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LO10-1: Understand what a waiting line problem is.  Queuing theory is the mathematical analysis of the waiting line.  A queuing (or waiting line) system is decomposed into three major parts:  1. The customers arriving to the system.  2. The servicing of the customers.  3. How customers exit the system.  Queuing theory assumes customers arrive according to a Poisson arrival distribution.  Queuing theory assumes customers are served according to an exponential service time distribution. Queues: A line of waiting persons, jobs, things, or the like. Queuing System: A process where customers wait in line for service. Arrival Rate: The expected number of customers that arrive each period. Exponential Distribution: A probability distribution associated with the time between arrivals. Poisson Distribution: Probability distribution for the number of arrivals during each time period. Service Rate: The number of customers a server can handle during a given time period. LO10-2: Analyze waiting line problems.  Model 1  Useful for simple situation where there is a single line of customers who arrive according to a Poisson distribution, and who are processed by a single server that serves each customer in the order they came according to an exponential distribution (for example, an automatic teller machine).  Model 2  Similar to Model 1 with the difference being that it takes exactly the same time to serve each customer (there is no service time variability), for

example, a robot making the same part over and over again.  Model 3  Similar to Model 1 but two or more servers are available (for example, a bank lobby with multiple tellers).  Model 4  Differs in that only a small number of customers exist (for example, a mechanic that services four specific printing presses when they break down).  Waiting Time Approximation Formulas

 PowerPoint Notes

 Cost-Effectiveness Balance  The trade-off relationship under steady-state traffic.

 Finite Population  Limited-size customer pool that will use the service and may form a line  When a customer leaves its position as a member for the population, the size of the user group is reduced by one  Infinite Population  Population large enough so that the population size caused by subtractions or additions to the population does not significantly affect the system probabilities  Phases

 Priority Rules  Determines the order of customers in the system  Exit Rule  Once service is complete, two exit fates are possible. The customer returns to the source population and may:  Immediately become a candidate for re service  Become a candidate with low (or zero) probability for reentry.

 Queuing Approximation  All you need is data on service times and times between arrivals.  Model 1 – Example  Assume a drive-up window at a fast food restaurant. Customers arrive at the rate of x per hour. The employee can serve one customer every y minutes. Assume Poisson arrival and exponential service rates. A. What is the average utilization of the employee? B. What is the average number of customers in line? C. What is the average number of customers in the system? D. What is the average waiting time in line? E. What is the average waiting time in the system? F. What is the probability that exactly two cars will be in the system?

 Model 2 – Example  An automated pizza vending machine heats and dispenses a slice of pizza in x minutes. Customers arrive at a rate of one every y minutes with the arrival rate exhibiting a Poisson distribution. A. Find: The average number of customers in line B. Find: The average total waiting time in the system

 Model 3 – Example  Recall the Model 1 example: Drive-up window at a fast food restaurant. Customers arrive at the rate of x per hour. The employee can serve one customer every y minutes. Assume Poisson arrival and exponential service rates. A. If an identical window (and an equally fast server) were added, what would be the effect on the average number of cars in the system and the time customers wait for service?

 Model 4 – Example  The copy center of an electronics firm has x copy machines that are all serviced by a single technician. Every z hours, on average, the machines require adjustment. The technician spends an average of y minutes per machine when adjustment is required. A. Assuming Poisson arrivals and Exponential service, how many machines are “down” (on average)?

 Queuing Approximation – Example  Average time between calls is x minutes with a standard deviation of s. Average service time is y minutes with a standard deviation of z. There are currently n operators. A. How long will customers wait? B. How would you perform sensitivity analysis?

LO12-1: Explain the scope of total quality management in a firm.  Total Quality Management is a comprehensive approach to quality with a focus on what is important to the customer.  The concept centers on two major operational goals:

 1. The design of the product or service.  2. Ensuring that the firm’s processes can consistently produce or deliver the design.  Basic Principles of TQM:  Focus on the customer  Continuous Improvement  Involvement  Quality Specifications are fundamental to a sound quality program.  These start by making sure that features of the design relate to what the intended market for the product expects and its inherent value.  Processes are designed so that specific design specifications such as size, surface, finish, or delivery speed are consistently met when the product is produced, or service delivered.  Costs related to quality include the expenses related to inspection, rework, and repair or warranty; some of these costs may be difficult to measure. Total Quality Management: Managing the entire organization so that it excels on all dimensions of products and services that are important to the customer. Malcolm Baldrige National Quality Award: An award established by the U.S. Department of Commerce given annually to companies that excel in quality. Design Quality: The inherent value of the product in the marketplace. Conformance Quality: The degree to which the product or service design specifications are met. Quality at the Source: Making the person who does the work responsible for ensuring that specifications are met. Dimensions of Quality: Criteria by which quality is measured. Cost of Quality (COQ): Expenditures related to achieving product or service quality, such as the costs of prevention, appraisal, internal failure, and external failure.

