FUNDAMENTAL STATISTIC BPT 2423 – STATISTICAL PROCESS CONTROL

CHAPTER OUTLINE Definition of Statistics Populations versus Samples Data Collection Data Analysis Graphical & Analytical Measurements Accuracy, Precision & Error Central Limit Theorem

LESSON OUTCOMES Recall or review basic statistical concepts Understand how to graphically and analytically study a process by using statistics Explain how to create and intercept a frequency diagram and a histogram Able to calculate the mean, median, mode, range and standard deviation for a given set of numbers Discuss the importance of the normal curve and the central limit theorem in quality assurance

INTRODUCTION If things were done right just 99.9% of the time, then we’d have to accept: One hour of unsafe drinking water per month 20,000 incorrect drug prescriptions per year 500 incorrect surgical operations each week 22,000 checks deducted form the wrong bank accounts per hour Each of the above statistics deals with the quality of life as we know it. We use statistics every day to define our expectations of life around us. Statistics, when used in quality assurance, define the expectations that the consumer and the designer have for the process. Processes and products are studied using statistics.

DEFINITION OF STATISTICS STATISTICS : the collection, tabulation, analysis, interpretation and presentation of numerical data. Provide a viable method of supporting or clarifying a topic under discussion Misuses of statistics have lead people to distrust them completely Correctly applied statistics are the key that unlocks an understanding of process and system performance.

POPULATIONS VS SAMPLES A population is a collection of all possible elements, values or items associated with a situation Example : Insurance forms at doctor’s office must be process in a day A sample is a subset of elements or measurements taken from a population Example : The doctor’s office may wish to sample 10 insurance claim forms per week to check the forms for completeness. This smaller group of data is easier to collect, analyze and interpret. A sample will represent the population as long as the sample is RANDOM and UNBIASED.

POPULATIONS VS SAMPLES In a random sample, each item in the population has the same opportunity to be selected In order to interpret and use the information, it is critical to know: How many were sampled Validity of a sample The size of the whole group The conditions under which the survey was made

DATA COLLECTION Variable Attribute 2 types of statistics exist : Deductive statistics – describe a population or complete group of data Inductive statistics – a limited amount of data or a representative sample of the population In quality control, 2 types of numerical data can be collected: Variable Attribute

DATA COLLECTION Those quality characteristics that can be measured Tend to be CONTINUOUS (measured value can take on any value within a range) in nature Those quality characteristics that are observed to be either present or absent, conforming or nonconforming Primarily are DISCRETE data (countable using whole numbers) VARIABLES DATA ATTRIBUTES DATA

DATA ANALYSIS: GRAPHICAL Frequency Diagrams Histograms Shows the number of times each of the measured value occurred when the data were collected Data are grouped into cells Score Frequency 1 /// 2 / 3 //// 4 // 5 Ungrouped data – data are without any order Grouped data – group together on the basis of when the values were taken or observed

DATA ANALYSIS: ANALYTICAL MEAN The mean of a series of measurements is determined by adding the values together and then dividing this sum by the total number of values. Exercise : Data represent thickness measure-ment (in mm) of the clutch plate. 0.0625, 0.0626, 0.0624, 0.0625, 0.0627 Calculate the mean value.

DATA ANALYSIS: ANALYTICAL MEDIAN The median is the value that divides an ordered series of numbers so that there is an equal number of values on either side of the center. Exercise : Determining the median for a set of numbers below: Question 1 23, 25, 26, 27, 28, 29, 25, 22, 24, 24, 25, 26, 25 Question 2 1, 2, 4, 1, 5, 2, 6, 7

DATA ANALYSIS: ANALYTICAL MODE The mode is the most frequently occurring number in a group of values Exercise : Determine mode value. Question 1 100, 101, 103, 104, 106, 107 Question 2 23, 25, 26, 25, 28, 25, 22, 24, 24, 25, 26 Question 3 658, 659, 659, 659, 670, 670, 671, 670, 672, 674, 674, 672, 672

DATA ANALYSIS: ANALYTICAL The Relationship Among the Mean, Median and Mode Symmetrical Skewed Left Skewed Right Mean, Median and Mode are the statistical values that define the center of a distribution, commonly called the measures of central tendency.

DATA ANALYSIS: ANALYTICAL RANGE Is the difference between the highest value in a series of values or sample and the lowest value in that same series R = X high – X low Range value describes how far the data spread STANDARD DEVIATION Shows the dispersion of the data within the distribution Sample , s =

DATA ANALYSIS: ANALYTICAL Range and standard deviation are two measurements that enable the investigator to determine the spread of the data These two describe where the data are dispersed on either side of a central value, often referred to as measures of dispersion. Exercise : At an automobile-testing ground, a new type of automobile was tested for gas mileage. Seven cars, a sample of a much larger production run, were driven under typical conditions to determine the number of miles per gallon the cars got. The following miles-per-gallon readings were obtained: 36, 35, 39, 40, 35, 38, 41 Calculate the sample range and standard deviation.

MEASUREMENTS ACCURACY Refers to how far from the actual or real value the measurement is PRECISION Is the ability to repeat a series of measurements and get the same value each time ERROR Is considered to be the difference between a value measured and the true value

CENTRAL LIMIT THEOREM States that a group of sample averages tends to be normally distributed; as the sample size (n) increases, this tendency toward normality improves.