Blaise Scientific Company St. Louis Mo. On Line Quality Reference Copyright Ronald Hartge 1992 ACCEPTABLE QUALITY LEVEL Maximum percentage of defective or non-conforming units which may be considered satisfactory as a process average. ACCEPTANCE SAMPLING Inspection of a sample for the purpose of determining whether to accept or reject a lot. Acceptance sampling applies to both variables and attributes sampling. ACCEPTANCE SAMPLING PLAN A specific plan that instructs the user as to the sampling sizes and the acceptance or non-acceptance criteria to be used. Possibly the most widely used Acceptance Sampling Plan is MIL-STD-105E. ACCURACY The number of measurements within a specified standard as compared to those outside the standard. Ratio of correct to incorrect measurements. ALPHA RISK The probability of rejecting a true null hypothesis. The experi- menter controls the probability of making a Type I error in his study by selecting his own alpha level before running the study. The probability of rejecting a lot when, actually , the lot is acceptable. The Alpha Risk is often called the Producers Risk in Acceptance Sampling. AMERICAN SOCIETY FOR QUALITY CONTROL A not-for-profit professional association that promotes Quality. ANALYSIS OF VARIANCE - ANOVA A statistical test for determining if there is a significant difference between two or more means. The ANOVA may always be used to analyze any number of data groups while the t-test may only be used to analyze two groups. Also the computing rules for the ANOVA are simpler than for the t-test. AVAILABILITY The ratio of the amount of time a product is operative (in standby or in use) and the amount of time the product cannot be operated (while being repaired, waiting for parts, etc.) operative time Availability = ------------------------------------- (operative time + non-operative time) AVERAGE CHART - X BAR CHART A control chart that uses sample averages (also called subgroup averages) to evaluate the process stability. AVERAGE OUTGOING QUALITY The expected average outgoin quality, expressed in percent of units non-conforming, that is satisfactory. Any lots not meeting this level should be 100% screened and the non-conforming units removed. AVERAGE OUTGOING QUALITY LEVEL For a sampling plan the maximum Average Outgoing Quality. ASSIGNABLE CAUSES Identifiable changes in the process that will effect process stability. Man Machine Method Material ATTRIBUTES DATA Also called count data or frequency data. Often expressed as Go-No go, pass-fail, etc. See VARIABLES DATA. BAYES THEOREM A theorem of statistics relating conditional probabilities. Bayesian sampling plans rely on calculations based on previous lot performance - thus allowing for smaller samples sizes. BENCHMARKING A process in which a company measures it's own performance against other companies - specifically companies that are recognized leaders such as Malcomb Baldridge Award Winners. BETA RISK The probability of accepting a false null hypothesis. The probability of accepting a lot when in fact it should be rejected. The Beta Risk is also called the consumer's risk. Also called Type Two Error. BELL SHAPED CURVE A distribution with a central peak and tapers off symetrically to tails. A normal curve is an example. * *** ***** ********* ************* BIMODAL DISTRIBUTION A frequency distribution with two peaks. This may indicate that two processes are being analyzed (through mixing) as one process. * * *** *** ***** ***** **************** ******************** BINOMIAL DISTRIBUTION A probability distribution in which a trial can have only one of two possible outcomes (pass or fail). See POISON DISTRIBUTION. Where P= Probability of an event q= 1-P n= Number of independant trials Then the probability of r occurances in n trials= +-------------------------+ n! |note: | --------- P^r q^n-r |(! = factorial) | r!(n-r)! |(^ = raised to the power)| +-------------------------+ BLEMISH A noticable imperfection that will not effect fuction. BLOCK DIAGRAM A diagram that shows interrelationships in a system. BRAIN STORMING Techniques used by teams to generate ideas. Individuals are encouraged to generate as many ideas as possible, and most importantly no judgement is made on the ideas until after the brain storming session. C-CHART An attributes data control chart where the number of defects found in a sample of a fixed size subgroup are charted. CALIBRATION Adjusting a piece of test or measurement equipment against a a reference standard to minimize the difference between the test equipment reading and the value of the reference standard. CAMP-MEIDELL CONDITIONS A frequency distribution or histogram meets CAMP-MEIDELL CONDITIONS if its mean and mode are equal and the frequency declines on either side of the mode. CAPABILITY INDEX A statistical technique which expressess the uniformity of a process versis