LO12-2: Understand the Six Sigma approach to improving quality and productivity.  Six Sigma is a philosophy and set of tools developed to measure and reduce defects.  Six Sigma projects follow five steps (DMAIC):  1. Define  2. Measure  3. Analyze  4. Improve  5. Control  Training in Six Sigma is recognized using martial arts titles that reflect skill levels such as black belts and green belts.  Often procedures can be included as a process that guarantees a very high level of quality, known as fail-safe procedures.

Six Sigma: A statistical term to describe the quality goal of no more than 3.4 defects out of every million units. Also refers to a quality improvement philosophy and program. Defects per Million Opportunities (DPMO): A metric used to describe the variability of a process.

DMAIC: Acronym for the define, measure, analyze, improve, and control improvement methodology followed by companies engaging in Six Sigma Programs. Lean Six Sigma: Combines the implementation and quality control tools of Six Sigma and the inventory management concept of lean manufacturing. Black Belts: Coaches or actually leads a Six Sigma improvement team. Master Black Belts: Receives in-depth training on statistical tools and process improvement (they perform many of the same functions as black belts but for a larger number of teams). Green Belts: Employees who have received enough Six Sigma training to participate in a team or, in some companies, to work individually on small-scale projects directly related to their own job. Fail-safe Procedures: Simple practices that prevent errors or provide some feedback in time for the worker to correct errors. Poka-Yokes: Includes things such as checklists or special tooling that (1) prevents the worker from making an error that leads to a defect before starting a process or (2) gives rapid feedback of abnormalities in the process to the worker in time to correct them. LO12-3: Illustrate globally recognized quality benchmarks.  The International Organization for Standardization (ISO) has developed specifications that define bestquality practices and are accepted internationally.  The two most accepted specifications are:  ISO 9000  Relate to manufacturing and business-tobusiness processes.  ISO 14000  Concerned with environmental management.

ISO 9000: Formal standards for quality certification developed by the International Organization for Standardization. External Benchmarking: Looking outside the company to examine what excellent performers inside and outside the company’s industry are doing in the way of quality.  PowerPoint Notes  Reliability  Rs = (R1) (R2) (R3) … (Rn)  Backup System Reliability  1.0 – (1.0 – R) m  TQM vs. Six Sigma  TQM tries to improve quality by ensuring conformance to internal requirements, while Six Sigma focuses on improving quality by reducing the number of defects caused by variation.  Lean Six Sigma  7 Wastes: Waiting, Over-Processing, Inventory, Overproduction, Motion, Transportation, Defects.  Cost of Quality (COQ)  Internal Failure Cost A. Problems addressed before they reach the customer.  External Failure Cost A. Worst case scenario- Highest potential for loss.  Appraisal Cost A. Cost of identifying root causes of problems and quality deficiencies in processes.  Prevention Cost A. Cost associated with process improvement and defect elimination.  Reliability – Example  Wiring: x%, Sensor: y%, Two Bulbs: z% each A. What is the Reliability?

 Six Sigma – DPMO Example 1  A customer of a bank expects to have a certain application processed within x days of filing. This would be considered a CCR (critical customer requirement) in Six Sigma terms. Often there are both upper and lower customer requirements. You sample n applications and find that y did not meet the CCR. A. What is the DPMO of this process? B. What does this number mean?

 Six Sigma: DPMO Example 2  A manager states that his process is really working well. Out of n parts, x were produced free of y different types of defects and passed inspection. A. Based upon Six-Sigma theory, how would you rate this performance, other things being equal?

