Basic Principles of MeasurementNO TOPIK DEFNISI KAPAN DIGUNAKAN PERTANYAAN KUNCI KETERANGAN

1 SCALES OF MEASUREMENT

A measurement is simply a numerical assignment to something, usually anon-numerical element. Measurements convey certain information about therelationship between the element and other elements. Measurement involves atheoretical domain, an area of substantive concern represented as an empiricalrelational system, and a domain represented by a particular selected numericalrelational system

NominalOnly the presence/absence ofan attribute; can only countitems

Contoh :go/no go;success/fail;accept/reject

Statistic :percent;proportion;chi-square tests

Ordinal

Can say that one item hasmore or less of an attributethan another item; can order aset of items

Contoh :taste;attractiveness

Statistic :rank-ordercorrelation

Interval Di!erence between any twosuccessive points is equal;often treated as a ratio scale

Contoh :calendar time;temperature

Statistik :correlations;t-tests; F-tests;

NO TOPIK DEFNISI KAPAN DIGUNAKAN PERTANYAAN KUNCI KETERANGANeven if assumption of equalintervals is incorrect; can add,subtract, order objects

multipleregression

Ratio

True zero point indicatesabsence of an attribute; canadd, subtract, multiply anddivide

Contoh :elapsed time;distance; weight

Rusmus statistic :t-test; F-test;correlations;multipleregression

2 RELIABILITY AND VALIDITY OF DATA

Fundamentally, any item measure should meet two tests:1. The item measures what it is intended to measure (i.e., it is valid).2. Aremeasurement would order individual responses in the same way (i.e.,it is reliable).

Bias The difference between the average measured value and a referencevalue is referred to as bias. The reference value is an agreed-upon standard,such as a standard traceable to a national standards body (seebelow). When applied to attribute inspection, bias refers to the abilityof the attribute inspection system to produce agreement on inspectionstandards. Bias is controlled by calibration, which is the process ofcomparing measurements to

NO TOPIK DEFNISI KAPAN DIGUNAKAN PERTANYAAN KUNCI KETERANGANstandards.

Repeatability

AIAG defines repeatability as the variation in measurementsobtained with one measurement instrument when used severaltimes by one appraiser, while measuring the identical characteristic onthe same part. Variation obtained when the measurement system isapplied repeatedly under the same conditions is usually caused by conditionsinherent in the measurement system

Reproducibility

Reproducibility is the variation in the average of the measurementsmade by different appraisers using the same measuringinstrument when measuring the identical characteristic on the samepart

Stability

Stability is the total variation in the measurements obtained witha measurement system on the same master or parts when measuring asingle characteristic over an extended time period. A system is said tobe stable if the results are the same at different points in time

Linearity the difference in the bias values

NO TOPIK DEFNISI KAPAN DIGUNAKAN PERTANYAAN KUNCI KETERANGANthrough the expected operatingrange of the gage

3OVERVIEW OF STATISTICAL METHODS

Enumerative versus analytic statistical methods

Deming (1975) defines enumerative and analytic studies as follows:Enumerative studyLa study in which action will be taken on the universe.Analytic studyLa study in which action will be taken on a process toimprove performance in the future

Enumerative versus analytic statistical methodsEnumerative statistical methods

The term inference is defined as 1) the act or process of deriving logical conclusionsfrom premises known or assumed to be true, or 2) the act of reasoningfrom factual knowledge or evidence. Inferential statistics provide informationthat is used in the process of inference. As can be seen from the definitions, inferenceinvolves two domains: the premises and the evidence or factual knowledge.

NO TOPIK DEFNISI KAPAN DIGUNAKAN PERTANYAAN KUNCI KETERANGANAdditionally, there are two conceptual frameworks for addressing premisesquestions in inference: the design-based approach and the model-basedapproach

Assumptions and robustness of tests

It is important at the outset to comment on what we are not discussing herewhen we use the term ‘‘robustness.’’ First, we are not talking about the sensitivityof a particular statistic to outliers. This concept is more properlyreferred to as resistance and it is discussed in the exploratory data analysissection of this book. We are also not speaking of a product design that canperform well under a wide variety of operating conditions. This design-baseddefinition of robustness is discussed in the Taguchi robustness conceptssection.

