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    Ghaleb Y. Abbasi, Hussein S. Ketan, and Mazen B. Adel

    October 2005 The Arabian Journal for Science and Engineering, Volume 30, Number 2B 245

    INTEGRATING DESIGN AND PRODUCTION PLANNINGWITH KNOWLEDGE-BASED INSPECTION PLANNING

    SYSTEM

    Ghaleb Y. Abbasi*

    Industrial Engineering Department, Faculty of Engineering & Technology, University of

    Jordan

    Hussein S. Ketan and Mazen B. Adil

    Industrial Engineering Department, University of Technology, Baghdad, Iraq

    :.

    "."

    .

    .

    .

    ABSTRACT

    In this paper an intelligent environment to integrate design and inspection was

    introduced to bring inspection earlier to the design stage. A hybrid knowledge-based

    approach integrating computer-aided design (CAD) and computer-aided inspection

    planning (CAIP) was developed, thereafter called computer-aided design and inspection

    planning (CADIP). CADIP was adopted for automated dimensional inspection planning.

    Critical functional features were screened based on certain attributes for part features forinspection planning application. Testing the model resulted in minimizing the number

    of probing vectors associated with the most important features in the inspected prismatic

    part, significant reduction in inspection costs and release of human labor. In totality, this

    tends to increase customer satisfaction as a final goal of the developed system.

    Key Words:Planning, inspection, prismatic parts, integration, CAD, CAM, and CMM.

    *Address for correspondence:

    Associate Prof. and Chairman, Industrial Engineering Department, Faculty of Engineering & Technology, University of Jordan,

    Amman Jordan. Tel. + 962 6 535 5000, Fax + 962 6 535 5888. E-mail: [email protected]

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    The Arabian Journal for Science and Engineering, Volume 30, Number 2 B October 2005246

    INTEGRATING DESIGN AND PRODUCTION PLANNING WITH KNOWLEDGE-BASED

    INSPECTION PLANNING SYSTEM

    1. INTRODUCTION

    Due to market competitiveness, the demand to apply modern tools and techniques to automate product inspectionhas increased. An automated product quality inspection not only reduces the inspection costs but also releases human

    labor from a heavy workload. The main objective of a modern manufacturing company is to bring new and carry-over

    products to customers before competitors, with lower cost, and improved quality. This mechanism is called quality

    function deployment (QFD), which represents a change from the old manufacturing quality control to product

    development quality control [1].

    Quality engineering uses robust design to improve product quality and reduces the effects of variation [2].

    Computer-based product quality inspection has introduced fresh perspectives in production control. This is primarily due

    to the advances in image processing, pattern recognition, classification, computer vision and robotics, artificial

    intelligence, and above all in the microelectronics and sensors [3].

    Computer aided design (CAD) is the corner stone of the modern manufacturing environment. Computer integrated

    manufacturing (CIM), and the CAD and computer aided manufacturing (CAM) systems are well established in the

    literature. It is strongly recognized in the literature that to take a component model from present CAD systems andautomatically generate all the information needed for down stream activities, such as inspection, is smething far from

    being accomplished. Hence, the linking and automation of CAD and computer-aided inspection (CAI) systems for

    product is considered a fertile research ground [47].

    Due to the change brought about by the spreading use of CAD/CAM systems and concurrent engineering inindustry dimensional accuracy has been one of the primary concerns in manufacturing. Among many forms of

    metrological apparatus is the use of a coordinate measuring machine (CMM) in dimensional inspection [8]. CMM is an

    electromechanical system designed to perform coordinate metrology. It consists of a contact probe positioned in three-

    dimensional (3-D) space relative to the surfaces of the work part; the x, y, and z coordinates of the probe can beaccurately and precisely recorded to obtain dimensional data concerning the part geometry to accomplish measurement

    in 3-D. Basic CMM is composed of the following components: probe head to contact the work part surfaces, mechanical

    structure to provide motion of the probe in three Cartesian axes, and displacement transducers to measure the coordinatevalues of each axis. In addition, many CMMs have a drive system and control unit to move each of the three axes, and

    digital computer system with application software [9, 10].

    Inspection is an important element toward assuring customer satisfaction. In this paper a knowledge-basedapproach is used to integrate a hybrid of computer-aided design (CAD) and computer-aided inspection planning (CAIP).

    This system is called computer-aided design and inspection planning (CADIP), which is used in automated dimensional

    inspection planning [11].