specifications limits. The most popular capability index are CP, CpK, CR, and Zmax/3. CAUSE AND EFFECT DIAGRAM A pictorial diagram which shows the relationship between causes and effects. This diagram is sometimes called an Ishikawa diagram or fishbone diagram. The diagram highlights main causes and sub causes for an effect. Example: Cause and Effect Diagram For Making BAD COFFEE. GRIND BEANS Used drip grind| \ Old-\ not perculate |----\ \-Not Columbian \ \ =============================>>>BAD COFFEE / / | Cheap Aluminun--/ / | /-Dirty /-Cold | / / | COFFEE POT TEMPERATURE | | <<------------- Causes ---------------->>| Effect CELL A interval into which individual data points are grouped. For frequency distributions or historgrams the full range of a variable is usually divided into seven or more intervals of equal size. * * * Histogram * * * * * * * * * * * * * * * * * * | | | | | | | | Cell Number 1 2 3 4 5 6 7 8 CENTERLINE On a control chart the Grand Average. CENTRAL LIMIT THEOREM The Central Limit Theorem states that under general conditions averages of samples of random measurements drawn from a population tend to possess, approximately, a bell shaped distribution in repeated sampling. CENTRAL TENDENCY A measure of where, in a frequency distribution, values tend to cluster. Some measures of central tendency are: Mean Median Mode CHARACTERISTIC Any dimension or parameter on a part. CHECK LIST Sometimes called a countdown. It is a tool to ensure that all steps of an operation have been taken - in an effort to foolproof an operation. CHI-SQUARE Most significance tests for frequency data employ the chi-square. Although other tests may be used with frequency data chi-square has the advantage of simplicity. The two most popular uses of chi-square are: 1. Tests of association. 2. Tests of deviation from expected frequencies or goodness-of-fit tests. The data is place into classes and the observed frequency is compared to the expected frequency for each class. (Observed Count - Expected Count)^2 Chi-Square = the sum of ----------------------------------- Expected Count CHRONIC CONDITION A continuously repeating or long term problem. The opposite of a chronic condition would be a temporary condition. COMBINATIONS The number of combinations of n objects taken r at a time where order is NOT important. See PERMUTATIONS. n! Combinations = -------- note ! = factorial r!(n-r)! Example: How many ways can three suppliers be chosen from five. n! 5! 5x4x3x2x1 120 Combinations = -------- = ---- = --------- = --- = 10 r!(n-r)! 3!2! 3x2x1x2x1 12 COMMON CAUSE Causes of variation that are inherent in a process. When a process is in a statistical state of control the variation that is seen is due to common causes. CONFIDENCE INTERVAL A range of values which includes, with a preassigned probability known as a confidence level, the true value of a population parameter. See CONFIDENCE LIMITS. Confidence Interval |<------- True Population Average ---------->| | | -----(---------------------|----------------------)---- _ Sample _ X-r Avg. X+r _ +-------------------------+ X +---------------------+ | _ sigma | | _ sigma | |r=X +/- Z --------- |>==or for 95% level==>|r=X +/- 1.96 ------- | | a/2 SQRT n | | SQRT n | +-------------------------+ +---------------------+ CONFIDENCE LEVEL The probability, selected by the experimenter at the start of an experiment, that the test parameter will fall within the confidence interval. A confidence level of 95% is typical. See ALPHA RISK. CONFIDENCE LIMITS See CONFIDENCE INTERVAL. See CONFIDENCE LEVEL. _ + sigma _ + sigma Mean of a normal population X - Z ------- or X - (1.960) ------- known standard deviation. a/2 SQRT n SQRT n At the 95% Level sample sample _ + sigma _ + sigma Mean of a normal population X - t -------- or X - (2.064) ------- unknown standard deviation. a/2 SQRT n SQRT n At the 95% Level CONFORMANCE Adherence to some relevant specifications. (As a side note the term nonconforming MAY have different legal connotations than defective or rejected) CONSTANT CAUSE SYSTEM Variations in a system that are random and constant. The probabilities in a coin tossing experiment illustrate a constant cause system. CONSUMER'S RISK The probability that a lot is accepted, through sampling, when in fact the lot should be rejected. See BETA RISK. CONTINUOS DATA Variables data. Data where the resolution is only dependent upon the measurement system used. Examples: 12.3 volts 10.0 inches CONTINUOS VARIABLE A variable that a can be expressed by continuos data. Examples: Inches Pounds (Note - variable that can only be expressed by go/no-go would NOT be an example of a continuos variable) CONTROL - OF PROCESS A process is said to be in statistical control if the variation in the process is do only to random variations. CONTROL CHART A control chart is a graphic representation of process performance data to computed statistical control limits. The control chart was developed by Walter Shewart in 1924. --------------------------X----------- Specification Limit ______________________________________ Upper Control Limit X X X X X X X X ============X========================= Grand Average X X X ______X___________X___________________ Lower Control Limit -------------------------------------- Specification Limit <............ Time ................> CONTROL GROUP - FOR EXPERIMENTS An experimental group that receives no special treatment. The treatment group is then compared to the control group to be certain any changes are due to the experimental treatment. CONTROL LIMITS The limits within which a process is expected to remain. Control limits are not the same as specification limits. Most often control limits are associated with statistical process control (an example of control limits being set without the aid of statistical process control would be the practice of guard banding a specification). See CONTROL CHART. CORPORATE CULTURE The values and behaviors held by a corporation. It is the responsibility of top management. CORRECTIVE ACTION Actions taken to eliminate an identified problem. COST OF POOR QUALITY Cost associated with poor quality or "not doing it right the first time". There are four cost categories associated with poor quality 1. Internal Failure The cost associated with defective products that fail to meet quality requirements and result in losses before being delivered to the customer. 2. External Failure The costs that result from defective parts or products after having been shipped to the customer. 3. Appraisal Costs The costs associated with measuring, appraising or auditing products or services to ensure conformance to quality standards. 4. Prevention Costs The costs associated with activities of planning and maintaining the Quality System. COST OF QUALITY Another term for COST OF POOR QUALITY. See COST OF POOR QUALITY. COVARIANCE A measure to determine if two variables are related - or correlated. n = sample size _n _ _ >_ (X - X ) ( Y - Y ) X = the "first" variable i=1 i i Y = the "second" variable Sigma = ------------------------- _ xy n - 1 X = average of 1st variable _ Y = average of 2nd variable X = individual X reading i Y = individual Y reading i _n _ >_ = repeat X - X for each i=1 i CP CP is a capability index. CP does not show how centered a process is. A CP of 1.33 is generally desired. Tolerance CP = ----------- 6 X Sigma CPK CpK is a capability index. If Cpk is a negative number the process average is outside of the specification limits. If Cpk is between Zero and one then some of the six sigma spread is outside of the process limits. If Cpk is larger than one then all of the six sigma spread is within the process limits. A Cpk of 1.33 or greater is generally desired. Cpk = The lesser of: USL = Upper Spec Limit (USL - Mean) (LSL - Mean) LSL = Lower Spec Limit ------------ or ------------ 3 sigma 3 sigma CR The inverse of CP. See CP. CROSBY, PHILIP Author of "Quality is Free" and "Quality Without Tears". First to use the "Zero Defects Concepts". CU-SUM CHART (CUMULATIVE SUM CHART) The cumulative sum chart plots the difference between each sub group's average from the nominal value. If the process produces parts near the nominal the plot will be an almost flat line. When the process begins to shit the plot will show a line with an upward or downward trend. The cumulative sum chart is very sensitive. DEFECT Departure of a characteristic from it's specification. A part may have any number of defects. See DEFECTIVE. See also non- conformance. DEFECTIVE A part containing one or more defects - that makes the part unacceptable. DEMING, EDWARDS The U.S. War Department sent Deming to Japan in 1946 to help Japan recover from World War II - the rest is history. Deming developed the fourteen points for managing. DEMING PRIZE The award given to organizations that have successfully applied company-wide quality control based on statistical quality control. The award process is overseen by the Deming Prize Committee of the Union of Japanese Scientists and Engineers in Tokyo. DEPENDABILITY See AVAILABILITY. DEPENDENT VARIABLE In experimental research this is the variable that is not manipulated by the experimenter. See INDEPENDENT VARIABLE. DESIGN OF EXPERIMENTS A methodology for planning, conducting, analyzing and interpreting controlled tests. See also: Research Experimental Research Dependent Variable Independent Variable Factorial Design Between Subjects Design Within Subjects Design Statistical significance test Alpha and Beta Level Null and Alternative Hypothesis DISCRETE VARIABLE A variable that can only be expressed by integer numbers. Such as the number of people in a certain zip code. DISPERSION The amount of variability in a group of values. Usually