LO13-1: Illustrate process variation and explain how to measure it.  Variation is inherent in all processes and can be caused by many factors.  Variation caused by identifiable factors is called assignable variation and can possibly be managed.  Variation inherent in a process is called common or random variation.  Statistical Quality Control (SQC) involves sampling output from a process and using statistics to find when the process has changed in a nonrandom way.  When a product or service is designed, specification limits are assigned relative to critical parameters.  Designed to work so that probability of output these limits is relatively low.  The Capability Index (Cpk) of a process measures its ability to consistently produce within the specification limits. SQC: Statistical Quality Control. A number of different techniques designed to evaluate quality from a conformance view. Assignable Variation: Deviation in the output of a process that can be clearly identified and managed. Common Variation: Deviation in the output of a process that is random and inherent in the process itself. Upper and Lower Specification Limits: The range of values in a measure associated with a process that is allowable given the intended use of the product or service. Capability Index (Cpk): The ratio of the range of values allowed by the design specifications divided by the range of values produced by a process. LO 13-2: Analyze process quality using statistics.  Statistical process control involves monitoring the quality of a process as it is operating.

 Control Charts are used to visually monitor the status of a process over time.  P-chart  C-chart  Attributes are characteristics that can be evaluated as either conforming or not conforming to the design specifications.  When the characteristic is measured as a variable measure, for example, weight or diameter, X- and Rcharts are used. SPC: Statistical Process Control. Techniques for testing a random sample of output from a process to determine whether the process is producing items within a prescribed range. Attributes: Quality characteristics that are classified as either conforming or not conforming to specification. Variables: Quality characteristics that are measured in actual weight, volume, inches, centimeters, or other measure. LO13-3: Analyze the quality of batches of items using statistics.  Acceptance sampling is used to evaluate if a batch of parts, as received in an order for example, conforms to specification limits.  Useful in the area where material is received from suppliers.  An acceptance sampling plan is defined by a sample size and the number of acceptable defects in the sample.  Since the sampling plan is defined using statistics, there is the possibility that a bad lot will be accepted, which is the consumer’s risk, and that a good lot will be rejected, which is the producer’s risk.

 Process Control Charts Using Attribute Measurements

Represents: Specific Width / Actual Process Width  Many Companies look for a C pk of 1.3 or better  Six Sigma companies require a Cpk of at least 2  Operating Characteristic Curve  The OCC displays the concepts of supplier’s risk, consumer’s risk, sample size and max number of defects. 

 Process Control X- and R- Charts

 PowerPoint Notes  Order Required  Order Required = Actual Demand / Proportion of Acceptable Product per Order  Square Root Rule  Allows you to see how much inventory will be required to maintain similar stock-out rates when changing the number of warehouses.  (SQRT Future Number of Warehouses / SQRT Present Number of Warehouses) * Total Stock Present = Total Stock Future

 Process Capability  C PK is a measure of how good a process is.

 Cost of Defects – Example  Suppose you need n light bulbs for a project. A. x % will arrive at the retailer defective and must be returned. B. y % will be damaged during transportation to the retailer. C. There is a z % breakage rate at the warehouse. D. a % of those produced is defective. E. b % of raw material purchased were contaminated, impure or otherwise unsuitable for manufacturing.  How many light bulbs should you plan for in order to get n defect free to the customer?

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 Risk Pooling – Example 1  A company is considering reducing the warehouses used from x1 to x2.  Present State (4 Warehouses):  Warehouse 1: n units  Warehouse 2: n units  Warehouse 3: n units  Warehouse 4: n units  Future State (2 Warehouses):  Warehouse 1: ?  Warehouse 2: ?  What stock level will be required to maintain their stock-out rate of y %?

 Cpl Cereal Box – Example  We manufacture and distribute a certain type of cereal. Consumer Reports just published an article that shows that we frequently fill the boxes with less than x oz of cereal. Government regulations state that we must be within + - y % of the weight advertised on the box (z oz in this case).  We sample n boxes of cereal and find that the average weight is a oz with a standard deviation of b oz.

What is the probability of a defect?

 Acceptance Sampling – Example  Zypercom, a manufacturer of video interfaces, purchases printed wiring boards from an outside vender, Procard. Procard has set an acceptable quality level of x % and accepts a y % risk of rejecting lots at or below this level. Zypercom considers lots with z % defectives to be unacceptable and will assume a b % risk of accepting a defective lot.  Develop a sampling plan for Zypercom and determine a rule to be followed by the receiving inspection personnel.

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Randomly select n, if more than c are found defective, reject....