    2. CURRENT STATE OF INTEGRATING DESIGN AND INSPECTION

    The design process consists of several phases ranging from analysis of customer requirements to downstreammanufacturing, including inspection and testing. Inspection is the fulfilling of specifications laid down by designers and

    manufacturers. The preliminary product design stage involves finding the form, shape, and size of product to satisfy

    functionality, while the detailed product design stage involves determining product quality as dimensional accuracy,surface finish, and product final functionality [1].

    Inspection of the product/part requires knowledge and interpretation of the product design intent, process used,capabilities of inspection methods, and tools available. CAD is considered the cornerstone of CIM. To integrate CAD

    with subsequent applications, such as inspection, manufacturers have automating the function of product inspection as amean for improving productivity and quality and of reducing labor costs.

    In the physical world, a product consists of units and/or parts. Each unit is described by a number of geometric

    entities associated with technical specifications. Hence, the proposed design representation should provide detailed

    descriptions so that the product model can support variety of applications such as inspection. Featured based design(FBD) is a process in which parts are specified in terms of their constituent parameterized form features, instead of

    geometry command such as line, arc, or primitive commands such as cylinder and cone. It ensures that the featureinformation necessary for the downstream applications such as inspection as a part of process planning is incorporated as

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    October 2005 The Arabian Journal for Science and Engineering, Volume 30, Number 2B 247

    early as possible in the design cycle. FBD encompasses approaches to incorporate features into a CAD model such as

    automatic feature recognition (AFR) and design by features (DBF). The AFR approach is used to take the General CADmodel as it is available commercially and provides an automated interface to recognize and extract the manufacturing

    features from the model. This feature extractor will derive all part features based on geometric and topologicalinformation stored in the CAD database. In contrast the DBF approach, features are incorporated into the part model

    from the beginning. Generics feature definitions are placed in the library from which features are instanced by specifying

    dimension, location parameters, and various attributes [6].

    The major problem with transfer of CAD geometry to an off-line programming (OLP) system via CAD exchangestandards is that these do not encompass tolerance data important for the evaluation of specific results. This is often done

    with the CMM software, and by the automation of many inspection planning tasks. Efforts have been made in the past

    several years to address the problems associated with the integration of CAD and the automation measuring instruments.These efforts in cluude Cowling and Mullineux [6], Marefat et al [12], Ngo and Tan [13], Lin and Chen [14], OGrady et

    al [15], Legge [5], Jeang [2], Ziemian and Medeiros [16], and Huang and Gu [17]. These efforts were oriented in the

    following four directions:

    1. Using FBD technology.

    2. Development of algorithms and techniques to evaluate actual geometric tolerances using measurement data.

    3. Development of techniques for automatic generation for inspection programs from current CAD database.

    4. Application of artificial intelligent (AI) expert system in the building of inspection process planning systems.

    The above mentioned literature tackled the problems of probe selection, point selection, measuring sequence, andpath planning and feature accessibility. These inspection systems avoided explicit consideration to discuss determining

    the appropriateness of measuring features instead of the philosophy of checking all dimensions of a part to validate the

    product function or quality.

    It seems appropriate to develop some certain guidelines based on design and manufacturing knowledge along withinspection concept and practice for inspection planning. This paper implemented an environment based on this concept

    via the use of critical functional features (high level features) which are screened, based on certain attributes, for part

    features such as geometric parameter tolerances (GPT), geometric characteristic tolerances (GCT), and process capability(PC) as design, manufacturing, and inspection knowledge for the inspection planning application. The developed

    environment integrates CAD and CAIP systems to assist in inspection planning tasks, i.e. reduce measurement points,

    sequences and paths, traveling distances, positions of measurement points etc., to direct the operation of the flexible

    inspection system CMM for the dimensional inspection of the prismatic parts. In this research CMM will be directedtoward the most important features to be inspected to plan the inspection according to the inspection knowledge and

    rules that reside in the system, resulting in less workload and more reliability.

