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مقارنة مقدرات انحدار الحرف والمركبات الرئيسية والمربعات الصغرى الجزئية في نموذج الانحدار

Author name: زينب كاظم مزهر القريشي
Supervisor name: شروق عبد الرضا سعيد السباح
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Karbala
First pages:

استخدام المتغيرات الموزعة زمنيا في تحليل الانفاق الاستهلاكي في العراق للمدة (2014 - 1995) == The Use of Temporally Distributed Variables in the Analysis of consumer spending in Iraq for the Period (2014 - 1995

Author name: اسراء فالح فاضل المسافري
Supervisor name: عدنان كريم نجم الدين
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Karbala
First pages:

اختيار النموذج الافضل لصفوف الانتظار في تحدين الخدمة المصرفية == Choose the best model for queues In improving the banking service

Author name: انصاف جاسم مهدي المسعودي
Supervisor name: عبد الحسين حسن حبيب الطائي
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Karbala
First pages:

العلاقة بين جدول تحليل تباين الانحدار وجدول تحليل تباين التجارب العاملية الكاملة == The relationship between the regression ANOVA table and ANOVA Table in Complete Factorial Experiments

Author name: رواء نوري حسين الشيخلي
Supervisor name: عواد كاظم الخالدي
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Karbala
First pages:

اختيار افضل طرائق تقدير المتغير المعتمد متعدد الاستجابة == Choose the best estimation Methods for the multi - response dependent Variable

Author name: ليث علي محمد الحيالي
Supervisor name: عبد الحسين حسن حبيب الطائي
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Karbala
First pages:

تقديرات دالة المعولية لتوزيع بواسون مع تطبيق عملي == Estimation of reliability function for Poisson distribution With practical application

Author name: زينب محمد باقر صادق الباقر
Supervisor name: عبد الحسين حسن حبيب الطائي
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Karbala
First pages:

دراسة الارتباط القانوني في نماذج الانحدار الخطي واللا خطي : دراسة تطبيقية == Study Canonical correlation in regression models linear and non linear Applied study

Author name: الاء فلاح حسن عطوان
Supervisor name: شروق عبد الرضا سعيد السباح
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Karbala
First pages:

استخدام اسلوب البوتستراب في تحليل النماذج المعلمية و شبه المعلمية و المقارنة بينهما == Use The Bootstrap in Parametric Models and Semi - Parametric Analysis and Comparison Between Them

Author name: نـور عـباس عمران النــصــراوي
Supervisor name: شــروق عــبـــد الــــرضا الســـباح
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Karbala
First pages:

استخدام التحليل الشكلي لمقارنة تاثير بعض المواد الكيميائية على صفات نبات الخيار == The use of profile analysis to compare the effect of some chemicals on the properties of cucumber

Author name: نبراس صلاح مهدي الموسوي
Supervisor name: شروق عبد الرضا سعيد السباح`
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Karbala
First pages:

توظيف تحليلات التجربة العاملية في تقدير انتاجية محصول الباذنجان في البيوت الخضراء الزراعية == Utilizing the analysis of factorial experiment in estimating the productivity of eggplant crop in the greenhouses

Author name: حمزة عماد عباس الدبس
Supervisor name: عواد كاظم الخالدي
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Karbala
First pages:

تقدير معولية نظام Cascade الاجهاد - المتانة لتوزيع احتمالي == Estimation of the reliability of the Cascade Stress - Strength System For probability distribution

Author name: سناء علي محمد العبودي
Supervisor name: مهدي وهاب نعمة نصر الله
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Karbala
First pages:

توليد المتغيرات العشوائية لتخمين معلات توزيع لوجستك باستخدام محاكاة منت كارلو == Generating Random Variates for Estimating the Parameters of Logistic Distribution by Monte Carlo Simulation

Author name: زهراء امروي علي حيدر الحجار
Supervisor name: اكرم محمد العبود
General topic: Mathematics
Specific topic: Statistics
Degree: Master
Language: English
University location: Baghdad
First pages:
Abstract: In this work, we consider the Logistic distribution of two parameters for its importance in statistics. Mathematical and statistical properties of Logistic distribution are considered, moments and higher moments are illustrated to the distribution parameters, namely, moments methods, maximum likelihood method, modified moments method, least squares method are discussed theoretically and assessed practically by utilizing two procedures of Monte Carlo simulation for generating random variates from the Logistic distribution. Properties of the estimators, such as Bias, variance, skewness, kurtosis and mean square error measurement are tabulated.