expressed as : 1. The range 2. The Standard Deviation DODGE, HAROLD Known primarily for the acceptance sampling plans he developed with Harry Romig. DODGE-ROMIG SAMPLING PLANS Acceptance sampling plans developed by Harold Dodge and Harry Romig. EMPLOYEE INVOLVEMENT A practice where employees participate in making decisions concerning their work areas. EMPOWERMENT A practice where management gives employees the authority to make decisions and take action without prior approval. ENGLISH SYSTEM The system of measurement units based on the foot, the pound and the second. EVOLUTION OF OPERATIONS - EVOP A procedure to optimize a process by making small modifications to process parameters and observing the effects. EVOLUTION OF OPERATIONS differs from RESPONSE SURFACE METHODOLOGY in that in EVOP the experimental modifications are performed in a production situation while RESPONSE SURFACE METHODOLOGY is performed in a research and development situation. Thus with EVOP the process modifications must be small enough to meet specification tolerances. EXPERIMENTAL DESIGN A formal protocol that specifies the details for conducting an experiment. See DESIGN OF EXPERIMENTS. EXPONENTIAL DISTRIBUTION A probability distribution that is used extensively in making predictions concerning the reliability or the life of a product. The exponential probability function is: 1 P(X) = ---- * e^(x-mean) mean The Normal Distribution and the Exponential Distribution have very different shapes. In the Normal Distribution 50% or the values are above the mean and 50% are below the mean. In the Exponential Distribution 36.8% are above the mean and 63.2% are below the mean. * *** ** ***** *** ********* ****** ************* ********* | | Normal Dist. Mean Exponential Dist. Mean F-DISTRIBUTION The F-Distribution is a non-symetrical distribution that is used to determine whether or not the populations from which two samples were taken are equal. Sigma1 ^2 F = --------- Sigma2 ^2 F-TEST The F-Test is a test to determine whether or not two samples are drawn from populations with the same standard deviation. This test of significance is most often used with a confidence level of 95%. FAILURE MODE ANALYSIS A procedure where all syptoms which proceed a critical system failure are listed. All the possible causes for the syptoms are then listed and design changes implemented to eliminate the causes. FAILURE MODE EFFECTS ANALYSIS A procedure where each potential failure mode in a system is analyzed to determine its effect on other systems in a given product. FAILURE RATE The average number of failures per unit of time. The Failure Rate is used in assessing the reliability of a system or product. FAULT TREE ANALYSIS A flow chart which diagrams the failure process for a given system. +----------------+ |Spark Plug Fouls| +-------|--------+ +------+ | OR | +------+ | | | +---------------+ | +----------------+ | | | +--------------------+ +-----------+ +-----------+ |Defective Insulation| |Gas Mixture| |Gap On Plug| |On Plug Wires. | |too rich | |Set Wrong | +--------------------+ +-----------+ +-----------+ | +-------------+ |Oxygen Sensor| |Malfunction | +-------------+ FEIGENBAUM, ARMAND Author of the book "Total Quality Control" published in 1951. This book originated the concept of Total Quality Control (TQC). FISHBONE DIAGRAM See CAUSE AND EFFECT DIAGRAM. FITNESS FOR USE A term often used as a definition for "Quality". "Fitness For Use" indicates that a service or product meets customer requirements. FLOW CHART A diagram used to represent a process in order to better understand the process. A flow chart illustrates the main steps, branches, and final outcomes of the process. FOURTEEN POINTS W. Edwards Deming's fourteen key techniques for increasing Quality and productivity. 1. Create constancy of purpose for improving products and services. 2. Adopt the new philosophy. 3. Cease dependence of inspection to achieve quality. 4. End the practice of awarding business on price alone; instead, minimize total cost by working with a single supplier. 5. Improve constantly and forever every process for planning, production, and service. 6. Institute training on the job. 7. Adopt and institute leadership. 8. Drive out fear. 9. Break down barriers between staff areas. 10. Eliminate slogans, exhortations, and targets for the work force. 11. Eliminate numerical quotas for the work force and numerical goals for management. 12. Remove barriers that rob people of pride of workmanship and eliminate the annual rating or merit system 13. Institute a vigorous program of education and self improve- ment for everyone. 