    3. AUTOMATED DIMENSIONAL INSPECTION PLANNING

    Dimensional inspection planning consists of determining plans and instructions for measuring the dimensions and

    tolerances of the object's different attributes. A typical automating planning system must be able to [12]:

    1. Find the abstract shape information (higher-level feature) in a part.

    2. Determine the relationships between the features.

    3. Determine, on the basis of the above information, the physical entities (edges, etc.) to be measured.

    4. Determine the possible probe locations and a probe direction.

    5. Minimize probing operations while achieving successful measurement of all entities (optimization).An important aspect of automated inspection planning is to establish which planning elements are required to allow

    inspection of all component features. The automated inspection elements are as follows [5]:

    1. Component/probe orientation strategy.

    2. Probe point placement algorithms and probing density.

    3. Sequence of probing.

    4. Clash avoidance clash detection/evasion.

    5. Generation of DMIS programs.

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    The Arabian Journal for Science and Engineering, Volume 30, Number 2 B October 2005248

    There are two approaches to drafting the inspection plan [8, 18]. A generative approach, where the plan generated

    is completely new, the planning system must have enough intelligence to interpret the task-oriented instructions and inferthe inspection plan. The second is the variant approach, in which the sample inspection plans of product variants are

    stored in the computer. The planner retrieves these plans and fills in the parameters needed for describing the inspectedobject.

    Several researchers have addressed the integration of numerical CMM with CAD system via computer-aidedinspection process planning (CAIPP) including Dereli and Filiiz [19], Saini and Jovanovski [20], Rashed [21], Duffuaa

    and Al-Najjar [22], Cho and Kim [23], Lim and Menq [24], Yau and Meno [10], Menq et al. [9], and Cowling andMullinenx [6]. However, this work showed that the designers philosophy lies in inspecting all features to validate the

    part, with the drawbacks of the CMM as being only an accurate digitizer lacking inspection planning. Therefore

    automated inspection planning becomes increasingly important to enhance the CMM capability.

    Planning by computer has become an accepted method with the development of good expert systems for qualitycontrol (QC) planning [18]. It is certain that there will be no universal generic planning system to handle inspection of all

    products because there is no general definition of product features: design, manufacturing, inspection. Future planningsystems for inspection will be domain-specific for families of product variants. Hence, a prismatic part and three families

    of polyhedral features have been selected for system implementation.

    4. CADIP SYSTEM CONCEPT

    The system concept is explicit in the framework as shown in Figure (1), it is composed of four key elements: designby feature; data exchange format (DXF) files, feature recognizer, and inspection planner. A CADIP system is used toassist in flexible inspection planning to direct the operation of the flexible inspection system CMM inspection of the

    prismatic parts. This research aims at achieving inspection environment that will lead to automated dimensional

    inspection.

    Small scale CAD DBF

    Product design model

    AutoCAD Tool

    DXF Files

    Feature Recognation ModuleFeatures

    Recognation Exctraction

    Common PartDefinition Data

    File

    CAIPInspectionPlanner

    InspectionSystems

    y CMM

    Figure 1. Framework of CAD/CAIP integration

    5. CADIP SYSTEM METHODOLOGY

    This research develops an integrating environment including a hybrid CAD sub-system and a CAIP sub-system used togenerate the inspection plan and detailed instructions for inspecting the final products. These components share a

    common database that correlates and incorporates their data as shown in Figure 2.

    The goal is to develop a system in which design and inspection planning are integrated. In inspection planning, the

    strategy of measuring a components attributes which include high level features such as slots, steps, holes, etc. and thelow-level features such as lines, points, etc. is achieved by considering the interactions between these features. The

    methodology is achieved via the following:

    1. Rules, structures, and pointers-based representation of knowledge and modeling of behavior of theindividual components in the design and inspection planning

    2. Developing other necessary components such as interfaces data models to achieve the integratedenvironment.

    3. Developing a flexible approach for design by feature, feature recognition of 3-D prismatic parts, and aknowledge-based geometric reasoning approach for automated inspection planning.

    The CADIP system includes three basic modules: design by feature module; feature recognition module, andinspection planning module

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    October 2005 The Arabian Journal for Science and Engineering, Volume 30, Number 2B 249

    DXF F.R.

    D.B.D.B.F.

    InspectionPlanner

    UserInterface

    (U.I.)

    Figure 2. CADIP system components

    6. INSPECTION PLANNING KNOWLEDGE BASE

    The function of the inspection planning module is to generate the inspection plans and instructions for measuringthe dimensions and tolerances, optimizing probing and processing operations of the objects different attributes.