استخدام طريقة المربعات الصغرى المتناقصة والتمهيد المباشر في تقدير معلمات انموذج فورير للسلاسل الزمنية الموسمية == Using The Discounted Least Squares And Direct Smoothing Method For Estimate Fourier Parameters For Seasonal Time Series

Author name: محمد عبد الحسين محمد الغريباوي
Supervisor name: سلمى ثابت ذاكر الالوسي
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Baghdad
First pages:
Abstract: هناك العديد من الطرائق التي يمكن استخدامها في دراسة السلاسل الزمنية الموسمية , وطريقة فورير واحدة من هذه الطرائق التي تتعامل مع بيانات السلسلة الزمنية كسلوك جيبي باستخدام الدوال المثلثية. في هذا البحث تم استخدام (طريقة المربعات الصغرى المتناقصة والتمهيد

استعمال انموذجات بوكس جينكنز للتنبؤ بوفيات حوادث المرور في محافظة كربلاء المقدسة للمدة 2010 - 2015 == Using Box - Jenkins’s Models For Analysis Road Accident Fatalities In Holly Karbala For The Period (2010 - 2015)

Author name: صبا جسوم عكلة
Supervisor name: عدنان كريم نجم الدين
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Baghdad
First pages:
Abstract: Time series Aproach concidered of important topics that it deals with the behavior of phenomena and its interpretations through different periods of time. This thesis aims to analyse Road Accident Fatalities in Holly Kerbala for period (2010 - 2015 ) using time series technique ( Box&Jenkins ) method.The outcome of the series analysis showed that the appropriate model is ARIMA )0,1,1).According to this model 10 years forcasts in monthly base was obtained for the Road Accident Fatalities inHolly Karbala for the period (2016 - 2026 )One of the important findings of this thesis is the consistency of the forcasts with the observed one which refers to the efficiency of the model.

بناء انموذجي بقاء معلمي ولا معلمي لمرض التدرن في بغداد

Author name: حسنين جليل نعمة الساعدي
Supervisor name: حامد سعد نور الشمرتي
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Baghdad
First pages:
Abstract: ان الفكرة الاساس للبحث بدات من محاولة ايجاد تطبيق للانموذج الاحصائي المعلمي واللامعلمي في دراسات البقاء والحدث الحرج ( الوفاة , شفاء ) للمصابين بمرض التدرن الرئوي وغير الرئوي والتي تتطلب اتخاذ قرارات تستند على اسس علمية , حيث تم اختيار الانموذج اللوجستي ا

بناء منظومة خبيرة لتشخيص التقارب لبعض التوزيعات الاحتمالية المتقطعة == Design An Expert System To Determine The Approximation In Some of Probability Distribution

Author name: وليد مية رودين
Supervisor name: علي عبد الحسين الوكيل
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Baghdad
First pages:
Abstract: ان الاستخدام الكبير والمستمر للتوزيعات الاحتمالية جعل هذا الحقل المتخصص متميزا في علم الاحصاء حيث يدل على مجموعه من الاحتمالات المرتبطة بقيم متغير عشوائي ناتج عن نوع خاص من التجارب , فعلى سبيل المثال توزيع ثنائي الحدين فان قيم المتغير العشوائي المرتبط بت | The wide and continuous use for probability distribution made this specialized field distinctive in statistics science , that leads to a bunch of choices connected to values of random variable results from especial kind of experiments , as example binomial distribution the values of the random variable related to its experiments satisfies specific general conditions follows this distribution , when we study this distribution we can exclude expert on expectation related to all experiments that satisfies these general conditions according on what precedes it is suggested a(unit) instead of an statistics expert in searching field Depending of what precedes, we suggested a system instead of a statistical expert in the ( domain of determination of the approximation values ) between the probability distribution and determine the fit distribution of users data , The suggested system is an (statistical expert system ) , which have took its statistical knowledge from scientific resources and human experience to provide the needed consultation , which can be provided and any statistical expert (ITD) This system has a statistical knowledge base about , binomial distribution , and poisson and the relationship between a normal distribution , in addition to the statistical knowledge to determine the value that must the binomial approximate to the poisson , also the case is lead to approximated to the normal distribution.Also it has a statistical knowledge to calculate all distributions probabilities, in addition to all other measurements