14. Put everybody in the company to work to accomplish the transformation. FREQUENCY DISTRIBUTION A graphically method of summarizing data to show the number of occurrences of an outcome. Data organized this way is known as a histogram. GANTT CHART A type of chart used to display planned work and completed work in relation to time. A project management tool. GAUGE R AND R Gauge Repeatability and reproducibility. Repeatability is the variation when one person with one gauge measures the same dimension two or more times. Reproducibility is the average variation between different gauge/people combinations. GEOMETRIC DIMENSIONING AND TOLERANCING A method of dimensioning and tolerancing on a drawing that will illustrate the relationships and functions of features. GO-NO GO A type of inspection or test that yields one of two outcomes - Pass or Fail. GOODNESS OF FIT A statistical test to determine how well a set of data filts a proposed frequency distribution. GRAND AVERAGE _ Overall average of all data collected for an X Chart. The grand average is plotted on the control chart as the centerline. GRANT, EUGENE Coauthored with W. Grant Ireson and Richard S. Levenworth the book "Statistical Quality Control". HISTOGRAM See FREQUENCY DISTRIBUTION. HYPERGEOMETRIC DISTRIBUTION A probability distribution. HYPOTHESIS See NULL HYPOTHESIS. INDIVIDUALS CHART with MOVING RANGE A control chart where the subgroup size = 1. The primary use of this chart is when the output is homogenous; i.e. the specific gravity of a solution. INDEPENDENT VARIABLE The independent variable is the variable manipulated by the experimenter. The independent variable is under the experimenter's control and he can determine the values it will assume. INFANT MORTALITY A high failure rate which occurs early in the life cycle of a product. See the well known "bathtub" curve below. ^ | | |* * Number |** ** of |** ** Failures |*** *** |**** **** |******* ****** |********* ******** |**************************************** +---------|---------------------|-------- Infant Random Wear Out Mortality Failures Failures TIME ----->> INSPECTION Testing done to determine conformance to specifications. INTERNAL CUSTOMER Any person (or department) that receives a product, service or information from another person (or department) within the same organization. INSPECTION ACCURACY The percentage of units that an inspector correctly identifies as either defective or acceptable. The accuracy is determined by having a second inspector reinspect the first inspector. ISHIKAWA DIAGRAM See CAUSE AND EFFECT DIAGRAM. ISO 9000 STANDARDS A group of five international standards on Quality Management developed by the International Organization for Standardization. JURAN, JOSEPH Author of "Juran's Quality Control Handbook" and "Quality Planning and Analysis" (with F.M. Gryna). JUST IN TIME MANUFACTURING (JIT) A Material Requirement Planning system for manufacturing processes. JIT emphasizes lot size of one unit, little or no inventory on hand and minimal receiving inspection. KURTOSIS If a frequency distribution has longer tails than a normal distribution of equal standard deviation, then it has a positive kurtosis (a.k.a. playkurtosis); iif it has sorter tails, then it has negative kurtosis (a.k.a. leptokurtosis). LEPTOKURTOSIS See KURTOSIS. LOT A homogeneous group of product. LOT TOLERANCE PERCENT DEFECTIVE The worst quality in a lot, as expressed in percent defective, that should be accepted. The percent defective which has a low probability, less than .10, of being accepted by the sampling plan. MAINTAINABILITY MALCOLM BALDRIDGE NATIONAL QUALITY AWARD An award established by Congress to raise awareness of Quality Management and to recognize U.S companies that have implemented successful Quality Management Systems. MATRIX An array of data. Data arranged in rows and columns. MEAN The arithmetic average of a population. X + X + X X 1 2 3..... n MEAN = -------------------- n MEAN TIME BETWEEN FAILURE The average time between failures of a repairable product. MEASUREMENT ACCURACY The degree to which the average of a series of repeat measurements made on a single part under test differs from the true value. ************************* Precise but ************************** * +++ * not Accurate * target * * +++++ * (small spread * true value * * ************+++ * not on target)* +++++++++++ * * * target * * <------------ * +++++++++++++ * * *true value* * Accurate but * +++++++++++++++ * * ************ * not Precise * ++++++++++++ * * * (big spread) * * ************************* ------------> ************************** ************************* * ************* * (NOTE: + = measurement) * * ++++ * * Accurate and * * ++++++ * * Precise * * ++++ * * (small spread * ************* * on target) ************************* <------------ MEASUREMENT ERROR The Difference between the true and the measured value of a variable being measured. MEASUREMENT PRECISION The degree to which a repeated measurement give the same result. See MEASUREMENT ACCURACY. MEDIAN The point X where half the sample elements are above X and half the