lecture outline quality

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QUALITY COURSE LECTURE OUTLINE

A THINKING STUDENTS COURSE

CONCEPTS IN QUALITY:

Evolution of quality Beginning, inspection, preventing defect with SPC, designing quality into product andprocess

Big names in quality:

Frederick Taylor1875 (divide labor into component tasks with work standards industrial eng.), (incentive pay systems what are the effects on quality)Shewhart (1920 process variation and removal of process faults),Dodge and Romig1930 (acceptance sampling)W. Edwards Deming 1950 known for his 14 points showing management how to putquality on institutional basis rather than a departmental basis (also Juran),

Taguchi 1980 (robust design)Example of parameter design forgrade on test temp humidity interaction factorial design.Example fill bottles of water with cup speed affects variability-cup size affectsaverage],Loss function [example fill volume of coke: one can has 12.1 fl.oz., one can has

11.9 fl.oz., and one can has exactly 12.0 fl.oz.],

Dimensions of quality:Performance, Features, Conformance, Reliability, Durability, Service, Response,Aesthetics, Reputation What is a quality automobile?

Total Quality Management (TQM): One of several terms used to define a philosophyand principles associated with the continuous improvement of services andmanufacturing operations

- long term commitment and involvement by management- focus on internal and external customers- effective involvement of entire work force- continuous improvement in all critical processes (a way of life)- partnering with suppliers where mutual trust exist- establishing, tracking, and improving performance measures for critical

processes

Process: A transformation of inputs to outputs (appropriate for service andmanufacturing operations)

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Issues in Quality:

- who is responsible for quality- who is the customer- who is the supplier- can quality be inspected into the product- how do you know you have good quality

- what metrics do you use to measure quality- importance of who, where, when, how, what and why- are customers always right- how do you know if customers are satisfied with your product or service- what does quality cost- does it matter where in the process failures occur

Seven Tools of Quality (these are the very basic ones more later):

http://www.asq.org/learn-about-quality/seven-basic-quality-

tools/overview/overview.html

- pareto diagram vital few and useful many: plotted from most frequent events

to least frequent events- cause and effect diagram relationships between an effect and its causes:

causes are usually broken down into contributions resulting from people,materials, work methods, environment, equipment, and measurements

- check sheets used to insure that specific data is collected and documented- process flow diagrams diagram that shows the flow of products through

various processing stations including control points- scatter diagrams graphical plot to show the relationship between two

variables- histogram graphical plot depicting the spread of data throughout some range- control charts graphical tools used to track parameters of a process real time

Simple goal: On target with minimal variation examples (on target, lots ofvariability), (off target, little variability), WHICH IS BEST?

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Mean,Std. dev.

20,0.02

19.98,0.01

Normal Distribution

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Signal to noise ratio = average/std.dev. ---may see the inverse std.dev./average (calledcoefficient of variation, relative std. dev., % nonuniformity), Example- run inshallow/deep water with small/large waves. (semiconductor industry), Example response surface for mean and std. dev. - attempt to get on target with minimumvariability. If your paycheck each month is off by + $2000, why is that important to youbut not important to Mark Cuban (very rich person)?

Primary causes of variability materials, machines, methods, man (used forbrainstorming problems, designing process controls, experimental designs, etc.). Othercauses may be environment, measurement systems, etc.

Relationship between design quality versus manufacturing quality. Toy DumpTrucks: Tanka vs Plastic

Traditional view of quality

what do we mean by quality products

what do we mean by improving quality (how do you know)

what do we mean by quality product design

what do we mean by quality process design

Definitions of quality many definitions

best (?) the degree to which a product or service satisfies the customers

expectations

one we often talk about conformance to specifications

Concept of specifications (for a given product/service metric)

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specifications for measurement (continuous random variables) often stated

as a nominal value + a tolerance (20 + .1)

specifications for count data often stated as NMT (no more than) or LT

(less than)

essential that we know how our product/service conforms to spec???

Example spec for fill volume of 20 oz. bottle of coke is 20 + .1What is distribution of fill volume in relation to spec?[show different scenarios]If you measure two bottles resulting in 19.9001 and 19.8999,which one conforms to spec?What if you have some measurement system variability?Are you sure which, if either, conforms to spec?ISO standard available that specifies zone around spec limitswhich would require additional actions. (show picture)

Taguchis definition of quality

loss function: L = k(x T)2

if your goal is to be on target with minimal variability, what values should

you set the parameter of the process to in order to achieve this.

Example: process (fill 20 oz. bottle of coke), spec (20 + .1), process

parameters (speed of production line and temperature of liquid). SHOWRESPONSE SURFACE FOR BOTH SPEED AND TEMPERATURE.Now, what would you recommend the speed and temperature be set at?

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Mean,Std. dev

20,0.02

19.98,0.01

Normal Distribution

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Cost of Quality (traditional view)

Prevention Costs (keep failure and appraisal costs to a minimum) planning, new product reviews, training, SPC, data analysis, improvementprojects

Appraisal Costs (to discover the condition of the product) incoming

inspection, in-process inspection and testing, maintaining test equipment,cost of products

Internal Failure Cost (cost which would disappear if no defects existed

prior to shipment) scrap, rework, retest, downtime, yield losses

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External Failure Cost (cost which would disappear if no defects existed

after shipment to customer) complaint adjustment, returned material,warranty charges, concessions made to customers

Demings 14 Points:

1. create constancy of purpose for the improvement of produce or service.

driven by quarterly reports, management develops strategies to show

profits in the short term. Why?