المقارنة بين اختبار Shapiro - wilk وJureckova باستخدام المحاكات ولعدة توزيعات == Coodness - Of - Fit Test In Non Paramatric Tests

Author name: وفاء جاسم محمد العقابي
Supervisor name: دجلة ابراهيم مهدي العزاوي
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Baghdad
First pages:
Abstract: البحث يدرس عملية المقارنة بين اختبار (Shapiro - wilk) واختبار (Juareckova) قبل التوسيع وبعده. عندما اقترح Shapiro - wilk اختبار حسن المطابقة الحدسي( Nuisance location and Scaie Parameters ). ثم توسيعه الى حالة انحدار الازعاج المكاني ومعالم القياس (Nui | The research subject is the studying of the comparison between ( Shapiro - Wilk) and (Jurekov'a) test before and after the expansion , studying the effect of the sample size on the comparison, also the effect on test function distribution i.e.(diagnosing which tests asymptotic from the normal distribution ). Then applying the generating data which is simulated by several distributions which are normal distribution, Cauchy distribution, Laplace distribution, Logistic distribution, by changing the significance level ? by taking ( ? =0.01 ?= 0.05 ?= 0.1) The used assumption in this study is to study the matching between faults distribution and the distributions used in the study.

مقارنة طرائق تقدير المعلمات والمعولية لانماذج الاختبارات المعجلة والنمو لبيانات المراقبة من النوع الثاني مع تطبيق عملي

Author name: ورود باسم نور بهية
Supervisor name: انتصار عريبي فدعم الدوري
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Baghdad
First pages:
Abstract: نظرا لاهمية المعولية في التطبيقات الصناعية والهندسية فقد ظهرت الحاجة لاختبارات المعولية والتي هي سلسلة من الاختبارات والكشف عن العوامل التي تظهر خلال الاختبار وتاثيرات ومسببات عطل الماكنة نتيجة سوء الاستخدام وغيرها من الاسبباب وكذلك معرفة مدى ملائمة الان | Reliability has an important role in both the industrial and engineering applications. So the need for Reliability Tests appeared are series of tests a discover out of factors that appear through the test, also an effects too casese to defuse, probably to be created cases misuse a machine and other than, knowledge limit of fit a specifics production addition for getting on goodness of production. Therefore, the need for research to set of tests for censor data from ( Type II ) for exponential distribution with one parameter and these tests it’s (Accelerated Life Testing) to complete estimation parameters and reliability for the test models and these models it’s (Accelerated Cycling, Constant Stress ,Arrhenius and Eyring ) with tow methods ( maximum likelihood method, least squares method ) for all models above ,either Number of Units on Test To be complete calculation number of units inside in the test. And the other test is Reliability Growth includes three curves are Idealized Growth curve estimation parameters and reliability with maximum likelihood method, Duane Growth curve takes estimation parameters and reliability with least squares method, Exponential Reliability Growth Curve take estimation parameters and reliability by means of constraints for finding an optimal solution. Also The thesis so falls into four chapters. the first chapter is the introduction, the objective of the thesis as well as the review of literature. the second chapter tackles theoretical aspects contains exponential distribution,properties exponential distribution, estimation method, acceptance testing, accelerated life test, reliability growth testing and confidence intervals. The third chapter(application side)include tow parts,the first takes censor data (type II) from source (separate the soap off Al - Rasheed factory) and subjugate it for goodness of fit tests to be complete application on accelerated and growth tests, the second takes the simulation experimental and compared between estimation parameters for tests accelerated and growth for all models the test by depending on the statistic measure (MSE). Finally, the fourth chapter contains the more important findings and recommendations as well as the future visions which the thesis included. Also the thesis contains computer programs prepared by the researcher as well as another especial attaches.