    Preparation of an inspection knowledge base entails the listing of:

    1. Working faces in which features are created.

    2. High-level feature types created on a certain working face.

    3. Feature directions and probe locations.

    4. The settings for each feature, which are determined by, feature type and direction.

    5. Inspection parameters and measuring edges for each setting.

    6. Edge limits and edge value.

    7. Probe approach directions and probe inspection directions for measurable edges for each setting.

    By determining the list of setting features and their measurable entities of the part feature(s), inspecting methods

    can be determined. There is more than one way to inspect an attribute, for example as shown in Figure 3(a), a non-interacting S-slot has four edges that can be used to effectively determine its length (L). The higher-level shape

    information is extracted from the CAD model using geometric reasoning mechanism. This information is used todetermine the different attributes to be measured and the different methods for measuring each attribute.

    In modeling this knowledge the concept variant feature is exploited as a super class feature that is of two types:

    prismatic and rotational features. This concept captures a common model about subclass features of the super class

    feature. New feature shapes can be implemented as simple and compound shapes by simply adding a new supper classfeature to the subclass feature.

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    The Arabian Journal for Science and Engineering, Volume 30, Number 2 B October 2005250

    Figure 3. Descriptive knowledge details of S-slot feature.

    1

    1

    2 6

    5

    3

    4

    7

    8

    23

    4

    5

    67

    8

    Primary

    setting

    Secondary

    setting

    Secondary

    setting

    X

    Y

    Z

    6

    8

    7

    5

    4

    23

    1

    6

    8

    7

    5

    4

    23

    1

    DE

    DE

    AE

    AEAE

    AEAE AE

    AE

    AE

    DF-1

    AF-3

    AF-1

    AF-2

    DF-2 DF-3

    Figure 3(a) Boundary vertices, primary and secondary setting for object and S-slot feature.

    Figure 3(b) Dummy Faces (DF) and Active Faces (AF) for

    S-slot feature. Figure 3(c) Dummy Edges (DE) and Active Edges (AE) fors-slot feature.

    6

    8

    7

    5

    4

    23

    1

    L

    w

    d

    Figure 3(d) Geometric parameters for S-slot feature.

    8

    7

    5

    4

    3

    1

    Figure 3(e) Best loops and paths for measuring S-slot create

    on face-3 in x-direction with reference vertices (vertex-1 and

    vertex-2).

    2

    6

    1,2,6

    1,5

    4

    2 5

    1

    363,4,5

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    October 2005 The Arabian Journal for Science and Engineering, Volume 30, Number 2B 251

    To determine which geometric entities should be used during inspection, the system should know the abstract

    feature attributes that need to be inspected and how they are related to the geometric entities of the part. This informationis represented in rules and captured in the structure called inspection-structure which is used to model the collection of

    attributes to be measured for a particular feature, for example as shown in Figure (4) a S-slot creation in differentworking faces and directions and its inspection attributes viewed from different settings.

    The information for determining which geometric entities should be used for each attributes measurement isrepresented by rules in another structure calleddesign-structure and this information is retrieved as needed. These rules

    basically determine the different strategies one can use for an attributes inspection and are instrumental in reasoningwith abstract information about the part.

    Figure 4. S-Slot created on indifferent working faces and directions.

    1

    23

    45

    67

    81

    23

    4

    5

    67

    8

    1

    23

    4

    5

    67

    81

    23

    4

    5

    67

    8

    1

    2

    3

    4

    5

    6

    7

    8

    1

    2

    3

    4

    5

    6

    7

    8

    Figure 4(a) S-slot on face-1 in Y and Z directions. Figure 4(b ) S-slot on face-1 in Y and Z directions.

    Figure 4(c) S-slot on face-2 in X and Z directions Figure 4(d) S-slot on face-2 in X and Z directions

    Figure 4(e) S-slot on face-3 in X and Y directions. Figure 4(f) S-slot on face-3 in X and Y directions.

    X

    Y

    Z

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    The Arabian Journal for Science and Engineering, Volume 30, Number 2 B October 2005252

    Based on the primary setting faces (working faces) and the secondary faces (faces interacting with primary faces) as

    shown in Figure 3(a), the inspection plan parameter for each feature in any direction and location can be determined suchas probing locations (inspection points), probe approach directions, probe inspection directions, linked with a list of all

    the physical entities (currently edges) which can be successfully inspected. These settings and edges are illustrated in

    Table 1 for slot feature family.

