The document discusses operating characteristic (OC) curves, which describe the probability of accepting a lot based on the lot's quality level. The typical OC curve has an S-shape, with the probability of acceptance decreasing as the percent of nonconforming items increases. Sampling plans can approach the ideal step-function OC curve as the sample size and acceptance number increase. Specific points on the OC curve correspond to acceptance quality limits and rejection quality limits.
Acceptance sampling is a statistical quality control technique where a random sample is taken from a lot to determine whether the lot should be accepted or rejected. Key terms include acceptable quality level (AQL), lot tolerance percent defective (LTPD), sampling plans, producers risk, consumers risk, attributes and variables. Advantages are that it is less expensive and damaging than 100% inspection, while disadvantages include the risks of rejecting good lots or accepting bad lots. An exercise demonstrates how to determine a sampling plan using AQL, LTPD and reference tables.
1) The document compares single and double sampling plans using simulation to generate operating characteristic curves. Single sampling is simpler but double sampling may be preferable when sampling cost or timing is a constraint.
2) Simulation is used to model acceptance sampling scenarios and generate operating characteristic curves for single and double sampling plans. The curves show that double sampling has a higher probability of acceptance for lots with more defects.
3) While single sampling yields better quality lots accepted, double sampling may be better when minimizing sample size or timing is important, as it requires taking a second smaller sample less often.
This document discusses continuous sampling plans (CSP) as an alternative to lot acceptance sampling plans (LASP) for quality control during manufacturing. CSP involves continuously inspecting units at a specified frequency (f) until a clearing number (i) of defect-free units is reached, at which point inspection drops to the specified frequency. If a defect is found, inspection returns to 100% until the clearing number is reached again. The key parameters of a CSP are the frequency, clearing number, and resulting average outgoing quality (AOQ) and average fraction inspected (AFI). An example illustrates how a custom cart builder could use CSP on dynamometer testing to ensure cart specifications are met and analyze quality levels.
Acceptance sampling is a quality control technique where a random sample is taken from a lot and used to determine whether to accept or reject the entire lot. It aims to inspect a portion of items to draw a conclusion about the quality of the whole lot in a cost-effective manner. Key aspects include defining acceptance quality limits, sampling risks, developing sampling plans involving sample size and acceptance/rejection criteria, and understanding operating characteristic curves showing the probability of acceptance at different quality levels. The technique helps improve overall quality while reducing inspection costs and risks compared to 100% inspection.
This document discusses acceptance sampling, which is used to determine whether to accept or reject a sample based on predetermined quality levels. It defines key terms and outlines the advantages and disadvantages. Various sampling plans are described, including single, double, and multiple sampling plans. The operating characteristic curve is explained as a graph showing the probability of accepting lots at various quality levels. Producers' and consumers' risks are defined. Examples are provided to demonstrate calculating acceptance probabilities using Poisson distributions and constructing operating characteristic curves.
This document discusses military standards for acceptance sampling, including Military Standard 105E and Military Standard 414. MIL STD 105E provides sampling schemes for attributes data using single, double, or multiple sampling plans. It describes normal, tightened, and reduced inspection levels based on a vendor's quality history. MIL STD 414 provides variables acceptance sampling plans that use sample sizes based on lot size and inspection level, assuming the quality characteristic is normally distributed. It includes plans based on sample standard deviation, range, and known process standard deviation. The document provides examples of using these standards to determine acceptance sampling plans.
Lot-by-Lot Acceptance Sampling for AttributesParth Desani
This document discusses acceptance sampling for attributes, including lot-by-lot sampling. It covers single sampling plans, the operating characteristic curve, designing sampling plans, and Military Standard 105E/ANSI Z1.4, the most widely used sampling standard. MS 105E uses acceptable quality levels and inspection levels to determine sampling plans from tables for single, double, or multiple sampling. [/SUMMARY]
The presentation depicted herein presents briefly an introduction of acceptance sampling along with some major differences amongst the widely used sampling standards.
Acceptance Sampling standards comparison. MIL-STD-105E, MIL-STD-1916, ISO 2859, ISO 3951. About AQLs and OC Curves.
The document discusses process capability and statistical quality control. It provides information on different types of process variation and process capability indices. It also summarizes key concepts in statistical process control including control charts for attributes and variables as well as acceptance sampling plans. Examples are given for constructing control charts and solving acceptance sampling problems.
So this is from Inspection and quality control.
Today I share my presentation on Acceptance Sampling.
This is the 2nd most important tool of Statistical Quality Control
This is for the student of Production Management and from Business administration line.