Should develop strategy based on long term thinking to insure products,

processes, and systems will position company, in the future, to serve theneeds of their customers

2. adopt the new philosophy

management must be willing to change corporate culture, discard old

thinking of allowing some defective products, improvements are only

necessary up to some acceptable level of quality, and assume a leadershipposture.

There exists some optimal level of quality (greater than 0% defectives)

that should be strived for. Example- 50% defectives imply spend money toimprove, , .0001% (1 in a million) defectives imply you spent toomuch money and will never recover these costs. YOU TEND TOBECOME SATISFIED WITH THE CURRENT QUALITY LEVEL.

3. cease dependence on mass inspection for quality control

abandon defect detection as means of controlling quality

emphasize importance of defect prevention

like giving aspirin to reduce fever without finding out the cause of thefever

goal of production is to get the product out the door versus goal of quality

is to insure product going out the door is defect free. Same goal???

Example- [show standard process picture] is money better spent on a

more powerful acceptance sampling plan (OC curve) that requires a largersample size OR spend it on prevention activities? [Show picture of 2 OCcurves]

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4. end the practice of awarding business on the basis of price tag

advantages of several suppliers - compete for business with lowest price

allows flexibility in case one supplier cant deliver

advantages of single supplier long term partnership trust relationships

developed certification programs to reward suppliers who havedeveloped and maintained process control programs with multiyearcontracts

5. improve constantly and forever the system of production and service to improvequality and productivity, and thus constantly decrease costs

concept of continuous improvement built on four step procedure

step 1 recognize the opportunity (how do you do this?)(gap between

what your are doing and what you are suppose to be doing from acustomer perspective) PLAN

step 2 test the theory to achieve the opportunity (experimental designs,

data analysis, etc.)(data driven management Malcolm Baldrige corevalue) (what did you find out, what should you now do to potentiallyimprove the quality)(now do it!) DO

step 3 observe the test results ( was the improvement results what youexpected?)- CHECK

step 4 - act on the opportunity (incorporate changes in standard operating

procedures - SOP) ACT

where do you go from here? (back to step 1)

danger cycle above fails to become an integral part of the culture and

you become satisfied with status quo6. institute more thorough, better job-related training

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training and education are essential to continuous improvement and the

body of knowledge taught must become part of the culture of the company

training, without practice afterward, is of limited value employees must

understand that the value of this training is real and will become part ofthe normal day to day activities

training just to say your employees have been trained is a waste of money training budgets and lunches are the first to go during short/long term cash

flow problems

employees must have command of the tools necessary to do their jobs

(Example two people asked to put screw into board one withscrewdriver/ one without)

7. institute leadership

supervisors must be coaches and teachers, not police or dictators

praise for doing something right should replace criticism for doing

something wrong (what do you do as a supervisor if someone is doing

something wrong?) management by objective can lead to negotiated goals far less than the

employee is capable of, just to insure employee can meet those objectives.(tends to result in retirement when those objectives are then achieved)

8. drive out fear, so that everyone may work effectively for the company

why would fear play a role in quality what can foster fear (operator

knows that if they follow the SOP, defective product may result whichthey will be blamed for)

reducing fear requires a major change in philosophy by management

9. break down barriers between departments

all activities within the organization must work as a team easy to say

difficult to pull off (goes back to culture of organization) eliminating fear (point 8 above) is crucial (if I cooperate with other

departments/people, they will know as much as me and I will be less valueto the company, receive smaller raises, and damage my career growth)

employee performance appraisal systems play a role in this. How? (egos,

worked hard but still received marginal review so why try, etc.)10. eliminate slogans, exhortations, and targets for the work force that ask for zero

defects and new levels of productivity

good for personal motivation and improved awareness of needs of the

organization and will contribute to improvement, but are not a substitutefor other improvement tools

11. eliminate work standards on the factory floor

place cap (perceived acceptability) on productivity improvement

12. remove the barriers that rob employees at all levels in the company of their rightto pride of workmanship

supervisors must emphasize the need for quality, not volume

use of daily/weekly production performance reports must be abandoned

(management often dont know what went on that week that resulted in the

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performance)(nothing wrong with using productivity as a metric toimprove as long as other metrics (quality) take center stage)

13. institute a vigorous program of education and self-improvement

people are a resource/asset which can be improved with training/education

people must believe that management perceives them as a valuable asset

to the company and worth the investment to make them better14. put everybody in the organization to work to accomplish the transformation

transformations require a change in the culture of the organization and will

require obtaining new talent, training old talent, continual coaching, use ofstatistical methods, access to top management, and must be provided withthe resources to get the job done.

Danger start to slip by forgetting that continuous improvement means

continuous.

STATISTICAL PROCEDURES:

Definitions:

Population (or process): collection of all members of a group which you wish to knowsomething about

* fill volumes for a production run of cokes* removal torques associated with bottles of eye drops produced Monday* lot of firecrackers you plan to buy* fat content of hamburger meat made from a given type of cow* rates for one night stay in hotels in Dallas* automated welding machine used to weld a step on a trailer

* machine that manufactures light bulbs* bottles of a given wine made from this years crop of grapes* super filter used to keep a clean room free of particles over a certain size

Parameter: a numerical measure that describes some characteristic of a population* average or mean value (x): average amount of coke in cans of coke, average

torque needed to remove a bottle cap, average breaking strength of a weld* standard deviation (x): a measure of variability associated with a numericalpopulation (used to describe the how spread out the numerical values are in thatpopulation) has interpretative value* variance (x

2): the square of the standard deviation

* proportion defective( or p) : the proportion of light bulbs manufactured thatdont work* average number of events in a sample unit (): the average number ofparticles over a certain size in one cubic meter of air in a clean room, the averagenumber of auto accidents in one day on the university campus

Sample: a part of a population selected according to some appropriate procedure.