مقارنة طرائق تقدير معلمات الانـموذج الثنائي اللوجستك المختلط باستخدام المحاكاة مع تطبيق عملي == Comparing The Estimation Methods of The Parameters of The Logistic Linear Mixed Model By Using The Simulation With Practical Application

Author name: هند وليد عبد الرحمن الجبوري
Supervisor name: ظافر حسين رشيد النجار
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Baghdad
First pages:
Abstract: تم في هذا البحث دراسة احد اهم النماذج الواسعة الاستخدام والتطبيق في تحليل البيانات التي تاخذ شكل تجمعات Clustered والتي تكون ذات استجابات مرتبطة Correlated وهو الانموذج الخطي العام المختلطGeneralized Linear Mixed Model (GLMM) لتحليل البيانات الطولية Long | This research was conserning in the study of one of the important models that are widely used in analyzing the data which take clustered form and have correlated responses, this model is Generalized Linear Mixed Model (GLMM) for analyzing the longitudinal data which it's responses are correlated. So this research was dealing with this model in an expanded form including its importance, uses, feature, modeling and the estimation methods then focusing on one of the most widely used examples when the responses of longitudinal Data are Binary which is Binary Logistic Mixed Model taking into account its modeling, importance, uses and the parameters estimation methods, so three important estimation methods were used to estimate the fixed and random effects parameters and these are : 1) Classical maximum likelihood (ML) Method.That include three basic algorithm by which the maximum likelihood estimator is obtained and it's as follows : I) Monte Carlo Newton Raphson (MCNR).II) Monte Carlo Expectation Maximization (MCEM).III) Simulation Maximum Likelihood (SML).2) Robust Maximum Likelihood (RML) Method.3) Penalized - Quasi Likelihood (PQL) Method.In the experimental aspect comparison was done of which is the best among these methods through the simulation procedure by using Monte Carlo method and implementing several experiments using two of the important statistical measures which are Mean Square Error (MSE) and Bias, generally as a result it was found that Robust Maximum Likelihood (RML) Method is the best between these methods as it has minimum Mean square error and minimum bias comparing with the other methods.While in the application aspect practical application was done on data represent the successive monthly measurements for diebetic children whom depend on the insulin treatment which represent the fixed effect and the patient represents the random effect in order to study the effect of both the insulin dose and the patient on the blood sugar rate, it was found that the insulin dose has significant effect on the blood sugar rate while the patient has not that effect

تقديرات الهجرة الداخلية في العراق باستخدام النماذج السكانية == Internal Migration Estimates In Iraq By Using Population Models

Author name: هالة وليد حمدي الزبيدي
Supervisor name: بشرى علي يعقوب الجعفري | خالد زهدي مصطفى خواجه
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Baghdad
First pages:
Abstract: ادى تزايد حركة السكان في العراق الى حصول هجرة داخلية.و لاهمية هذه المشكلة وما ترتب عليها من نتائج، لذا فقد حاولت الباحثة من خلال هذه الدراسة تحليل البيانات التي لها علاقة في نماذج حركة الهجرة الداخلية.وتهدف الى استنباط تيارات الهجرة الداخلية في القطر،وذ | Population Increasing movements in Iraq cause an internal migration. In spite of danger of this problem and what effects of it, so the researcher has tried through this study analysis the data, which relation in internal migration on models. Aiming at internal migration streams in country by using special population models of internal migration by direct and indirect methods. First chapter including general entrance displays general concepts and determines the problem and the purpose of the research and its importance and the background. The second chapter is measuring internal migration in Iraq and discusses the methods of the measure, the principal data references for migration, population distribution, the internal migration data in Iraqi census, the problem and difficulty of migration, the method of measuring internal migration from the census data is discussed by direct methods like Birth place, Duration of residence, The last residence and The reason of changing the residence place. The indirect methods like Vital statistics, The Survival ratio and National growth rate. The third chapter discusses the study of migration rates and ratios in Iraq and the demographic trace and divided into direct method like migration stream rates and in - migration, out - migration, net - migration rates and Birth - residence index, Gross intercensal interchange of population and Basic model. Indirect method like migration rates by using Survival ratio rates method, Vital statistics rates method, National growth rates method, and discuss the mathematical model and its relationship to internal migration, migration economic, demographic traces and migration effect on population growth. And the impetuses to internal migrations movement. The forth chapter discuss some important conclusions and recommendations.