This document contains Abdullah Al Mahfuj's profile and presentation on acceptance sampling and acceptable quality level (AQL) in the textile industry. It discusses key points such as:
1) Sampling is selecting a suitable sample to make inspection decisions about accepting or rejecting lots based on predetermined standards. Acceptance sampling uses sampling plans to judge quality levels.
2) AQL refers to the average percentage of defective items that will be accepted in a lot. There are six common AQL levels used in apparel manufacturing from 1.0% to 10%.
3) Defects are classified into four categories - critical, major, minor, and slight - each with a different acceptable percentage range. Sampling
This document provides an overview of acceptance sampling techniques. It discusses key concepts like:
- Acceptance sampling involves inspecting a sample of items from a lot and using those results to accept or reject the entire lot.
- Important factors in acceptance sampling plans include the sample size (n), acceptance number (c), producer's risk, and consumer's risk.
- Operating characteristic (OC) curves graphically show the probability of lot acceptance for different quality levels and are used to evaluate sampling plans.
- There are different types of sampling plans like single, double, multiple, and sequential sampling that vary in their sample sizes and decision rules. Choosing the appropriate plan involves considering factors like costs of inspection.
“An AQL System for Lot-By-Lot Acceptance Sampling By Attributes Selecting an ...IOSR Journals
The choice among various possible types of acceptance inspection procedures is essentially an
economic one. In making a decision regarding acceptance inspection for any particular purpose, it may be
desirable to consider not only various possible systems or procedures of acceptance sampling by attributes but
also the alternatives of (1) no inspection at all, but imposition of a requirement that statistical evidence of
satisfactory quality be provided with each lot; (2) 100% inspection; and (3) possibilities of acceptance sampling
by variables. It also is true that a satisfactory evaluation of all the pertinent economic factors is often quite
difficult. For this reason, the choice of an acceptance procedure is commonly made on an intuitive basis. An
important element of the selection of an acceptance inspection procedure should be the probable contribution of
the procedure to quality improvement. The acceptance sampling systems and procedures described in this and
the following chapters have often been strikingly successful in leading to such improvements.
This document discusses different types of acceptance sampling plans including single sampling plans, double sampling plans, multiple sampling plans, and sequential sampling plans. It notes that double sampling plans may reduce the total amount of required inspection compared to single sampling plans by allowing lots to be accepted or rejected after inspecting a smaller first sample. Double sampling also allows rejecting a lot without completing inspection of the second sample.
Acceptance sampling is a quality control technique where samples are taken from a production lot to determine whether to accept or reject the entire lot. It involves taking a sample, inspecting it for defects, and using pre-defined acceptance criteria based on the sample results to decide whether to accept the lot. The key advantages are that it reduces inspection costs and improves overall quality by eliminating poor quality lots. There are different types of sampling plans like single, double, and multiple sampling based on attributes or variables.
A multi-cylinder engine has multiple cylinders arranged in various configurations with a crankshaft that coordinates piston motion. It offers advantages over single-cylinder engines by counteracting imbalances through opposing piston movements. For primary and secondary force balancing, the reciprocating masses are considered transferred to the crank pins. The algebraic sum of forces and couples must equal zero by closing the force and couple polygons. Balancing is achieved by arranging cylinders at specific angular positions with respect to crank 1. The method of direct and reverse cranks is also used to balance radial and V-engines.
This document discusses dynamics of machinery and includes sections on force analysis, balancing, and free vibration. The force analysis section covers static and dynamic force analysis, D'Alembert's principle, and analyzing forces in reciprocating engines. The balancing section discusses static and dynamic balancing of rotating and reciprocating masses. Methods for balancing single, multi-cylinder, and V-engines are presented. The free vibration section introduces concepts of vibration systems including degrees of freedom, undamped and damped free vibration, and natural frequencies of single and multi-rotor shaft systems. Sample problems are provided on balancing multiple rotating masses and analyzing the vibration of a spring-mass system.
The various forces acts on the reciprocating parts of an engine.
The resultant of all the forces acting on the body of the engine due to inertia forces only is known as unbalanced force or shaking force.
1. Electrochemical grinding (ECG) is a non-traditional machining process that removes electrically conductive material by grinding with a negatively charged abrasive wheel, electrolyte fluid, and a positively charged workpiece. Materials are removed through electrolysis and some abrasion, leaving a smooth burr-free surface.
2. ECG can machine very hard and brittle materials more effectively than traditional processes due to generating little heat. Key parameters that affect the material removal rate include the abrasive wheel properties, workpiece material and surface, machining conditions, electrolyte type and properties, and voltage applied.