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Statistic A single number calculated from some data

Estimators for parameters: Statistics used to estimate (guess) at the value for somepopulation parameter: x-bar, s2, s, Range/d2, sample proportion, etc.

Interpretation of standard deviation and what it means:

Empirical rule: If data is mounded approximately 68% of data will be within + 1std deviation of mean, 95% will be within + 2 std deviations of mean, and almost all(99.7%) will be within + 3 std deviations of mean.

Chebyshevs theorem: If data is not mounded, at least (1 1/k2)100% of datawill be within + k std deviations of mean

Tolerance Analysis: A statistical tool that allows you, based on a

sample, to make statements such as We are 95% confident that atleast 99% of the population is between LTL and UTL. If the data isassumed to be from a normal distribution, these limits are (X-Bar) +k*(sample standard deviation) where the constant k is found inquality literature [Jurans Handbook on Quality or my web site]

Descriptive Statistics: histograms plot with excel,

Histogram

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Classroom Example: Assume final grade averages for students taking statistics lastsemester are normally distributed with mean 75 and standard deviation 6. Use Excel Tools Data Analysis Random Number Generation to simulate 200 grades.Now use Excel Data Analysis Histogram to plot a histogram with cellboundaries (bins) set at 50, 55, 60, , 100. You might play around with the cellboundaries to make you histogram look better. This exercise is a good example ofhow you can use simulated data [from a known distribution] to see what happenswhen you use various statistical tools.

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Box and whisker plots (interpretation only most statistical software will have box

and whisker plots), examples [display grade distribution of several faculty teachingsame course to see if some faculty have more rigorous grading standards, display datacollected from day and night shift to see any differences, display data collected over 5work days to see if all days appear to be similar]

Dr Baker

Dr Karl

Dr Wilson

Box-and-Whisker Plot

57 67 77 87 97 107

Grade

Fac

ulty

Random Number Simulation Homework: [TURN IN NEXT WEEK]1. Generate 100 random numbers from a normal distribution with mean 20 and

standard deviation 0.5 . Plot a histogram of the data. Select your bin ranges(cell boundaries) such that you have a pretty histogram.

2. Generate 100 random numbers from a normal distribution with mean 22 andstandard deviation 0.5 . Plot a histogram of the data. Select your bin ranges(cell boundaries) such that you have a pretty histogram.

3. Now combine all the data (200 observations) in problems 1 and 2 above andplot a histogram.

4. Put all 3 histograms on one sheet and turn in.5. If you data set was that used in 3. above, what would you suspect about the

process that generated the data?

Events: Something that happens [next baby born at hospital is a boy, firecracker pops,fill volume for can of coke is in spec, employee graduated from a given university,etc.]

Probability: We calculate probabilities of events. For example, if you areinterested in the event that you make an A in this course, you would want to knowwhat the probability of this event occurring is.

Definition: P(A) = ??? where 0 < P(A) < 1.0

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Some people will display a probability of 0.8 as 80% since most people understandwhat 80% means better than a probability of 0.8 .

Contingency tables: Used extensively for categorical data. Example: A sample of100 students who took statistics last semester were asked their gender and whether or

not they liked statistics, resulting in the following data.

Like

Stat(L)

Don't

Like

Stat(D)

Male (M) 15 36 51

Female (F) 36 13 49

51 49 100

P(M) = 51/100 = 0.51

P(F) =P(L) =P(D) =P(L/M) = 15/51 = 0.294P(D/M) =P(L/F) =P(D/F) =P(M/L) =P(F/L) =P(M/D) =P(F/D) =

P[L/(M+F)] =

Multiplicative law: P(A*B) = P(A and B) = P(A)*P(B/A) = P(B)*P(A/B)P(M*L) = P(M)*P(L/M) = (0.51)*(0.294) = 0.15 OR 15/100 =0.15P(M*D) =P(L*D) =

Additive law: P(A + B) = P(A or B) = P(A) + P(B) P(A*B)P(M+L) = P(M) + P(L) P(M*L) = 0.51 + 0.51 0.15 = 0.87

OR(15+36+36)/100 = 0.87P(M+D) =

P(L+D) =

Independent events: Two events are independent if the occurrence or non-occurrence of one event has no effect of the occurrence or non-occurrence of theother event.

[Snows in Denver day you take 1st test, Pass 1st test][Snows in Arlington day you take 1st test, Pass 1st test][Observe # 2 when you roll a die, Observe an even # when you roll die]

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Mutually exclusive events: Two events are mutually exclusive if both cannotoccur in one experiment.

[Snows tomorrow in Denver, Snows tomorrow in Arlington][Make an A in this course, Make a B in this course]

Discrete random variables, discrete probability distribution, examples (binomial,poisson) the number of firecrackers that pop in a sample of 100, the number ofstudents who drop a stat course containing 60 students, the number of scratches on aone square foot piece of window glass, the number of accidents that occur on theUTA campus during a given day. [usually count data]

Continuous random variables, continuous probability density function, examples(normal, t-distribution, f-distribution) the fill volume of a can of coke, the time ittakes a NASCAR crew to change 4 tires during a race. [usually measurement data]

Mathematical expectation: expected value and variance of Y = c1*x1 + c2*x2 + c3*x3where all xi are independent.

Y = c1*x1 + c2*x2 + c3*x3

Y2 = c12*2x1 + c2

2*2x2 + c32*2x3

Example: A medical company manufactures surgical packs by randomly selecting3 clamps, 2 needles, and 1 mask from their inventory. If they are interested in theweights (Y) of the surgical packs, what is the mean weight and standard deviation ofthe weight for the surgical packs manufactured by this company? Assume that

clamps have a mean weight of6 oz and std. dev. of0.2 oz, needles have a meanweight of2 oz and std. dev. of0.1 oz and masks have a mean weight of4 oz and std.dev. of0.3 oz.

