equal to or more extreme than the actual observed results. • What is a good P value? • The smaller the p-value, the stronger the evidence that you should reject the null hypothesis. A p-value less than 0. 05 (typically ≤ 0. 05) is statistically significant. It indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null is correct (and the results are random). 17
• What is a nominal P value? • The nominal p-value is a calculated observed significance based on a given statistical model. When the statistical model reflects the actual test performed the nominal and actual pvalue coincide. . Violating any of the prerequisites of a significance test will render the nominal p-value more or less non-actionable. • What is p value in Anova? • The p-value is the area to the right of the F statistic, F 0, obtained from ANOVA table. It is the probability of observing a result (Fcritical) as big as the one which is obtained in the experiment (F 0), assuming the null hypothesis is true. Low pvalues are indications of strong evidence against the null hypothesis. 18
• What do the probability symbols mean? • The conditional probability of Event A, given Event B, is denoted by the symbol P(A|B). . The probability of the intersection of Events A and B is denoted by P(A ∩ B). If Events A and B are mutually exclusive, P(A ∩ B) = 0. The probability that Events A or B occur is the probability of the union of A and B. 19
• What are the 6 steps involved in statistical process control? Statistical Process Control technique steps include detection, study, prioritization, illumination and then charting. Before using quality control software collect proper data for analysis. What are the limitations of statistical quality control? The limitations of statistical quality control are: It cannot be indiscriminately applied as a solution to all quality evils. Implementation of statistical quality control is a costly endeavour. A false sense of security is created in absence of general awareness. 20
• What is meant by statistical quality control? • Statistical quality control: Use of statistical methods to measure and improve the quality of manufacturing processes and products. The term "statistical process control" is often used interchangeably. Synonyms. statistical process control. • What are process control techniques? • Statistical process control (SPC) is a method of quality control which employs statistical methods to monitor and control a process. This helps to ensure that the process operates efficiently, producing more specification-conforming products with less waste (rework or scrap). 21
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BRIEF DEFINITION & EXPLANATION OF THE 7 BASIC QUALITY TOOLS OF THE SPC METHODS • The 7 Basic Tools of QC are fundamental instruments to improve the process and product quality. They are used to examine the production process, identify the key issues, control fluctuations of product quality, and give solutions to avoid future defects. They are The Appropriate Techniques for Solving Quality Problems in the Organizations. • Figure 1 indicates the relationships among these seven tools and their utilizations for the identification and analysis of improvement of quality (Kerzner, 2009): Figure 1: The seven quality control tools (Kerzner, 2009). 23
• Check Sheet: simple forms with certain formats that can aid the user to record data in an firm systematically. Data are “collected and tabulated” on the check sheet to record the frequency of specific events during a data collection period. • Histogram: is very useful tool to describe a sense of the frequency distribution of observed values of a variable. It is a type of bar chart that visualizes both attribute and variable data of a product or process, also assists users to show the distribution of data and the amount of variation within a process. It displays the different measures of central tendency (mean, mode, and average). Figure 3 illustrates a histogram of the frequency of defects in a manufacturing process: Figure 2: Histogram for variables 24
• Pareto Chart: is a special type of histogram that can easily be applied to find and prioritize quality problems, conditions, or their causes of in the organization. . On the other hand, it is a type of bar chart that shows the relative importance of variables, prioritized in descending order from left to right side of the chart. The aim of Pareto chart is to figure out the different kind of “nonconformity” from data figures, maintenance data, repair data, parts scrap rates, or other sources. Figure 3: Pareto Charts 25
• Scatter Diagram: is a powerful tool to draw the distribution of information in two dimensions, which helps to detect and analyze a pattern relationships between two quality and compliance variables (as an independent variable and a dependent variable), and understanding if there is a relationship between them, so what kind of the relationship is (Weak or strong and positive or negative). The shape of the scatter diagram often shows the degree and direction of relationship between two variables, and the correlation may reveal the causes of a problem. The scatter diagram can indicate that there is which one of these following correlation between two variables: a) Positive correlation; b) Negative correlation, and c) No correlation, as demonstrated in Figure 4: Figure 6: Scatter Diagrams 26
• Flow Chart: presents a diagrammatic picture that indicates a series of symbols to describe the sequence of steps exist in an operation or process. On the other hand, a flowchart visualize a picture including the inputs, activities, decision points, and outputs for using and understanding easily concerning the overall objective through process. This chart as a problem solving tool can apply methodically to detect and analyze the areas or points of process may have had potential problems by “documenting” and explaining an operation, so it is very useful to find and improve quality into process, as shown in Figure 5: Flow chart of review process 27
• Cause-&-Effect Diagram: also called ‘Fishbone’ diagram, because the shape of the diagram looks like the skeleton of a fish. It is a problem-solving tool that investigates and analyzes systematically all the potential or real causes that result in a single effect. It is to identify quality problems based on their degree of importance. On the other hand, it is an efficient tool that equips the organization's management to explore for the possible causes of a problem. This diagram can provide the problemsolving efforts by “gathering and organizing the possible causes, reaching a common understanding of the problem, exposing gaps in existing knowledge, ranking the most probable causes, and studying each cause”. The generic categories of the cause and effect diagram are usually six elements (causes) such as environment, materials, machine, measurement, man, and method, as indicated in Figure 6. Furthermore, “potential causes” can be indicated by arrows entering the main cause arrow. Figure 6: The cause and effect diagram (Fishbone Diagram) 28