    Based on dummy and active faces, the different combinations of the proposed probe locations, approach directions,and inspection directions are systematically explored and simple classification procedure is performed to determine

    whether a minimum set of required entities of the part could be measured from the particular probing combination. Forexample, based on analysis of dummy and active faces analysis as shown in Figure 3 and Table 2 one can determine the

    best loops and paths for inspection attribute to S-slot feature as following: best loops are (14) and (37). The best paths

    from vertex (1) to vertex (7) are path (1) = 17, path (2) = 17, and path (3) = 17. While, from vertex (2) to vertex (8)

    the best paths are: path (4) = 28, path (5) = 28, and path (6) = 28. The best combination of probe parameters (probeapproaches, and probe inspection direction), feature attribute's edges, edge value, etc. are used to construct an inspection

    plan. After the inspection plan construction, the plan is logically represented to be used by the inspection system.

    Table 1. Geometric Inspection Knowledge for Slot Feature Family.

    Feature

    TypeWorkFace

    Direction

    Setting - 1 Setting - 2 Setting - 3

    L w1 w2 d1 d2 L w1 w2 d1 d2 L w1 w2 d1 d2

    S. slot Y E1-2 E2-3 E2-3 E6-7 E2-6 E3-7

    B. slot E3-4 E1-4

    V. slot Z E1-4 E1-2 E3-4 E7-8 E4-8 E3-7

    D. slot

    F1

    E2-3 E3-4

    W. slot X E3-4 E7-8 E4-8 E3-7 E4-1 E1-2

    E2-3 E3-4

    Z E1-2 E2-3 E2-3 E6-7 E2-6 E3-7

    F2

    E3-4 E4-1

    X E3-4 E7-8 E4-8 E3-7 E1-4 E1-2

    E2-3 E3-4

    Y E2-3 E6-7 E2-6 E3-7 E1-2 E2-3

    F3

    E3-4 E1-4

    7. INSPECTION PLANNING MODULE

    The inspection planner is a knowledge-based system that is an AI technique, as shown in Figure 5. A major

    component of inspection planning is the inspection planning knowledge, which includes the following.

    1. Declarative knowledge: this about the problem part information and features, inspection characteristics specification,and manufacturing processes, etc. A sample of this knowledge is illustrated in Figures 3 and 4 and Table 1 for theslot feature family.

    2. Procedural Knowledge: this is about how to solve problems that reside in the system, sample of this knowledge isillustrated in Table 3 for S-Slot feature. Declarative and procedural knowledge constitute the system's problem

    solving knowledge.

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    October 2005 The Arabian Journal for Science and Engineering, Volume 30, Number 2B 253

    Functional FeatureGeometry Inspection Attributes

    Knowledge of Inspection

    FunctionalFeature

    Attributes

    Inspection Plan

    Figure 5. Framework of inspection planner

    In order to automate the inspection planning, inspection attributes are stored in CAD database along with geometric

    model for making inspection plan. Geometric knowledge consists of a hierarchal description including part CADboundary representation, which consists of the description of faces, edges, and vertices. Since this information is not

    sufficient for the required reasoning at higher description level, information about the type of shape features such assteps, holes, etc. and its locations represented and tied with lower level descriptions.

    The activities of the CADIP system are built for the inspection of machining and net shaped products of prismatic

    parts. The function of inspection planning module is to generate the inspection attributes, inspection points, and probing

    directions (probe approach and inspection directions) for the selected feature attributes. The example shown in Table 3

    represents knowledge that is used to generate inspection plan for the S-slot feature.

    After inspection, data is generated from the inspection planning module and downloaded to CMM.

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    Table 2. Dummy faces, active faces, best inspection loops, and best inspection paths for S-slot feature.

    Active Face

    (AF)

    Dummy Face

    (DF)

    Active Edge

    (AE)

    Dummy Edge

    (DE)

    Feature

    Type

    AFs loop

    vertices

    DFs Loop

    vertices

    AEs

    No.

    Edges DEs

    No.

    Edges

    S-Slot AF-1 1-4-8-5 DF-1 3-4-8-7 10 1-4, 4-8, 8-5,5-1

    2 1-2, 3-4

    Create on AF-2 5-6-7-8 DF-2 1-2-3-4 5-6, 6-7, 7-8

    F-3 in AF-3 2-3-7-6 DF-3 1-2-6-5 2-3, 3-7, 2-6

    X-direct-

    Ion

    Inspection Loops Inspection Edges Direct accessibility loops For

    G. parameters Inspection

    No loop

    vertices

    No Edges Inspection

    loops

    edge G.