Y = 3*6 + 2*2 + 1*2 = 24 ozY2 = 9*0.04 + 4*0.01 + 1*0.09

EXPLAIN WHY THIS IS A BAD EXAMPLE!!

HOMEWORK:1. Assume that the distribution of surgical pack weights is normally distributed and

draw a picture of this distribution [be sure to show the scale on the X-axis].Assuming you cannot see inside the surgical packs to detect missing parts,present an argument as to how you can weigh a given surgical pack and detectone missing clamp.

2. Currently, when you check the fill volume for bottles of liquid pain killer, youtake the cap off the bottle and pour the contents into a measuring device that canmeasure the volume within + .001 fl.oz. (in effect you destroy one bottle ofproduct each time you do this). Since you get a big bonus for suggestions that

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result in cost savings, you find out that the actual volume of pain killer in a bottlecan be calculated from the weight of the pain killer in that bottle (something youremembered from chemistry). So, if you could just weigh the bottle of pain killerwithout taking the cap off, you would be able to save thousands of units ofproduct each year. A bottle of pain killer is comprised of a glass bottle, a cap,

and the actual pain killer inside the bottle. Therefore the weight of a bottle ofpain killer (WB) is given by

WB = WGB + WC + WPK

where WGB ,WC , and WPKare the weights of the glass bottle, cap, andpain killer respectively.

Before todays production run, you go out to the warehousewhere they store component parts and estimate the mean andstandard deviation of the weight of the glass bottles to be 5.00

and 0.10 grams and the mean and standard deviation of thecaps to be 0.40 and .02 grams from a very large sample of glassbottles and caps. After todays production run, you take a verylarge sample of bottles of pain killer (complete units containinga bottle, cap, and the pain killer) and estimate the mean weightand standard deviation to be 20.00 and .50 grams.a. Based on the information above, estimate the mean and

standard deviation of the weight of the pain killer in eachbottle.

Normal Distribution: normal density function (parameters), calculate probabilities,relationship between normal density function and z scores (standard normaldistribution), targeting mean of normal distribution

PROBLEMS:1. The time it takes a Nascar crew to change all 4 tires during a race is known to benormally distributed with a mean of 12 seconds and standard deviation of 0.8seconds.a. Draw a picture of this normal distribution [be sure to label the X-axis].b. What is the probability they take longer than 13 seconds to change all 4 tires?c. What is the probability they take less than 13 seconds to change all 4 tires?

d. What is the probability they take exactly 13 seconds to change all 4 tires?e. If they are currently leading the race by 12 seconds over the second place car andthe crew chief decides to have a pit stop and change all 4 tires, what is theprobability they are still leading the race after the pit stop?

f. If the crew chief want to reduce the mean time to change the tires such that theyhave a 97.%% probability of changing all 4 tires in less than 13 seconds, whatwould their target value for the mean be?

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HOMEWORK:2. The amount of active ingredient in a blood pressure pill is known to be

approximately normally distributed with mean 20 mg. and standard deviation 0.3mg.

a. Draw a picture of this normal distribution [be sure to label the X-axis].b. Doctors discover that patients develop a rash if the blood pressure pill has morethan 20.6 mg. of active ingredient. What is the probability that the pill you taketoday has more than 20.6 mg. and you develop a rash?

c. If 100 people in Arlington took this pill today, what is the probability that nonedevelop a rash? How many of these 100 people would you have expected todevelop a rash?

d. The pills are known to be ineffective if they have less than 18 mg. of activeingredient, but are quite effective as long as they have at least 18 mg. What is theprobability that a randomly selected pill has less than 18 mg. of active ingredient?

e. With so many patients developing rashes from taking these pills, the company

puts you in charge of fixing this problem. After forming a process improvementteam, the first suggestion is to change the process and target a mean less than thecurrent 20 mg. The entire team is aware that the cost of the active ingredient isvery high and the more pills manufactured [for a given volume of activeingredient] means more profit for the company. What would you suggest for anew target mean? Draw a picture to show what you are recommending here.

Sampling distribution of x-bar: large sample, small sample, (population normal/notnormal), central limit theorem

1. A production line filling bottles of liquid pain killer is known to target the meanfill at 12.132 fl.oz. Capability studies have indicated that the standard deviation offill is fairly constant and equal to 0.044. The goddess of statistics tells us that, fortodays production run of 200,000 bottles, the true mean fill is, in fact, 12.132 andstandard deviation is, if fact, 0.044 .

If you were to randomly sample 121 bottles and measure the fill for each

bottle, what is the sampling distribution of the sample mean?

Assuming a normal distribution for the fill volume, draw a picture, on the

same graph, of the fill volume of individual bottles and the samplingdistribution of sample means you calculated above. Show a scale on the

x-axis so I will know you drew the correct distributions.

HOMEWORK:Fill volumes of Koke are known to have a mean of 2.00 liters with standarddeviation of 0.10 liters. If you take a random sample of 25 Kokes,

a. what is the sampling distribution of the sample mean? List anyassumptions you make.

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b. Draw a picture of the distribution of fill volume and thesampling distribution of the sample mean on the samegraph.

Tests for normality assumption: When you use a statistical tool that assumes the datacame from a normal distribution, you should test for normality by using a normalprobability plot, histogram, chi-square test, etc.