3. ECG provides advantages like burr-free surfaces, less work hardening, higher precision
How to read a receiver operating characteritic (ROC) curveSamir Haffar
1) The document discusses how to evaluate the accuracy of diagnostic tests using receiver operating characteristic (ROC) curves.
2) ROC curves plot the sensitivity of a test on the y-axis against 1-specificity on the x-axis. The area under the ROC curve (AUC) provides an overall measure of a test's accuracy, with higher values indicating better accuracy.
3) The document uses ferritin testing to diagnose iron deficiency anemia (IDA) in the elderly as a case example. The AUC for ferritin was found to be 0.91, indicating it is an excellent test for diagnosing IDA.
This document discusses various nontraditional machining and thermal cutting processes. It begins by defining these processes as those that remove material using mechanical, thermal, electrical, or chemical energy without a conventional cutting tool. These alternative processes are important for machining new metals and non-metals, producing complex geometries, and avoiding surface damage from traditional methods. The document then groups and describes various nontraditional processes including mechanical (ultrasonic machining, water jet cutting), electrochemical (electrochemical machining), thermal (electric discharge machining, laser beam machining), and chemical (chemical milling) processes.
Electrochemical machining (ECM) is a non-traditional machining process that removes metal by electrochemical dissolution rather than mechanical forces. ECM was first introduced in 1929 and has since been used for complex machining applications. In the ECM process, an electric current is applied between an electrode tool and a conductive workpiece submerged in an electrolyte solution. This causes metal ions from the workpiece to dissolve into the solution, machining the workpiece without generating mechanical forces or heat. ECM can machine hard metals and complex shapes more accurately than traditional methods and is used for applications in industries like aerospace, electronics, and automotive.
The document discusses diesel engine emissions, including the formation of pollutants like CO, unburned hydrocarbons, NOx, smoke, and particulate matter. It explains the sources and mechanisms of emission formation during the two combustion phases in diesel engines. Variables like injection parameters, engine load, speed, and exhaust gas recirculation affect emission levels by influencing combustion temperature and equivalence ratios. Emission control technologies help reduce pollutants and allow engines to meet regulatory standards.
Electrochemical grinding (ECG) is a process where a rotating grinding wheel acts as a cathode and the workpiece is the anode. An electrolyte like NaNO3 is used and a voltage is applied, causing material to be removed from the workpiece electrochemically with some additional removal by abrasion from diamond or aluminum oxide particles on the wheel. ECG can machine difficult materials, achieve close tolerances on thin parts without distortion, and offers advantages over conventional grinding like higher removal rates and elimination of burrs. However, it also has higher costs and is limited to electrically conductive materials.
Unit 5- balancing of reciprocating masses, Dynamics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
Statistical Process Control & Operations Managementajithsrc
This document discusses statistical process control and quality management techniques. It defines key terms like chance causes, assignable causes, control charts, attributes and variables. It also describes different types of control charts like Pareto charts, fishbone diagrams, mean charts, range charts, p-charts and c-charts. The document provides examples of how to construct and interpret these different control charts. It also discusses acceptance sampling and how to construct an operating characteristic curve.
Electro-chemical machining (ECM) is a non-traditional machining process that removes metal by dissolving it in an electrolyte with the use of electric current. In ECM, the workpiece acts as an anode and is dissolved by the electrolyte, while a tool with the desired shape acts as a cathode. Key factors in ECM include the electrolyte, which carries current and removes dissolved material, the tool and workpiece materials, and a DC power supply. ECM can machine hard metals and complex shapes with high accuracy and no tool wear. Common applications of ECM include machining turbine blades, aerospace components, and other difficult-to-machine metals.
Basic Mechanical Engineering - RefrigerationSteve M S
This document provides information about refrigeration and refrigeration systems. It discusses:
- The definition of refrigeration as the process of removing heat from a substance under controlled conditions.
- The main components and functioning of vapor compression refrigeration systems, including the compressor, condenser, expansion valve, and evaporator.
- Other types of refrigeration systems like air refrigeration and vapor absorption systems.
- Properties and examples of common refrigerants like ammonia and fluorocarbons.
- Key refrigeration concepts such as the coefficient of performance (COP) and units of refrigeration capacity.
- Major applications of refrigeration including food preservation, air conditioning, and industrial uses.
The document discusses various unconventional machining processes. It begins with introducing that unconventional machining uses indirect energy like sparks, heat or chemicals rather than direct contact between a tool and workpiece. It then covers different unconventional processes like EDM, laser beam machining, electrochemical machining and their characteristics. The document categorizes unconventional machining processes and provides details on processes like chemical machining, electrochemical grinding and ultrasonic machining. It concludes with discussing advantages and disadvantages of non-conventional machining.