    parameter

    6 1265 12 12,26,65,51 1234 12 w

    2376 23,37,76 23 L1485 14,48,85 34 w

    1234 34 14 L

    3487 87 3487 34 w

    5678 48 d

    87 w

    37 d

    1265 12 w

    26 d

    65 w

    51 d

    Best

    inspection

    loops

    Best motion

    paths

    No. of

    inspection

    points

    No. of

    settings

    Surface finish

    inspection loops

    1234 1487 4 2 AF1 1485

    And 1437 4 2 AF2 5678

    3487 1237 4 2 AF3 2378

    Or 2378 4 2

    1234 2348 4 2

    and 2148 4 2

    1265 4 2

    B

    A

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    Table 3. Inspection Plan Parameters for S-slot Feature Type

    Edge LimitsFeature

    type

    Working

    Face

    Face

    Direction

    Settings

    Inspection

    Parameter

    Parameter

    Edge

    From ToEdge

    Value

    Difference

    Probe

    approach

    orientation

    Probe

    Inspection

    orientation

    No. of

    Inspection point

    L 1-2 (1,1,1) (1,1,1) Y2-1 1,0,0 0,1,0 2

    3-4 (1,1,1) (1,1,1) Y4-3 1,0,0 0,1,0 2

    w 2-3 (1,1,1) (1,1,1) Z3-2 1,0,0 0,0,1 2

    1

    1-4 (1,1,1) (1,1,1) Z4-1 1,0,0 0,0,1 2

    w 2-3 (1,1,1) (1,1,1) Z3-2 0,1,0 0,0,1 2

    6-7 (1,1,1) (1,1,1) Z7-6 0,1,0 0,0,1 2

    d 3-7 (1,1,1) (1,1,1) X7-3 0,1,0 1,0,0 2

    0,1,0 2

    2-6 (1,1,1) (1,1,1) X6-2 0,1,0 0,0,1 2

    L 1-4 (1,1,1) (1,1,1) Z4-1 1,0,0 0,0,1 2

    2-3 (1,1,1) (1,1,1) Z3-2 1,0,0 0,0,1 2

    w 1-2 (1,1,1) (1,1,1) Y2-1 1,0,0 0,1,0 2

    1

    3-4 (1,1,1) (1,1,1) Y4-3 1,0,0 0,1,0 2

    w 3-4 (1,1,1) (1,1,1) Y4-3 0,0,1 0,1,0 27-8 (1,1,1) (1,1,1) Y8-7 0,0,1 0,1,0 2

    d 3-7 (1,1,1) (1,1,1) X7-3 0,0,1 1,0,0 2

    S-Slot

    created

    ondifferent

    work

    faces

    anddirections.

    F1

    0,0,1

    3

    4-8 (1,1,1) (1,1,1) X8-4 0,0,1 1,0,0 2

    8. INSPECTION PLAN GENERATION8.1 Critical Functional Feature Screening Criteria

    The developed system has been applied in two industrial firms, by inspecting and checking all features of the

    manufactured parts. A simple verification procedure uses three criteria to filter the more critical functional features forinspection planning purposes. These are:

    (i) - Geometric parameter tolerances (GPT) criteria: to classify the more critical feature(s) of a group of part features,

    this is achieved by increasing-order of the geometric parameter tolerances.

    (ii) - Geometric characteristic tolerances (GCT) criteria: to classify the more critical feature(s) of a group of partfeatures, this is achieved by the same manner in criteria (i).

    (iii) - Process Capability indexes (PCIs) criteria: which is the more comprehensive criteria giving indication based on

    the three types of knowledge i.e. GPT, GCT, and PC to determine the normal, critical, and the feature to be modified. For

    this reason the PCIs criteria proposes for best inspection plan generation by CADIP system implementation. The PCIswork as follow: define the process capability, define the tolerance limits for GP and for GC tolerances, then calculate the

    PCIs based on GP and GC tolerances as (PCIs)1 and (PCIs)2 respectively using the PCI formula:

    6..

    LUICP

    = (1)

    Where U,L = denotes upper and lower tolerance limits, = denote the standard deviation.

    Classify the results of PCI to be =1, >1,

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    Select GPTs Select GCTsManufacturing

    features

    Increaseing order oftolerance value

    Select PC values

    Select the first G P asa criteria

    Select the first GCas a criteria

    Determine ULand L

    Determine ULand L

    DeterminePCI =(U-L)/6

    ModifyPC or GP

    ModifyPC or GC

    PC =1 OR >OR OR SA or

    PA=

    PA