SINGLE MEAN PROBLEMS:

Hypothesis test (single mean large sample) steps to conduct hypothesis test. Forlarge sample problems, you may use the z-statistic, especially when working by hand.However, most statistical packages will automatically use the t-statistic regardless ofthe sample size since most problems estimate the population standard deviation fromthe data. NOTE: the t-statistic is approximately equal to the z-statistic when the

degrees of freedom for the t-statistic is large.

Specify null/alternative hypothesis

Specify level of significance () (meaning)

assume null is true

define sampling distribution for test statistic (assumptions)

identify rejection region based on

calculate value for test statistic from data (unstandardized and

standardized)

compare sample value for test statistic to determine whether or not it is in

the rejection region (reject null hypothesis or fail to reject hull hypothesis)

write managerial summary

calculate p-value

SKETCH POWER CURVE FOR TEST (WHY?) discuss type I errors (

risk/producter risk) and type II errors ( risk/consumer risk)

What is a 95% confidence interval estimate for mean

What are tolerance limits?

Go to SINGLE MEAN LECTURE on web site: Discuss sampling distribution of

sample mean, SINGLE MEAN LECTURE TAB, SINGLE MEAN PRACTICE

TAB,

HOMEWORK : DUE NEXT WEEK - SINGLE MEAN

1. Have you ever had trouble taking the cap off of a new bottle of eye drops (or any newproduct)? During the manufacturing process, the equipment is initially set up, beforeeach production run, to apply a specified torque to the caps. This is importantbecause if the cap is too loose, it might be possible that leaks occur causing a loss of

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sterility and if the cap is too tight, consumers, old like your professor, would not beable to remove the cap and refuse to buy your product again. In order to insure thatthe equipment is set up properly each morning, you decide to randomly sample 100bottles during the first 30 minutes of production and check to see if the averagetorque is on target. The target for the application torque is 50 ft-lbs. Consumer

research has found that old professors can still remove the cap as long as the torque isless than 90 ft-lbs and bottles will not leak as long as the torque is greater than 10 ft-lbs. The sample of 100 bottles resulted in the following:

a. Test the hypothesis that the mean torque is equal to 50 against the alternativehypothesis that the mean torque is not equal to 50 at a 5% level of significance.You may assume that torque data is approximately normally distributed.

b. What will you tell your manager about todays torque set-up?

c. For the previous hypothesis test, sketch the power curved. Your boss is charged with recommending process improvements resulting in costsavings but at the same time continue to produce quality products. In your opinion,what is the largest average torque you would consider acceptable? Give reason.

2. A similar product, packaged in the same bottles and using the same equipment as inthe previous problem, has a FDA requirement that the average torque be 50 ft-lbs, butno larger than 55 ft-lbs and no smaller than 45 ft-lbs. If it is larger than 55 or smallerthan 45, you get in a lot of trouble. How large a sample would you recommend wetake to test the hypothesis and stay out of trouble. Make whatever assumptions youwish to answer this problem (just write them down).

3. Additional homework problems can be found on TAB: SINGLE MEANHOMEWORK. Working these problems will help you understand the what thepower curve represents.

IN CLASS EXERCISE (WITH COMPUTERS)

1. Go to SINGLE MEAN LECTURE on web site and SAVE that Excel file todesk top, open desk top Excel file, tab to TWO TAIL SIM FOR POWERCURVE and do the following.

2. Simulate 50 random numbers from a normal distribution with mean 20 andstandard deviation 6 [be sure to locate them in the appropriate cells]. Test the

hypothesis that the true mean is equal to 20 at alpha of 0.05. Did you reject or failto reject the null hypothesis? Sketch the power curve.3. For the power curve you sketched, determine the value for the true mean (either

the LCV or UCV value) where you have a 50% probability of rejecting thehypothesis. Now simulate another 50 random numbers from a normal distributionwith mean UCV (or LCV) and standard deviation 6 [ be sure to locate them in theappropriate cells]. Did you reject or fail to reject the null hypothesis?????

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BOTTLE 1 2 100 SAMPLE MEAN SAMPLE STANDARD DEVIATION

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Hypothesis test (single mean small sample) steps to conduct hypothesis test. Inthis case we would use the t statistic with degrees of freedom equal to n-1,

BUT we also must be able to assume that the data comes from a normal

population.

Specify null/alternative hypothesis Specify level of significance () (meaning)

assume null is true




standardized)




calculate p-value what is a 95% confidence interval estimate for mean.

TWO POPULATION PROBLEMS (Diff in Variances and Diff in Means):

Hypothesis test (difference in two variances): This hypothesis test is needed before youconduct the difference in means hypothesis tests below. Used to test hypothesis thatthe variances of two populations are equal.

EXERCISE: In Excel simulate two columns of 11 data points each from a normaldistribution with mean 20 and standard deviation 6. [Use Random Seed: 12345]

Calculate the sample variances for both samples. In this case the ratio of the truevariances is 1. By hand, test the hypothesis that the two population variances are equalwith alpha of 0.05.

Specify null/alternative hypothesis

Specify level of significance () (meaning)

assume null is true


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calculate value for test statistic from data




calculate p-value

EXERCISE: Use the data simulated above to conduct the following hypothesis test.1. In Data Analysis use the F-Test Two-Sample for Variances module to test

hypothesis that the two variances are equal at alpha 0.05 [NOTE: The alpha youinput for this module is for one tail only. Therefore input 0.025 for alpha for

the one tail so that both tails would total 0.05]. Did you reject or fail to rejectyour hypothesis? What is the p-value for your test? Compare to your handcalculations above.

2. Test hypothesis that the two means are equal (or difference in means is equal to 0)at alpha 0.05. Your choice of which t-Test to use depends on whether of notyou can assume that the variances are equal or not equal.