4 Distributions Distributions are a set of numbers collected from a well-defined universe ofpossible measurements arising from a property or relationship under study.Distributions show the way in which the probabilities are associated with

NO TOPIK DEFNISI KAPAN DIGUNAKAN PERTANYAAN KUNCI KETERANGANthe numbers being studied

Probability distributions for Six Sigma

. Binomial distribution

. Poisson distribution

. Hypergeometric distribution. Normal distribution. Exponential distribution. Chi-square distribution. Student’s t distribution. F distribution

BINOMIAL DISTRIBUTIONPoisson distributionHYPERGEOMETRIC DISTRIBUTIONNORMAL DISTRIBUTIONEXPONENTIAL DISTRIBUTIONCHI-SQUARE, STUDENT’S T,ANDF DISTRIBUTIONSSTUDENT’S T DISTRIBUTIONF DISTRIBUTION

5 Statistical inference All statements made in this section are valid only for stable processes, i.e.,processes in statistical control. The statistical methods described in this sectionare enumerative. Although most applications of Six Sigma are analytic, thereare times when enumerative statistics prove useful. In reading this material,

NO TOPIK DEFNISI KAPAN DIGUNAKAN PERTANYAAN KUNCI KETERANGANthe analyst should keep in mind the fact that analytic methods should also beused to identify the underlying process dynamics and to control and improvethe processes involved.

POINTANDINTERVAL ESTIMATION

So far, we have introduced a number of important statistics including thesample mean, the sample standard deviation, and the sample variance. Thesesample statistics are called point estimators because they are single values usedto represent population parameters. It is also possible to construct an intervalabout the statistics that has a predetermined probability of including the truepopulation parameter

HYPOTHESIS TESTING Statistical inference generally involves four steps:1. Formulating a hypothesis about the population or ‘‘state of nature,’’2. Collecting a sample of observations from the population,

NO TOPIK DEFNISI KAPAN DIGUNAKAN PERTANYAAN KUNCI KETERANGAN3. Calculating statistics based on the sample,4. Either accepting or rejecting the hypothesis based on a predeterminedacceptance criterion.

RESAMPLING (BOOTSTRAPPING)

A number of criticisms have been raised regarding the methods used for estimationand hypothesis testing:. They are not intuitive.. They are based on strong assumptions (e.g., normality) that are often notmet in practice.. They are di⁄cult to learn and to apply.. They are error-prone.

6 PRINCIPLES OF STATISTICAL PROCESS CONTROLDISTRIBUTIONS A central concept in statistical process

control (SPC) is that every measurablephenomenon is a statistical distribution. In other words, an observed setof data constitutes a sample of the effects of unknown common causes. It

NO TOPIK DEFNISI KAPAN DIGUNAKAN PERTANYAAN KUNCI KETERANGANfollowsthat, after we have done everything to eliminate special causes of variations,there will still remain a certain amount of variability exhibiting the stateof control

CENTRAL LIMIT THEOREM

The central limit theorem can be stated as follows:Irrespective of the shape of the distribution of the population or universe,the distribution of average values of samples drawn from that universewill tend toward a normal distribution as the sample size grows withoutbound.

PREVENTION VERSUS DETECTION

A process control system is essentially a feedback system that links processoutcomes with process inputs. There are four main elements involved, the processitself, information about the process, action taken on the process, andaction taken on the output from the process

Common and special causes of variation

A phenomenon will be said to be controlled when, through the use of pastexperience, we can predict, at least within limits, how the phenomenon

NO TOPIK DEFNISI KAPAN DIGUNAKAN PERTANYAAN KUNCI KETERANGANmay be expected to vary in the future. Here it is understood that predictionwithin limits means that we can state, at least approximately, theprobability that the observed phenomenon will fall within the given limits