تقدير الفعالية النسبية لانموذج القطع المكافئ في تجارب نسبة الميل لقياس تاثير زيتي الزعتر والكتان على الوزن == Estimation of Relative Potency For Parabolic Model In Slope Ratio Assays To Measure Effect of Thyme And Flax Oils On Weight

Author name: نضال بهجت محي الحيالي
Supervisor name: قيس سبع خماس
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Baghdad
First pages:
Abstract: يتناول البحث تقدير الفعالية النسبية (Relative Potency) لزيت الزعتر(الاختباري) نسبة الى الكتان (القياسي) لانموذج غيرخطي (parabolic model) باستعمال طريقة احصائية تكرارية وهي : (طريقة البحث الخطي) ودراسة تاثيرالتكرار عند الجرعة صفر فقط لمعرفة مدى الابتعاد عن | This study deals with the problem of estimation the relative potency of thymus oil and linum oil , for parabolic model by using the : line search method , and we study the effect of replication at zero dose and near zero dose on the type of relationship whether is linear or not , we partition the thesis into five chapters , the first included the introduction and the aim of this research work and historical review, the second chapter included the theoretical part where we stated the relative potency estimation method for nonlinear model, the third chapter went through the experiential part of this research work, the four chapter went through the practical part of this research work, finally chapter five went through the conclusions and recommendations of this research work, we conclude that the potency of thymus oil is (0.115) times the linum oil according to the parabolic model

مقارنة مقدر المنوال الحصين مع بعض المقدرات الاخرى ولمعلمة الموقع == Comparing The Robust Estimator of The Mode With Some Other Estimators For Location Parameter

Author name: نازك جعفر صادق
Supervisor name: عماد حازم عبودي
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Baghdad
First pages:
Abstract: The robust estimators are these estimators which resist all cases of data contamination by outlier values which are suitable to a wide sector of distribution. The present values deals with searching for the best estimator for location because this topic is important for the high frequency cases of contamination. Hence it is important to use robust ways in choosing the best robust estimator which being affected by outlier values. The aim of this study is to choose the estimator which is most immune to asymmetric distributions and to any rate of contamination. It also aims at studying the function of such an estimator through simulation experiments which take many cases into consideration.The study falls into four chapters. The first chapter is an introductory one which includes the introduction, the aim and a historical servey for certain general concepts which have close relation to the topic understudy. The second chapter deals with the median and robust estimation which include median estimator and other location estimators and the criterion used in the present study. As for the third chapter, it includes the experimental side of the study. Finally, the fourth chapter, it deals with the conclusions and recommendations which the study comes up with.Some of the important which researcher has come up with are that has been able to find a most robust estimator after comparing it with a group of estimators. This estimator is the Robust Parameter Estimator (RPM). It can be considered much better than many available robust estimators.

الاسقاطات السكانية لمحافظـــة البصـــرة للفتـــرة (1997 - 2022) باستخدام نتائج التعداد العام لسنة 1997 في العراق == The Populational Projections of Basrah Governorate For The Period 1997 - 2022

Author name: نادية علي عايد الحميداوي
Supervisor name: بشرى علي يعقوب الجعفري | زهرة حسن عباس التميمي
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Baghdad
First pages:
Abstract: ان الاسقاطات السكانية من الطرائق الاساسية التي تستند عليها اغلب الدراسات والبحوث في مجالات متعدده، اذ ان معرفة اعداد السكان والتغيرات الحاصلة له بصورة مستمرة تعد الركيزة الاساسية التي تعتمد عليها خطط التنمية ولان التعدادات السكانية تجري كل خمس او عشر سن | Populational projections are considered to be the basic methods , which most studies and researches depend upon. By these methods it could be knowing the demographical , social , and economic features of the society , which these are considered to be the bases of most development plans. As the population census is carried out in every five or ten years , so the importance of following the populational projections has been apperied as a good way to be used.The aim of this study is to show the populational projections of Basrah governorate for the peried 1997 - 2022. According to the census of the year 1997 and by using the component method, which requires projections and estimations for the fertility , mortality and migration separatily therefore , we study the level and the direction of fertility for the period before year 1997 , taking into consideration the impacts of the current and future circumstances in the governorate. Besides , we analyse the death data to get the suitable level for these projections. After satisfying all the requirement of population projections , and using components method , the results are got and population of Basrah governorate from the year 1997 to 2022 is evaluated