Conduct hypothesis test (difference in two means small/large samples):

Use t-Test: Two-Sample Assuming Equal Variances or t-Test: Two-Sample AssumingUnequal Variances in data analysis. When sample sizes are small, we would use the tstatistic with degrees of freedom equal to n1+n2-2, IF we are able to assume the variancesof the two populations are equal, BUT we also must be able to assume that the datacomes from a normal population. For cases where the variances are not equal, it is still

appropriate to use the t-statistic, BUT the degrees of freedom will be something otherthan n1-n2-2 (formula for degrees of freedom in this case can be found in most statistics

texts)

S1 S2 F-Test Two-Sample for Variances

15.60 21.29 Variabl

e 1

Variable

2

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24.78 22.73 Mean 20.97 19.25

14.46 23.40 Variance 20.59 14.20

25.93 14.16 Observations 11 11

27.27 23.40 df 10 10

19.34 19.27 F 1.45

21.89 22.53 P(F


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assume null is true

define sampling distribution for test statistic (assumptions) (std devsequal/unequal)



standardized)



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calculate p-value

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Homework1. In Excel, simulate two columns of 100 data points each from a normal distribution

with mean 20 and standard deviation 6. [USE Random Seed = 12345] In thiscase the true difference in means is zero [20-20]. In Data Analysis use the t-

Test: Two-Sample Assuming Equal Variances module to test hypothesis that the twomeans are equal at alpha 0.05. Did you reject or fail to reject your hypothesis?What is the p-value for your test?

2. Now simulate 100 data points [USE some Random Seed other than 12345 orleave blank] from a normal distribution with mean 21.7 and standard deviation 6and replace ONE of the columns of data you generated above. In this case thetrue difference in means is 1.7 [21.7-20]. In Data Analysis use the t-Test: Two-Sample Assuming Equal Variances module to test hypothesis that the two meansare equal at alpha 0.05. Did you reject or fail to reject your hypothesis? What isthe p-value for your test?

3. Based on what happened, could we roughly sketch a power curve? We will

answer this in class after everyone comes to class with the answers to 1 and 2above.

HOMEWORK: Due next class.1. Generate 2 samples of size 100 each from a normal distribution with mean 30 and

standard deviation 2 (2 columns of data). From this dataa. Test hypothesis that the variances are equal at alpha of 0.05b. Test hypothesis that the means are equal at alpha of 0.052. Now replace the 2nd column of data with simulated data from a normal

distribution whose mean is 31.79 and standard deviation 2. Repeat the twohypothesis test above.

3. Now replace the 2nd column of data with simulated data from a normaldistribution whose mean is 30 and standard deviation 9. Repeat the twohypothesis tests above.

One Way/Two Way Analysis of Variance (Hypothesis test for equality of multiplemeans)

Use Excel Data Analysis Anova: Single Factor/Two Factor

Test hypothesis that the mean weld strength for the 4 welders are equal.

What is the test statistic?

What value will you use for the level of significance?

What is the p-value?

Should you reject hypothesis that the means are equal?

EXERCISE: Go to DOE Seal Data on web (tab WORKSHEET) and do a one wayanalysis of variance to test hypothesis that the mean seal strength is equal for the sevenseal locations (Seal 1, Seal 2, Seal 7)

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REVIEW QUESTIONS:1. Discuss the brief history of how quality has evolved over the last 100 years?2. What did Taylor, Shewhart, Dodge, Deming, and Taguchi do to gain fame?3. What does on target with minimal variability mean? Show examples with pictures.

4. Identify the 4 primary causes of variability.5. Define attribute acceptance sampling by providing an example.6. Considering Demings 14 points, which three do you consider most valuable (and why)?

Which point do you consider least valuable (and why)?7. Provide several definitions of quality. Which do you prefer and why?8. What does a spec 20 + 3 imply?9. If the fill volume of koke is normally distributed with an average of 21 and standard

deviation of 0.5, draw this distribution and show the spec above on your graph.10. What is Taguchis loss function and how does it allow you to compare several different

distributions to determine which distribution is best?11. What are the 4 major quality cost categories and give an example of each.12. What are the seven tools of quality? Give examples for those tools covered so far in

class.13. Define a random variable, population, parameter, sample, and statistic with your own

example. [i.e. like x = time for you to drive home]14. Calculate by hand, the sample mean, sample variance, and sample standard deviation for

a small sample. [i.e. (2, 4, 8)]15. Given a mean (12) and standard deviation (2), interpret what they mean using the

empirical rule and Tchebycheffs theorem.16. Be able to construct a histogram for a given set of data (sorted from smallest to largest),

interpret this histogram, and guess as to whether or not this data comes form a normaldistribution.

17. Use the multiplicative and additive law of probability for events that are independent, notindependent, mutually exclusive, or not mutually exclusive.

18. From a contingency table, be able to calculate various probabilities.19. Distinguish between a discrete random variable and a continuous random variable.20. Give an example of a discrete probability distribution.21. Determine the mean and standard deviation for a linear combination of independent

random variables, each with known mean and standard deviation.22. Use either the binomial formula or the binomial tables to calculate binomial probabilities.23. Use the normal tables to calculate normal probabilities.24. For large samples from a population with known mean and standard deviation, determine

the sampling distribution of the sample mean.25. Conduct a two tailed single mean hypothesis test for a large sample (x-bar and s

provided), determine the p-value, sketch the power curve, and calculate a 95%confidence interval estimate for the population mean.

26. Conduct a two tailed single mean hypothesis test for a small sample (data only provided).27. Interpret the excel output for a hypothesis test for equality of two population variances,

for the difference in two population means assuming equal variances, and for thedifference in two population means assuming unequal variances, and which one to usebased on the results of the hypothesis test for equality of two variances.