sample points are below X. Note: With the normal distribution the median, mean and mode are all the same value. Examples: * ** * *** *** **** ***** ***** ******* ******* ********* *********** ********* ^ ^ ^ | | | median median median MEDIAN CHART A control chart of the median of subgroups. See MEDIAN. METROLOGY The science of measurement. MODE The most frequently observed value in a sample. In a normal distribution the mean, median and mode are all equal. Examples: * * ** *** ** ***** *** ******* ******* *********** ^ ^ | | Mode Mode MONTE CARLO SIMULATION A method of statistical tolerancing. A computer model is created with each component defined in terms of the form of the distribution and the numerical parameters, e.g. a normal distribution with a mean of 1.028 and a standard deviation of .008. The computer then uses a random number generator to select values at random from each component distribution and combine them to observe the effects of tolerance build up. MOVING AVERAGE AND MOVING RANGE CHART Most often used when the sample size (sub group size) equals one. The moving average of the last four (typically) subgroups are then plotted, as opposed to plotting the individual subgroup. n AND N n = number of items in a sample. N = number of items in a population. NOMINAL The target value for a dimension on a part. NOMINAL AS ZERO Setting the nominal value to zero. See NOMINAL CHART. NOMINAL CHART A control chart which plots the deviation from the nominal. This allows multiple part numbers manufactured with similar processes to be plotted on the same control chart. This is very useful when manufacturing short runs. NONCONFORMITY A departure of a characteristic from its intended value. See DEFECT. NONCONFORMING A unit which has one or more noncomformities. See DEFECTIVE. NONDESTRUCTIVE TESTING Testing methods that do not damage the unit under test. NORMAL DISTRIBUTION The normal distribution is a good approximation for a large number of situations. _ 1. In the case of X control charts the Central Limit Theorem allows the averages of subgroups to be treated as a normally distributed group. 2. In the case of tests of significance for mean values i.e. ANOVA, there is good empirical work on the effects of violating the assumptions of normality and homogeneity of variance. In most cases, violations of these assumptions, even extreme ones, do not severely affect the outcome of the analysis of variance. Although tests have been developed to determine non-normalcy and heterogeneity of variance they are less robust than the analysis of variance itself. NP-CHART A control chart for the number of defective units in a subgroup. Sample size must remain constant. See P CHART. NULL HYPOTHESIS The null hypothesis makes a statement about the value of certain population parameters and is generally phrased to negate the possibility of a relationship between the independent and dependent variables. The null hypothesis is assumed to be true unless the results of a statistical test of significance permit it to be rejected. OPERATING CHARACTERISTIC CURVE The operating characteristic curve is a graphic representation of the producer's and consumer's risk associated with an acceptance sampling plan. The curve shows the probability of accepting a lot versus the percentage of defective units in the lot. P-CHART A control chart for the percentage of defective units in subgroup. Sample size may vary. See NP CHART. PARETO ANALYSIS An analysis of the frequency of occurrence of some events. This allows focus to be given to the most frequent concerns. Key to the use of the Pareto Analysis is the concept that 80% of the effects come from 20% of the possible causes. See PARETO DIAGRAM. PARETO CHART See PARETO DIAGRAM. See PARETO ANALYSIS. PARETO DIAGRAM A "histogram" showing the frequency of occurrence of various events in descending order. This histogram helps to prioritize your efforts. See PARETO ANALYSIS. Example: Reason ABC ****************** Reason XYZ *************** Reason 123 ***** Reason 456 ** Reason 789 * Reason 987 * Reason 654 * Reason 321 * PERCENT DEFECTIVE The percentage of units in a lot which are defective. Number Defective Percent Defective = ---------------- X 100 Number Tested PERMUTATIONS An ordered arrangement of r distinct objects. See COMBINATIONS. n! Permutations = ------ note: ! = factorial (n-r)! Example: A piece of equipment is composed of five parts which may be assembled in any order. If each order is to be tested once how many tests must be conducted. n! 5! 5x4x3x2x1 Permutations = ----- = ------ = --------- = 120 (n-r)! (5-5)! 