مقارنة بعض الطرق الحصينة للمربعات الصغرى الجزئية == Compare Some of Robust Methods For Partial Least Squares

Author name: ميسون علي رحمن المندلاوي
Supervisor name: هلال عبود البياتي
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Baghdad
First pages:
Abstract: الحمد لله والصلاة والسلام على رسول الله سيدنا محمد (صلى الله عليه وسلم )وعلى اله وصحبه وسلم اما بعد...يتناول البحث استخدام انحدار المربعات الصغرى الجزئية PLS)) Partial Least Squares وهي تقنية انحدار خطي طورت للتعامل مع انحدارات ذات ابعاد عالية لمتغير وا | Partial least squares regression ( PLRS) is a linear regression technique developed to deal with high - dimensional regression and one or several response variables. In this paper we introduce robustified version of the SIMPLS algorithm being the leading PLRS algorithm because of its speed and efficiency. Because SIMPLS is based on the empirical cross - covariance matrix between the response variables and the regressors and on linear least squares regression, the results are affected by abnormal observations in the data set. Two robust methods covariance matrix for high - dimensional data and robust linear regression. We introduce robust RMSECV and RMSEP values for model calibration and model validation diagnostic plots are constructed to visualize and classify the outliers. Several simulation results and the analysis of real data sets show the effectiveness and the robustness of the approaches. Because RSIMPLS is roughly twice as fast as RSIMCD, it stands out as the overall best method.

بناء انموذج للمعاينة البيزية المفردة بافتراض مربع كاي كتوزيع مسبق == Constructing A Model For Bayesian Single Sampling Plan Assumed Chi - Squaar As A Prior Distribution

Author name: ميسون حميد فرج محمد
Supervisor name: محمد صادق عبد الرزاق الدوري
Specific topic: Statistics
Degree: Master
Language: Arabic
University location: Baghdad
First pages:
Abstract: يتضمن هذا البحث بناء انموذج لخطط المعاينة البيزية باستخدام نظرية القرار، هدف الانموذج التوصل الى معالم خطة بيز المفردة (n,c) حيث n تمثل حجم العينة، c تمثل عدد القبول الضروريان لفحص المنتوج واتخاذ قرار لرفض او قبول الدفعة. قمنا باشتقاق ومناقشة خصائص نظام خ | This research deals with the process of Constructing a model for Bayesian Single Sampling Plan by using decision making theory. The aim of this Model is to obtain the parameters (n,c) which represent Sample size (n) and acceptance number c, which are necessary to inspect the lot and to make a decision whether to accept or reject the product. We drive and discussed the properties of the system of single sampling attributes plan obtained from minimizing the average Expected cost under the assumption that cost decision is a linear function in lot size and sample size. The distribution of the sampling is a mixed Poisson distribution i.e, each lot produced is in Poisson Control but the process average varies from lot of anther according to frequency distribution which is assumed to be derived in the neighbor points of the break - even quality level. We explain all the notation and steps of obtained the total Expected cost of quality Control, which contain the item of cost (Cl,C2...C6) upon the decision of acceptance or rejection, and then how to solved mathematically using forward Variances function to reach the Optimal Parameters (n*,c*). Then the Optimal size of the Sample size is identified is linear function from square root of the lot size. Some auxiliary tables are given, Which represent the results we obtained which indicate that the prior distribution of quality is Chi - Square with m degree of freedom, we apply NP - Chart to make decision about process, we apply also the test of goodness of fit for testing the hypothesis.
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