CONTROL CHARTS:

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1. How to set up x-bar/R control charts to determine statistical stability2. How to interpret patterns reflected in x-bar and R charts to determine out of

control conditions3. Understanding the conceptual reason x-bar and R charts work4. Use Excel to simulate out of control conditions to see effect on x-bar and R

control charts5. What is a rational subgroup?6. What variability should a rational subgroup capture? [common, assignable]7. How large should the sample be and how frequent should it be taken?8. What is an example of stratification?8. For stable process, calculate and interpret capability indices Cp/Cpk and standarddeviation.9. What does the expression over control of the process imply?10. Set up and interpret individual control charts based on moving range.11. Define defect, defective, number of defectives, number of defects, and fraction

defective

12. Understand the binomial distribution and poisson distribution13. Set up p-chart, determine statistical stability, and understand conditions needed touse.

14. Set up c-chart and determine statistical stability15. When do you use p-charts or c-charts?16. What are the three primary categories of variation associated with a part during

production (within piece, piece to piece, time to time)17. What are the major causes of variation present in a process (equipment, material,

environment, operator)18. What is the difference in chance/common causes and assignable causes of

variation19. What allows you to delete some samples from your x-bar/R chart analysis20. What would cause you to revise your control charts21. What are Type I and Type II errors as they pertain to control charts22. Be able to reflect what would happen to X-bar/R charts when the mean and/or the

variability change.

Problems:1. For the following data collected for an x-bar and R chart

a. calculate control chart limits and plot on the graphs.b. If appropriate, calculate Cp and Cpk for specification 6 + .4c. What do you think is going on with the process? Be specific.

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SAMPLE X-BAR RANGE

1 5.901 6.118 5.928 5.842 5.947 0.2762 5.888 5.924 6.055 5.967 5.958 0.1673 5.955 5.918 5.867 5.871 5.903 0.0884 6.118 5.926 5.943 6.076 6.016 0.1935 6.240 6.072 5.909 5.934 6.039 0.3316 6.181 6.097 5.972 5.926 6.044 0.2557 6.059 5.885 6.231 6.001 6.044 0.3468 5.903 6.003 5.875 6.195 5.994 0.3209 5.952 5.944 5.958 6.140 5.999 0.19610 6.028 6.107 6.080 6.015 6.058 0.09211 5.946 5.920 6.081 5.998 5.986 0.16112 5.949 6.142 5.806 6.178 6.019 0.37213 6.003 6.199 5.904 6.016 6.031 0.29614 6.091 5.916 6.058 5.960 6.006 0.17515 6.125 6.019 5.912 6.125 6.045 0.21316 5.865 5.923 5.944 5.981 5.928 0.11717 5.949 5.952 5.932 5.965 5.949 0.03318 5.958 6.072 5.738 6.001 5.942 0.334

19 6.007 6.106 5.948 5.938 6.000 0.16820 5.889 6.060 5.989 5.846 5.946 0.21421 6.238 6.165 6.273 6.323 6.250 0.15822 6.454 6.370 6.215 6.218 6.314 0.23923 6.336 6.201 6.457 6.326 6.330 0.25524 5.830 6.035 6.138 6.035 6.010 0.30925 5.873 5.985 6.130 6.003 5.998 0.258

X-BarBar =6.030

R-BAR = 0.223

DATA

X-Bar Chart

5.600

5.800

6.000

6.2006.400

1 3 5 7 9 11 13 15 17 19 21 23 25

Sample

X-bar

R Chart

0.000

0.100

0.200

0.300

0.400

1 3 5 7 9 11 13 15 17 19 21 23 25

Sample

Range

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2. For the following data collected for an x-bar and R charta. calculate control chart limits and plot on the graphs.b. If appropriate, calculate Cp and Cpk for specification 6 + .4c. What do you think is going on with the process? Be specific.

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3. If a process is determined to be stable with an x-bar-bar equal to 6.4 and R-barequal to .12 , draw a picture of this process. (you may assume it is normal). Show

SAMPLE X-BAR RANGE

1 5.901 6.118 5.928 5.842 5.947 0.2762 5.888 5.924 6.055 5.967 5.958 0.1673 5.955 5.918 5.867 5.871 5.903 0.0884 6.118 5.926 5.943 6.076 6.016 0.1935 6.240 6.072 5.909 5.934 6.039 0.3316 6.181 6.097 5.972 5.926 6.044 0.2557 6.059 5.885 6.231 6.001 6.044 0.3468 5.903 6.003 5.875 6.195 5.994 0.3209 5.952 5.944 5.958 6.140 5.999 0.19610 6.028 6.107 6.080 6.015 6.058 0.09211 5.946 5.920 6.081 5.998 5.986 0.16112 5.949 6.142 5.806 6.178 6.019 0.37213 6.003 6.199 5.904 6.016 6.031 0.29614 6.091 5.916 6.058 5.960 6.006 0.17515 6.125 6.019 5.912 6.125 6.045 0.21316 5.865 5.923 5.944 5.981 5.928 0.11717 5.949 5.952 5.932 5.965 5.949 0.03318 5.958 6.072 5.738 6.001 5.942 0.334

19 6.007 6.106 5.948 5.938 6.000 0.16820 5.889 6.060 5.989 5.846 5.946 0.21421 6.042 5.952 5.926 6.075 5.999 0.14922 5.888 5.842 6.101 6.020 5.963 0.25923 5.926 6.074 5.733 5.947 5.920 0.34024 5.934 6.126 6.106 6.007 6.043 0.19325 6.069 5.918 5.969 5.777 5.933 0.291

X-BarBar =5.988

R-BAR =0.223

DATA

X-Bar Chart

5.800

5.850

5.900

5.9506.000

6.0506.100

1 3 5 7 9 11 13 15 17 19 21 23 25

Sample

X-bar

R Chart

0.000

0.100

0.200

0.300

0.400

1 3 5 7 9 11 13 15 17 19 21 23 25

Sample

Range

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enough detail to convince me that you know what the process actually looks like.Assume the sample size (n) is 4.