This document provides an overview of non-conventional machining processes including ultrasonic machining, water jet machining, electro-chemical machining, electro-chemical grinding, and electrical discharge machining. The objective is to make audiences aware of the merits of these non-conventional processes over traditional machining for machining complex, less machinable, or brittle materials in a faster and more economical way using computer-controlled processes with minimal human intervention. An outline and brief description is given for each non-conventional machining technique.
The document discusses transportation problems and assignment problems in operations research. It provides:
1) An overview of transportation problems, including the mathematical formulation to minimize transportation costs while meeting supply and demand constraints.
2) Methods for obtaining initial basic feasible solutions to transportation problems, such as the North-West Corner Rule and Vogel's Approximation Method.
3) Techniques for moving towards an optimal solution, including determining net evaluations and selecting entering variables.
4) The formulation and algorithm for solving assignment problems to minimize assignment costs while ensuring each job is assigned to exactly one machine.
The document discusses time and space complexity analysis of algorithms. Time complexity measures the number of steps to solve a problem based on input size, with common orders being O(log n), O(n), O(n log n), O(n^2). Space complexity measures memory usage, which can be reused unlike time. Big O notation describes asymptotic growth rates to compare algorithm efficiencies, with constant O(1) being best and exponential O(c^n) being worst.
This document discusses conceptual problems in statistics, testing, and experimentation in cognitive psychology. It identifies three main sources of variability in psychological data: (1) participant interest and motivation, (2) individual differences, and (3) potentially stochastic cognitive mechanisms. Addressing this variability poses challenges for developing normative and descriptive models of cognition and for making inferences from group-level data to individuals. The document also discusses approaches like individual differences research and modeling heterogeneous groups to help address these challenges.
The document summarizes key concepts about queuing systems and simple queuing models. It discusses:
1) Components of a queuing system including the arrival process, service mechanism, and queue discipline.
2) Performance measures for queuing systems such as average delay, waiting time, and number of customers.
3) The M/M/1 queuing model where arrivals and service times follow exponential distributions with a single server. Expressions are given for performance measures in this model.
4) How limiting the queue length to a finite number affects performance measures compared to an infinite queue system.
Scatter diagrams and correlation and simple linear regresssionAnkit Katiyar
The document discusses scatter diagrams, correlation, and linear regression. It defines key terms like predictor and response variables, positively and negatively associated variables, and the correlation coefficient. It also describes how to calculate the linear correlation coefficient and interpret it. The document shows an example of using least squares regression to fit a line to productivity and experience data. It provides formulas to calculate the slope and intercept of the regression line and how to make predictions with the line. However, predictions should stay within the scope of the observed data used to fit the model.
This document provides an introduction to queueing theory, covering basic concepts from probability theory used in queueing models like random variables, generating functions, and common probability distributions. It then discusses fundamental queueing models and relations, including Kendall's notation for describing queueing systems and Little's Law relating average queue length and waiting time. Specific queueing models are analyzed like the M/M/1, M/M/c, M/Er/1, M/G/1, and G/M/1 queues.
This document provides an introduction to queueing theory. It discusses key concepts such as random variables, probability distributions, performance measures, Little's law and the PASTA property. It then examines several common queueing models including the M/M/1, M/M/c, M/Er/1, M/G/1 and G/M/1 queues. For each model it derives the equilibrium distribution and discusses measures like mean queue length and waiting time. The goal is to provide the fundamental mathematical techniques for analyzing queueing systems.
This document provides an introduction to queueing theory. It discusses key concepts such as random variables, probability distributions, performance measures, Little's law and the PASTA property. It then examines several common queueing models including the M/M/1, M/M/c, M/Er/1, M/G/1 and G/M/1 queues. For each model it derives the equilibrium distribution and discusses measures like mean queue length and waiting time. The goal is to give an overview of basic queueing theory concepts and common single-server and multi-server queues.
Probability mass functions and probability density functionsAnkit Katiyar
This document discusses probability mass functions (pmf) and probability density functions (pdf) for discrete and continuous random variables. A pmf fX(x) gives the probability of a discrete random variable X taking on the value x. A pdf fX(x) defines the probability that a continuous random variable X falls within an interval via its cumulative distribution function FX(x). The pdf must be non-negative and have an area/sum of 1 under the curve/over all x values.