1 note: 0! = 1 PLATYKURTOSIS See KURTOSIS. POISSON DISTRIBUTION A probability distribution where the probability of an event occurring 0,1,2...r times under conditions when the probability p of its occurrence is small, but the number of occasions on which it can occur is large. An approximation of the Binomial Distribution when n is large and p is small. See BINOMIAL DISTRIBUTION. POPULATION The total universe of all possible observations that can be identified by a given set of rules. Descriptive statistics, such as the mean, median, mode, and standard deviation are known as parameters when they are based on all of the values in a population. Population parameters are seldom actually measured, but they may be estimated from the values of a sample drawn from the population. PRECISION OF MEASUREMENT The degree to which repeated measurement of a standard yields the same result. See the example given for ACCURACY OF MEASUREMENT PRE-CONTROL A method of controlling the number of defects produced by "guard-banding" the specification limits. Pre-control is not based on statistical methods and does not attempt to minimize process variation. PROBABILITY The chance that a specific event has a specific outcome. n Probability of an event = - N Example: On a perfectly balanced six sided dice the probability of any one side ending up after rolling the dice is: 1 Probability = - = .17% 6 PROBABILITY DISTRIBUTION A mathematical formula that relates the values of the characteristic with their probability of occurrence in the population. Quality Management Uses For Various Probability Distributions Distribution Primary Area of Use ------------ ------------------- Normal Variables data - process control Exponential Reliability Weibull Reliability Poisson Acceptance sampling & process control Binomial Acceptance sampling Hypergeometric Acceptance sampling PROCESS CAPABILITY The measure of process performance relative to some engineering specification. Process Capability may be expressed in terms of percent defective or in terms of capability indexes such as Cp and CpK. Process Capability is determined by sampling or 100% testing of units produced during a time when the process is statistically in control. PROCESS CAPABILITY INDEX See Cp and Cpk. PROCESS CONTROL Activities to reduce variation in a process and to keep the process at it's capability level. These activities would include sample inspection, control charting, and eliminating causes of variation. PRODUCERS RISK See ALPHA RISK. PRODUCT LIABILITY The obligation of a company to provide compensation for losses related to personal injury or property damage caused by its product. Product liability is the result of a product not per- forming to customer expectations and may or may not result in a lawsuit. See WARRANTY. QUALITY In technical terms: 1. Fitness for use. 2. Free of defects. 3. Satisfying customer expectations. QUALITY ASSURANCE The planned and systematic actions necessary to provide adequate confidence that a product will conform to established requirements. QUALITY AUDIT A systematic review to determine if sufficient management systems are present to guarantee a quality product or service. QUALITY CIRCLES An employee involvement technique. A circle is a team who meet regularly to identify and solve problems. The circle is a means of allowing and encouraging people from all levels and functional areas to participate in rendering decisions that will improve quality and/or reduce costs. QUALITY CONTROL A management function whereby control of quality of products or services are exercised for the purpose of preventing defects. QUALITY COSTS See COST OF POOR QUALITY. QUALITY ENGINEERING The analysis of a system to maximize the quality of services and products produced by the system. QUALITY LOSS FUNCTION The costs that occur when a quality characteristic deviates from it's target value. QUALITY TRILOGY A method of managing for quality which emphasizes a three pronged approach. 1. Quality Planning 2. Quality Control 3. Quality Improvement R-BAR The average range. See R CHART. See RANGE. RANGE The difference between the highest and lowest values in a group. R-CHART A control chart which uses the range within subgroups to analyze process variability. RANDOM SAMPLE A subset of observations drawn from a population in such a way that each observation contained in the population has an equal chance of being included in the sample. REGRESSION ANALYSIS The study of the relationship between two or more variables. In quality control the primary uses of Regression Analysis is to: 1. Determine optimum operating conditions. 