• Control Chart or Shewhart control chart: is a special form of “run chart that it illustrates the amount and nature of variation in the process over time”. Also, it can draw and describe what has been happening in the process. Therefore, it is very important to apply control chart, because it can observe and monitor process to study process that is in “statistical control” (No problem with quality) accordant to the samplings or samplings are between UCL and LCL (upper control limit (UCL) and the lower control limit (LCL)). “statistical control” is not between UCL and LCL, so it means the process is out of control, then control can be applied to find causes of quality problem, as shown in Figure 7 that A point is in control and B point is out of control. The main aim of control chart is to prevent the defects in process. A Control Chart is presented in the following Figure: Figure 8: The Shewhart control chart 29
THE POPULAR SPC TOOLS • The control chart, helps one record data and lets you see when an unusual event, such as a very high or low observation compared with "typical" process performance, occurs. • Control charts attempt to distinguish between two types of process variation: • Common cause variation, which is intrinsic to the process and will always be present • Special cause variation, which stems from external sources and indicates that the process is out of statistical control • Various tests can help determine when an out-of-control event has occurred. However, as more tests are employed, the probability of a false alarm also increases. • More Control Charts were shown in Slides # 35 and 36 below. 30
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CONCLUSION OF APPLYING ALL 7 QC TOOLS • This study identified that is very essential to apply all seven QC tools for Troubleshooting issues within production processes in the Pharmaceutical Industry. Doubtlessly, all of the aforementioned quality tools should be considered and used by management for identifying and solving quality problems during producing the products and services. Thus, the production processes can be affected and improved by multiple factors of these statistical QC tools. Also, based on the performance of these tools, it was designed and developed an effective layout for using these QC in the industry in order to apply appropriately these quality tools for solving quality problems and quality improvement, as demonstrated in Figure 9 below. Accordingly, the following Figure interprets how the 7 QC should be employed from first step to end of production processes for identifying the 33
7 Steps To Set Up Statistical Process Control (SPC) On Production Processes • What is Statistical Process Control? Before we break down the steps, we first need to understand what Statistical Process Control (SPC) is. SPC can help a factory measure and control quality by gathering data to monitor the production process. It not only allows factories to operate at its highest capacity but also sets the foundation for continuous improvement. • Statistical Process Control technique steps include detection, • - study, • - prioritization, • - illumination and then • - charting. Before using quality control software collect proper data for analysis. • - • 34
To understand how this SPC tool works, it is best to follow the logical steps in its implementation in a factory: • 1. Select critical-to-quality (CTQ) product characteristics • 2. Select critical processes • 3. Determine if machines can calculate SPC by themselves • 4. Gather data and process knowledge of what impacts the output of the process • 5. Control independent variables that have a sizeable impact on the process output • 6. Look for ways to reduce variation • 7. Keep it up in the long term 35
FIGURE SUMMAEIZING THE 7 QC TOOLS FROM FIRST STEP TO END OF PRODUCTION PROCESSES Figure 9: An appropriate layout for using 7 QC tools with the aim of improving extremely quality performance 36
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References • 1. Forbes, L H. & Ahmed S. M. (2011). Modern construction : lean project • delivery and integrated practices. Boca Raton, Fly: Taylor and Francis Group. • 2. Juran, M. , and Godfrey, A. (1998). Juran’s quality handbook (5 th ed. ). • Washington, DC: Mc. Graw-Hill Companies, Inc. • 3. Kerzner, H. (2009). Project Management: A Systems Approach to Planning, Scheduling, and Controlling (10 th ed. ). Hoboken, New Jersey: John Wiley & Sons, Inc. • 4. Mirko S. , Jelena J. , Zdravko K. , & Aleksandar V. (2009). Basic Quality Tools in Continuous Improvement. Journal of Mechanical Engineering, 55(5), pp. 1 -9. • 5. Montgomery, D. C. (2009). Introduction to Statistical Quality Control (6 th ed. ). Danvers, MA: John Wiley & Sons, Inc. 40
• 6. Neyestani B. (2017, February). “Principles and Contributions of Total Quality Management (TQM) Gurus on Business Quality Improvement. ” https: //doi. org/10. 5281/zenodo. 345428 • 7. Oakland, J. S. (2003). Total Quality Management: text with cases (3 rd ed. ). Jordan Hill, Oxford, UK: Butterworth-Heinemann, an imprint of Elsevier. • 8. Oberlender, G. D. (2000). Project Management for Engineering and Construction (2 nd ed. ). New York, USA: Mc. Graw-Hill Companies, Inc. • 9. Omachonu, V. K. & Ross, J. E. (2004). Principles of total quality (3 rd ed. ). Boca Raton, Florida: Taylor & Francis. • 10. Neyestani B. (2017, March). “Seven Basic Tools of Quality Control: The Appropriate Quality Techniques for Solving Quality Problems in the Organizations. ” 41 https: //doi. org/10. 5281/zenodo. 400832
Definition of the Techniques used in SQC. • Statistical quality control requires usage of acceptance sampling and process control techniques. Statistical quality control extensively uses chart to measure the acceptance level of the product samples. Objective is to ensure that products fall within pre-decided upper control and lower control limits. • QC Tools and Techniques Include: Chart Control Chart Fish-bone Diagram Pareto 42
Histogram Scatter plot Flowchart 43
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