4. Given specifications 20 + 1 and a process that is stable, draw a picture of aprocess that would have a Cp = 2 and a Cpk = 1. Show enough detail to

convince me that you know what you are doing.

5. If the weight of men is normally distributed with mean 160 and standard deviation20 pounds and the weight of women is normally distributed with mean 120 andstandard deviation 15 pounds, what would the the mean weight and standarddeviation of the weight of a randomly selected couple (1 man and 1 woman) be.Assume that men and women do not marry each other based on weight.

6. In you own words, what is meant by a process being in statistical control for thefollowing examples.a. fill volume for cans of cokeb. proportion of defective TV picture tubes manufactured in lots of 200.

7. Assume that you collected data, calculated control chart limits for you x-bar andrange charts, and determined that your process was in a state of statistical control. Youhad acceptable capability, and you were now going to use these control charts to monitorfuture production. (the actual numbers do not matter in this problem).a. show a pattern of data you would expect for the next 10 samples assuming the processwere still in control.

X-BAR UCL

LCL

1 2 3 4 5 6 7 8 9 10

RANGE UCL

LCL

1 2 3 4 5 6 7 8 9 10

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b. show a pattern of data you would expect for the next 10 samples assuming the processvariability were to increase substantially at sample number 3.

X-BAR UCL

LCL

1 2 3 4 5 6 7 8 9 10

RANGE UCL

LCL

1 2 3 4 5 6 7 8 9 10

c. show a pattern of data you would expect for the next 10 samples assuming the processvariability were to substantially decrease at sample number 5.

X-BAR UCL

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LCL

1 2 3 4 5 6 7 8 9 10

RANGE UCL

LCL

1 2 3 4 5 6 7 8 9 10

d. show a pattern of data you would expect for the next 10 samples assuming the processmean were to slightly increase at sample number 5 to a value half way between the centerline and UCL for the x-bar chart..

X-BAR UCL

LCL

1 2 3 4 5 6 7 8 9 10

RANGE UCL

LCL

1 2 3 4 5 6 7 8 9 10

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ACCEPTANCE SAMPLING:

1. Understand concept of attribute acceptance sampling (single, double, and

multiple) and how it is used within the context of Z 1.4 Sampling Proceduresand Tables for Inspection by Attributes.2. Be able to use Z 1.4 to select an appropriate acceptance sampling plan.3. Understand what the operating characteristic curve is and how it can be used to

select an acceptance sampling plan that satisfies your risk levels.4. Be able to sketch an operating characteristic curve for a given single sampling

plan.5. Understand AQL, RQL, ASN6. Understand the role acceptance sampling plays in the quality process.7. Dangers associated with acceptance sampling does this affect quality, improve

quality, insure quality products delivered to customer? How does acceptance

sampling relate to process controls (SPC)? When is 100% inspection useful ordangerous (is it perfect count letter e on this page)8. Be able to sketch the OC curves for several different sampling plans in order to

compare the relative powers of each plan.

ACCEPTANCE SAMPLING PRACTICE PROBLEMS.

1. Specific Motors Corp. has a new supplier for spark plugs and is concerned aboutthe incoming quality. They purchase spark plugs in lots of 100,000 at a time andwant to use Z 1.4 to determine an acceptance sampling plan. Corporate officershas agreed on an AQL value of 0.1% defectives and the use of general inspectionlevel II.

a. Determine the acceptance sampling plan you would recommend using Z 1.4 as aguideline.

b. Sketch the operating characteristic curve.c. What is the value for the RQL (LQ or LTPD) for this sampling plan. (assume =

0.10)d. If the incoming quality is actually 0.539% defective, what is the probability that

your acceptance sampling plan accepts the lot?e. After a lot was accepted, many Specific Motors cars appeared to not run very

good and it was determined that the cause was defective spark plugs. After anextensive study, it was determined that the actual percent defective was in fact0.53% defective (much larger that the AQL of 0.1% defective). In order toprotect yourself from taking the risk of accepting this level of quality in thefuture, what sampling plan would you suggest they switch to and why?

2. For a given AQL of 1% defective and general inspection level II, explain the logicassociated with the continual increase in sample size (or sample size code letter)associated with larger batch sizes. Show several OC curves showing this effect.

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3. Z 1.4 is an acceptance sampling scheme. Explain the reasoning behind theswitching rules associated with normal, tightened, and reduced inspection.

4. Z 1.4 also includes, in additions to single sampling plans, double and multiplesampling plans. Explain the advantage of using double or multiple sampling

plans over single sampling plans for a given AQL.

EXPERIMENTAL DESIGN PRESENTATION:

1. Understand the role Design of Experiments plays in process improvement.2. Understand terminology used in DOE: replication, randomization, confounding,

interactions, response surfaces, treatment combinations, factors, blocking, fixedeffects models, random effects models, resolution of a design.

3. Be able to set up a factorial (2k) design, collect data, analyze data, fitmodel, determine optimal levels of process factors to hit target

and minimize variability, and make managerial decisions.4. Understand standard experimental designs use for screening experiments andresponse surface modeling.

MEASUREMENT SYSTEMS STUDIES:

1. Understand the role measurement systems play in variability.2. Be able to design a measurement system study, collect data, analyze data, and

determine the variation associated with a measurement system.

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lecture outline quality

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