2. Determine the variables causing some result. REJECTABLE QUALITY LEVEL The poorest quality in a lot, as expressed in percent defective, that should be considered acceptable. RELIABILITY The probability that a device will operate properly for a specified period of time, under specified conditions. REPEATABILITY The degree to which repeated measurements on the same object with a specific instrument yield the same value. REPRODUCIBILITY The variation between people using the same instrumentation and making the same measurement. See MEASUREMENT ACCURACY, ACCURACY, and PRECISION. RESPONSE SURFACE METHODOLOGY Determining the optimum operating parameters of a process by varying the parameters and observing the results on the product. Response Surface Methodology differs from Evolutionary Operations (EVOP) in that EVOP uses small changes during actual production, so as to minimize production losses, while Response Surface Methodology is conducted with greater changes while in a research mode where poor yield may be tolerated. RESOLUTION Fineness of measurement. The smallest unit of measurement that a measuring device is capable of indicating. |---|---|---| Figure One 0 1 2 3 |-|-|-|-|-|-| Figure Two 0.5 1.5 2.5 3 Figure Two has twice the resolution of Figure One. ROMIG, HARRY Developer of the first sampling plans for variables data and the concept of Average Outgoing Quality Limit. Developed with Harold Dodge the Dodge-Romig sampling plans. RUN Consecutive units - sequential in time. SAMPLE A subset of a population. SCATTER PLOT A plot of two variables as a dot on an X and Y axis. A very useful tool in the analysis of the relationship between two variables. | . . | . . . . . | . .. . . . | . . | . . | . . | . . |----------------------- SHEWHART CONTROL CHART See CONTROL CHART. SHEWHART, WALTER Creator of the Control Chart. SEVEN TOOLS OF QUALITY 1. Cause and Effect Diagram 2. Check Sheet 3. Control Chart 4. Flowchart 5. Histogram 6. Pareto Chart 7. Scatter Plot SI SYSTEM The metric system. SIGMA The standard deviation of a population. SIGNAL TO NOISE RATIO The ratio of experimental effect to experimental error due to chance. SIX SIGMA QUALITY A term use to indicate that a process is controlled to +/- 3 standard deviations from the mean (center line). SKEWNESS A measure of a distribution's symmetry. | * | * | ** | **** | **** | ******* | ******** | ********* | ********** | ************* | *************** | ******************* |------------------ |--------------------- Positive Skew Negative Skew SPECIAL CAUSE Sometimes called assignable causes, special causes are causes of variation that are not inherent to the process. SPECIFICATION A document listing the requirements of a product. STANDARD DEVIATION A measure of variation. /-------------- / _n /\ / >_ _ \ / i=1 (X - X) Standard Deviation = \ / i For Normal Distribution \ / --------------- \/ n - 1 STATISTIC A numerical property of a sample. Statistics have two general functions in quality control: 1. Descriptive statistics - used to clarify the meaning of quantitative data. The classification of data, the drawing of histograms; the computation of sample means, modes, medians and standard deviations are all activities that deal with descriptive statistics. 2. Inferential statistics - used to draw generalizations and test validity of these generalizations. Inferential statistics is the science of making decisions based on incomplete information. STATISTICAL CONTROL A process is in statistical control when it exhibits only random variation - typically +/- 3 standard deviations from the mean or center line. STATISTICAL INFERENCE See STATISTIC. STATISTICAL PROCESS CONTROL (SPC) Statistical methods for analyzing the variation of a process. STATISTICAL QUALITY CONTROL Statistical techniques for improving quality. SPC is only one of many Statistical Quality Control techniques. SUBGROUP A sample for control charts all taken at virtually the same time. SUPPLIER QUALITY ASSURANCE A technique for assuring that purchased product will be fit for use with minimal inspection and corrective action based on a relationship with a supplier. According to Juran there are nine activities required for Supplier Quality Assurance: 1. Define product and program quality requirements. 2. Evaluate alternative suppliers. 3. Select suppliers. 4. Conduct joint quality planning. 5. Cooperate with the supplier during the execution of the contract. 6. Obtain proof of conformance to requirements. 7. Certify qualified suppliers. 8. Conduct quality improvement as required. 9. Create and use supplier quality ratings. T-DISTRIBUTION The distribution of the means of samples of given size, standardized using estimated values of the parent standard deviation. See T-TEST. T-TEST A statistical test of significance for testing mean values. TAGUCHI, GENICHI The director of the Japan Industrial Technology Institute. Taguchi is best known for developing a methodology to improve quality and reduce costs. See QUALITY LOSS FUNCTION. See TAGUCHI METHODS. TAGUCHI METHODS The American Supplier Instititute's trademarked term for the Quality engineering methodology developed by Genichi Taguchi. In this engineering approach Taguchi calls for: 1. Off line quality control 2. On line quality control 3. A unique system of experimental design TAMPERING Action taken to compensate for variationArticle Unavailable