The document outlines a lesson on basic statistical concepts for comparative studies. It covers terminology used in comparative studies including factors, levels, treatments, response variables and experimental units. It discusses topics like randomization to avoid confounding, Simpson's paradox, and the difference between experiments and observational studies. Factorial experiments involving multiple factors are also introduced.
This document discusses histograms and stem-and-leaf plots for analyzing and visualizing the distribution of a single set of numerical data. It provides examples using yearly precipitation data from New York City to demonstrate how to create histograms and stem-and-leaf plots in R. Histograms partition data into bins to show the frequency or relative frequency of observations in each bin, while stem-and-leaf plots list the "stems" and "leaves" of values to show their distribution.
This document discusses inventory management for multiple items and locations. It introduces the concepts of:
1) Setting aggregate inventory policies to meet system-wide objectives when dealing with multiple items and locations.
2) Using exchange curves to analyze the tradeoffs between total inventory levels and other factors like number of replenishments and service levels. These curves allow setting parameters like order costs and carrying costs.
3) Determining optimal reorder quantities, cycle stock, and safety stock levels across an inventory system using techniques like exchange curves. This helps allocate limited inventory budgets across items to maximize performance.
The document summarizes the economic production quantity (EPQ) model and its extensions. It discusses:
1) The EPQ model balances fixed ordering costs and inventory holding costs to determine optimal production/order quantities and intervals.
2) The economic order quantity (EOQ) model is a special case where production rate is infinite and demand is met through ordering.
3) Sensitivity analysis shows how the optimal solutions change with different parameters like production rate and setup costs.
The Kano Model classifies customer needs into three categories - threshold, performance, and excitement - based on their effect on customer satisfaction. Threshold attributes are basic needs whose absence causes dissatisfaction. Performance attributes directly improve satisfaction as implementation increases. Excitement attributes unexpectedly delight customers when implemented. The model is useful for identifying needs, setting requirements, concept development, and analyzing competitors to maximize performance attributes while including excitement attributes.
This document provides an overview of basic probability and statistics concepts. It covers variables, descriptive statistics like mean and standard deviation, frequency distributions through histograms, the normal distribution, linear regression, and includes a practice test in the appendices. Key topics are qualitative and quantitative data, parameters versus statistics, measures of central tendency and dispersion, and generating frequency tables and histograms from data sets.
Conceptual foundations statistics and probabilityAnkit Katiyar
This document provides guidance for a 6th grade statistics and probability unit of study. It outlines key concepts students should understand, including developing questions that anticipate variability, understanding data distributions in terms of center, spread and shape, and summarizing and describing distributions using various graphs such as dot plots, histograms and box plots. Students learn to analyze subgroups within data sets and how to match statistical questions to the appropriate graph. The document emphasizes interpreting and constructing dot plots, histograms and box plots to display and analyze numerical data.
This document provides an overview of basic statistical concepts including populations, samples, parameters, statistics, and sampling methods. It defines key terms like population, sample, parameter, statistic, and discusses sampling methods like simple random sampling and stratified sampling. It also covers sampling variability, estimation, hypothesis testing, prediction, and issues around representative vs non-representative samples.
The document outlines 5 axioms of probability:
1) Probabilities are non-negative
2) Probabilities of mutually exclusive events add
3) The probability of the sample space is 1
It then proves 5 theorems about probability:
1) The probability of an event equals 1 minus the probability of its complement
2) The probability of the impossible event (the empty set) is 0
3) The probability of a subset is less than or equal to the probability of the larger set it is contained within
4) A probability is between 0 and 1
5) The addition law - for two events the probability of their union equals the sum of their probabilities minus the probability of their intersection
Applied statistics and probability for engineers solution montgomery && rungerAnkit Katiyar
This document is the copyright page and preface for the book "Applied Statistics and Probability for Engineers" by Douglas C. Montgomery and George C. Runger. The copyright is held by John Wiley & Sons, Inc. in 2003. This book was edited, designed, and produced by various teams at John Wiley & Sons and printed by Donnelley/Willard. The preface states that the purpose of the included Student Solutions Manual is to provide additional help for students in understanding the problem-solving processes presented in the main text.
A hand kano-model-boston_upa_may-12-2004Ankit Katiyar
This document introduces the Kano Model, a framework used to classify product features based on their impact on customer satisfaction. It explains that some features are "basic" and expected, while others provide linear satisfaction proportional to quality or performance. Some "excitement" features unexpectedly delight customers. The document outlines a process to apply the Kano Model to user experience design including researching customer needs, analyzing data, plotting features on the Kano diagram, and strategizing priorities with clients. It provides an example workshop applying the model to a fictional business and discusses extending the model with personas and use cases.