1 Topic: DOE (Design of Experiment) Development of a Problem Solving Model for the Hong Kong Textiles and Clothing Industries Project HKRITA Ref. No. : RD/PR/001/07 ITC Ref. No. : ITP/033/07TP
2 Why we need DOE? Design of Experiment
3 Why DOE? Full Factorial DOE Speed Octane Tire Pressure Miles per Gallon
4 Purpose of DOE and Terms Definition Purpose of DOE To identify the relationships of all the factors those affect the desired performance of a process under investigation Definitions of terms commonly used in DOE Process Any activity or group of activities that takes an input, adds value to it, and provides an output to an internal or external customer. A series of definable, repeatable, and measurable task leading to a result for a customer. Factor(s) Item(s) that affect the output (Y) of the target process Controllable factors can be controlled by appropriate actions. Uncontrollable factors cannot be controlled, e.g. noise, world economic growth, earthquake, flood etc. Level(s) Specific values of factors (inputs i.e. Xs). It can be continuous or discrete e.g. High 25 deg C. Vs Low Temp or 100 deg C Vs
5 Response Measured output (Y) value. e.g. product delivery time, warehouse inventory level Replication Completely re-run experiment with same input levels. Used to determine impact of measurement error Interaction Effect of one input factor depends on level of another input factor Taste Taste Baking Time Flour A 10 min Flour B 30 min 100 C 150 C 100 C 150 C
6 Range Possible value (s) of the factor within the process of interest e.g. 0 <Temp<100, the range is 100 Symbol Representation of the value of the Range covered by a factor in the process e.g. +1 for temp 0 <Temp<100 and -1 for -100 <temp<0 Orthogonal Table Table that shows the relationship of various factors within the process
7 Example A high school administration wants to reduce absenteeism of students in high school. Many factors can affect school absenteeism. It may include the following: Student : age, sec, ethnic background, etc. School : location, teacher, class, etc. Time : day of week, class period, etc. For purpose of illustration, consider initially only three of the two-level factors : Symbol Level Factor - + A: Day of week Friday Monday B: Call-back when absent Yes No C: School 1 2 Level Factor 3 2 =8 Run
8 Trail No. 1 represents : the total absenteeism of 100 students on Monday with no call-back for School 2. (response = total number of days absent from each category for 100 students.) Factor Designation Orthogonal Table Trail No. A B C Response Full Factorial Design Friday and call-back are best. However, this model does not address the interaction.
9 Consideration of interaction among factors. Trial No. Factor Designation A B C AB BC AC ABC Response
10 How to cook a delicious cake? Y = f (Temp, Time, Flour, Butter, Baking Powder,.) Temp = 165 deg C or 180 deg C???? Time = 35 min or 44 min?????
11 TCP IC Heat Seal Bonding LCD HS Bonding Peel Off Force = f (Temp, Press, Time, Cushion Material.)
12 OBJECTIVES of DOE Maximize the amount of information Identify factors that (a) affect the average response; (b) affect the variability; (c) do not contribute significantly. Identify the mathematical model relating the response to the factors. Identify optimum settings for the factors. CONFIRM the settings.
13 Major Steps In DOE Design of experiment (DOE) is an iterative decision-making process. Like any area of applied science, the steps involved in DOE can be grouped into three stages: analysis, synthesis, and evaluation. These phases are characterized as: Analysis: (a) Recognition of the problem; (b) formulating the experimental problem; (c) analysis of the experiment. Synthesis: (a) Designing the experimental model; (b) designing the analytical model. Evaluation: (a) Conducting the experiment; (b) Deriving solution(s) from the model; (c) Make appropriate conclusions and recommendations.
14 Basic Concepts in DOE Test run: Single combination of factor levels that yields an observation on the response. Block: A group of homogeneous experimental units. Blocking an experiment is arranging the runs of experiment in group ( block ) so that runs within each block have as much extraneous variation in common with each other as possible e.g. using material from the same lot, evaluation under the same machine/line. Randomization: This refers to assigning the experimental units randomly to treatments. Replication: It means independent runs conducted at identical set of factor levels, in which all sources of inherent variation are present. By measuring different times within the same run. It is REPEAT. Sample 1 To generate another set of data with different run (same factor and level). It is REPLICATION. Sample 1 Sample 2 Sample 2
15 Basic Concepts in DOE Confounding: When one or more effects that cannot be unambiguously be attributed to a single factor or interaction. Covariate: An uncontrollable variable that influences the response but is unaffected by any other experimental factors. Covariates are not additional responses and hence their values are not affected by the factors in the experiment. Treatments: e.g. For example if a teacher wishes to compare the relative merits of four teaching aids: a) text book only, b) text book and class notes, c) text book and lab manual, d) text book, lab manual and class notes. i.e. treatment = four teaching aids.
16 Selection of Variables and Factors Usually there will be only one response variable and the objective of the experiment will indicate the response variable. The response variable can be qualitative or quantitative. The selection of factors is a critical one and involves a detailed plan. At first all possible factors, irrespective whether they are practical to be measured or not, should be included in the experiment. A common approach is to use a cause-and-effect diagram listing all the factors.
17 EXAMPLE A new brand of printing paper is being considered by a leading photographic company. The study will be focusing on the effects of various factors on the development time. So, the response variable for this is the development time. The experiment will consists of the following steps: (i) a test negative will be placed on the glass top of a contact printer; (ii) a sample of printing paper will be placed on top of the negative; (iii) the light on the contact printer will be turned on for a specific amount of time; and (iv) the printing paper will be placed on a developing tray until an image appears.
18 EXAMPLE (cont d) The following factors are considered to play a role: (1) exposure time; (2) density of test negative; (3) temperature of the laboratory where the developing is done; (4) intensity of exposing light; (5) types of developer; (6) amount of developer; (7) grade of printing paper; (8) condition of printing paper; (9) voltage fluctuations during the experiment; (10) humidity; (11) number of times the developer will be used; (12) size of printing paper; and (13) operator.
19 EXAMPLE (cont d) After careful study, the company decided to use three factors: 1) exposure time; 2) type of developer, and 3) grade of printing paper The remaining factors are either controlled or made as experimental error in the experiment.
20 EXAMPLE (cont d) - SMT Y=f(Xs)
21 Mean response Mean response Level 1 of factor 2 Level 2 of factor 2 Level 1 of factor 2 Level 2 of factor Levels of factor Levels of factor 1 (a) Only factor 1 significantly affects the mean response (b) Only factor 2 significantly affects the mean response Mean response Mean response Level 1 of factor 2 Level 1 of factor 2 Level 2 of factor 2 Level 2 of factor Levels of factor 1 Levels of factor 1 (c) Both factors 1 and 2 significantly affect the mean response: no interaction (d) Both factors 1 and 2 significantly affect the mean response: with interaction
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