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Basic Distributions โ Depicts the amount of variation in outcomes of a process, used to represent the behavior of a process outcome. Usually described in terms of its shape, mean, and standard deviation Central Tendency - Descriptive Statistics โ measures data location using the mean, mode and median Dispersion โ a measure of spread around a central point, includes the measures range, standard deviation and variance Mean (distribution) โ typically used with normal data, provides a reference point for relating all other data points ex. 1,1,2,3,4,5,5 = mean = 3 Median (distribution) โ Center point. Equal number of data points to each side ex: 2,3,4,4,5,5,5,5,6,6,7,7, Mode (distribution) โ Not used to generate statistical data, typically used with non-normal data, may have multiple modes ex: 1,1,2,3,4,5,5: mode = 1 and 5 Binomial distribution โ Modeling discrete (attribute) data having only two possible outcomes... (ex: yes or no ) Poisson distribution โ estimating probability (Note: the binomial and poisson distributions are known as discrete distributions) Normal distribution โ produces a bell-shaped curve Weibull distribution โ statistical approach evaluating a design to deduce the percentages of failures Skewed distribution
โ Not normal Skewness โ = mean - mode / standard deviation Bimodal Distribution โ a probability distribution having two distinct statistical modes (Note: Skewed and bimodal distributions are not normal distributions. They are skewed to either side or toward both ends Variability โ Spread of data Standard Deviation โ Used for measuring dispersion, measures the spread of the values in the data set Range โ a measure of dispersion Variance โ measures the extent of dispersion around the central tendency. Probability โ The chance of an event occurring Independent event โ The occurrence of one event does not affect the probability that the other occurs Mutually exclusive events โ two events that cannot occur simultaneously General addition rule โ Calculates the probability of the union of two events General multiplication rule โ Calculates the probability that both of two events occur Combinations โ With combinations the order of the objects does NOT matter Permutations โ Very similar to combinations, except that the order DOES matter Successful performance โ When a product performs its intended functions
โ A measurement scale that refers to positions in a series where order is important, but precise differences between values are not defined (ex: dissatisfied, neutral satisfied, or rating 1,2,3,4,5, etc.) Interval Scale โ A measurement scale. Has meaningful differences but no absolute zero. (Ratios are NOT meaningful) (Ex: A temperature thermometer (F), zero value does not mean that there is an absence of temperature, and values cannot be multiplied or divided) Ratio Scale โ A measurement scale that has meaningful differences and an absolute zero exists. (Ex: length in inches. 0 has no length, and 10 is twice as long as 5.) Symbol of a Union โ โช Symbol of an Intersection โ โฉ Multiplication Rule: P(ABCD) = โ P(A) x P(B) x P(C) x P(D) Conditional Probability โ The result of an event depending on the sample space or another event P(A/B) = P(AโฉB) / P(B) Probability โ The chance of an event occuring Reliability โ The probability that a product will perform successfully under specified operating conditions for a given period of time without failure Continuous data โ Also called variable data. Information obtained on the characteristics of the item or unit in the population or sample. Continuous data โ Involves a measuring device and answer a question like, how much, how far, how long... Recorded at many different points Possible presence of a decimal Generally more powerful than discrete data Information measured on a continuum or scale Also called variable data
Continuous data examples โ Physical measurements (length, volume, width, time, temperature, etc.) Using a rule to measure a single dimension to the nearest 0.1" Using a micrometer to measure the same dimension to the nearest 0.000001", or a vernier caliper to the nearest 0.005" Monetary values Discrete Data โ Also called attribute date Countable data Data involves counts of classifications rather than measurements (ex: a tally of sodas sold) Discrete Data examples โ # of units unfit for sale
of imperfections on an automobile
eggs
Shoe size, eye colors, hair colors Choice based classifications such as good/bad, yes/no, pass/fail Convert attributes data to variable measures โ Instead of accept or reject, measure the degree in or out of spec. Instead of like or dislike, use a degree of like or dislike Instead of reporting the # of dents, report the total surface area the dents cover Collecting data and generating useful information by planning and implementing steps โ What do we want to know? What will we do with the data? From whom do we want to know it? When do we want to know it? Why do we want to know it? Who is the audience for the results? (Customer or mgmt) Length of time (per hour, day, shift, batch, etc) Type (cost, errors, ratings, etc) Source (reports, observations, surveys, etc.) Cost (internally and externally) Collector (team member, associate, subject expert ect) Lot size โ Collection of units from which a sample is to be drawn & inspected to determine conformance with acceptability criteria, (eg. production, shipment, etc) May different from a collection of units designated as a lot or batch for other purposes. (different shifts, etc) Inspection Level โ Designates the relative amount of inspection Ex: If inspection levels I, II, III are given - use level II unless otherwise specified.
plan: 1. samples size n and acceptance number Ac, 2. count the number of defective units in the sample, 3. if the number of defective units is greater than Ac, reject lot. Attribute sampling โ Involves the evaluation of the sample results in a count of the number of defective units Variables sampling โ Requires calculations to develop statistics to compare to a critical value defined in a plan Rational subgrouping โ Is a subset defined by a specific factor. (It identifies and separates variations by special causes) Select a Measurement for Rational Subgrouping โ Identify a significant process variable or product characteristic to track Focus on the vital few, not the trivial many Select the appropriate data for the charts you may want to use Practice similar subgroup elements Number of Subgroups for Rational Subgrouping โ Establish subgroups (important for dividing observations) Compute statistics for each subgroup separately before plotting on the control chart Define a minimal chance of variation within a subgroup Defect โ An undesirable result on a product. Also known as a nonconformity (defect vs. nonconformity: defect has the product liability associated with it) Defective โ An entire unit failing to meet spec; also known as a nonconformance ... โ Metrology โ The science of precision measurements. (Measurement is any act or process of quantitatively comparing results with requirements) Error โ The difference between the indicated value and the true value , may involve any combination of 3 factors (instrument, operator, and the environment) Accuracy
โ The closeness of agreement between a test result or measurement result and the true value Precision โ The closeness of agreement between randomly selected individual measurements or test results Bias โ The inaccuracy in a measurement system occurring when the mean of the measurement result is consistently or systematically different from its true value Measuring equipment calibration โ A factor that affects accuracy. Periodic recalibration of measurement and test equipment is usually needed for measurement accuracy Measurement error โ The difference between the indicated value and the true value of a measured quantity Repeatability โ Precision under conditions where independent measurement results are obtained with the same method on identical measurement items by the same operator using the same equipment within a short period of time. Reproducibility โ Precision under conditions where independent measurement results are obtained with the same method on identical measurement items with different operators using different equipment. Gauge (R&R) study โ A type of measurement system analysis that quantifies the capabilities and limitations of a measurement instrument, often estimating its repeatability and reproducibility. Factors that affect accuracy The environment โ Temperature, humidity, air pollution, electrical and radio frequency noise, and lighting Factors that affect accuracy Calibration of the measuring equipment โ Needed periodically to eliminate inaccuracy. Must be communicated clearly and in writing. Factors that affect accuracy The operator
