Principles of Operations Management Semester Of Notes
Principles of Operations Management Semester Of Notes OPT MGMT 301
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OPTMGMT301 Notes 211 CH18 Mgmt of Waiting Lines Non value added occurrence waiting lines Queuing theory mathematical approach to the analysis of waiting lines Why are there waiting Average both arrivals and service times exhibit a high degree of variability Managerial implications of waiting lines 1 The cost to provide waiting space 2 A possible loss of business should customers leave the line before being served or refuse to wait at all 3 A possible loss of goodwill 4 A possible reduction in customer satisfaction 5 The resulting congestion that may disrupt other business operations andor customers TC Customer waiting cost Capacity Cost Unlike the EOQ model the min point on the TC curve is not usually where the 2 cost lines intersect Characteristics of Waiting Lines 1 Population source 2 Number of servers channels 3 Arrival and service patterns 4 Queue discipline order of service Population Source In nite source situation customer arrivals are unrestricted Finite source situation the number of potential customers is limited Ex repairman responsible for a certain number of machines in a company Number of Servers Channel a server in a service system Generally assumed that each channel can handle one customer at a time Single or multiple channel Waiting lines are most likely to occur when arrivals are bunched or when service times are particularly lengthy and they are very likely to occur when both factors are present If service time is exponential service rate is Poisson If the customer arrival rate is Poisson t interarrival time is exponential Assumptions often appropriate for customer arrivals but less likely to be appropriate for service Models assume customers are patient Other possibilities 1 Waiting customers grow impatient and leave the line reneging 2 If there are multiple waiting customers customers may switch to another line jockeying 3 Upon arriving decide the line is too long and therefore not to enter the line balking Queue discipline the order in which customers are processed Measures of waiting line performance 1 The avg number of customers waiting either in line or in the system The avg time customers wait either in line or in the system System utilization which refers to the percentage of capacity utilized The implied cost of a given level of capacity and its related waiting line The probability that an arrival will have to wait for service Under normal circumstances 100 utilization is not a realistic goal H w4gts x should try to achieve a system that minimizes the sum of waiting costs and capacity costs Queuing models In ite source Assume the avg arrival and service rates are stable 1 Single server exponential service time 2 Single server constant service time 3 Multiple servers exponential service time 4 Multiple priority service exponential service time As the system capacity increases the system utilization for a given arrival rate decreases Multiple priority model customers are processed according to some measure of importance Constraint Management Use temporary Workers Shift demand Standardize the service Look for a bottleneck One important factor possibility of reducing variability in processing times by increasing the degree of standardization fo the service being provided OPTMGMT301 Notes 32 Chl7 Project Mgmt Projects unique one time operations designed to accomplish a speci c set of objectives in a limited time frame Projects go through life cycle Project manager responsible for effectively managing each of the following 1 Work 2 Human resources 3 Communications 4 Quality 5 Time 6 Costs Project champions a person who promotes and supports a project Life Cycle 1 De nition 7 Concept recognizes the need for a project or responds to a request for a proposal from a potential customer or client f Feasibility analysis which examines the expected costs bene ts and risks of undertaking the project 2 Planning 3 Execution 4 Termination Phases can overlap Work breakdown structure WBS a hierarchical listing of what must be done during a project Gantt chart popular tool for planning and scheduling simple projects PERT program evaluation and review technique for planning and coordinating large projects CPM Critical path method for planning and coordinating large projects Using these managers can obtain 1 A graphical display of project activities 2 An estimate of how long the project will take 3 An indication of which activities are the most critical to timely project completion 4 An indication of how long any activity can be delayed wout delaying the project Network or precedence diagram diagram of project activities that shows sequential relationships by use of arrows and nodes Activity on arrow AOA network diagram convention in which arrows designate activities Activity on Node AON network diagram convention in which nodes designate activities Activities project steps that consume resources andor time Events the starting and nishing of activities designated by nodes in the AOA convention Path sequence of activities that leads from the starting node to the nishing node Critical path the longest path determines expected project duration Critical activities activities on the critical path Slack allowable slippage for a path the difference between the length of a path and the length of the critical path Deterministic time estimates that are fairly certain Probabilistic estimates of times that allow for variation A computing algorithm ES earliest time activity can start assuming all preceding activities start as early as possible EF the earliest time the activity can nish LS the latest time the activity can start and not delay the project LF the latest time the activity can nish and not delay the project These nd 1 Expected project duration 2 Slack time 3 The critical path Finding ES and EF times involves a forward pass through the network Finding LS and LF times involves a backward pass through the network Slack LS ES or LF EF Determining Path Probabilities Z indicates how many SD of the path distribution the speci ed time is beyond the expected path duration More positive the better Z 3 or more e probability of path completion by the speci ed time as 100 Find probability that each path will nish by the speci ed time then multiply those probabilities probability that the project will be completed by the speci ed time Independence assumption that path duration times are independent of each other requiring that activity times be independent and that each activity is on only one path simulation in practice Dependent cases Crash shortening activity durations In order to make a rational decision on which activities if any to crash and on the extent of crashing desirable a manager needs certain information 1 Regular time and crash tie estimates for each activity 2 Regular cost and crash cost estimates for each activity 3 A list of activities that are on the critical path General procedure for crashing 1 Crash the project one period at a time 2 Crash the least expensive activity that is on the critical path 3 When there are multiple critical paths nd the sum of crashing the least expensive activity on each critical path Advantage of using PERT and potential sources of error 1 Use of these technique force the manager to organize and quantify available information and to recognize where additional information is needed 2 The techniques provide a graphic display of the project and its major activities 3 They identify 77 Activities that should be closely watched because of the potential for delaying the project f Other activities that have slack time and so can be delayed wout affecting project completion time This raises the possibility of reallocating resources to shorten the project Among the most important sources of errors 1 When developing the project network managers may unwittingly omit one or more important activities 2 Precedence relationships may not all be correct as shown 3 Time estimates may include a fudge factor managers may feel uncomfortable about making time estimates bc they appear to commit themselves to completion win a certain time period 4 There may be a tendency to focus solely on activities that are on the critical path As the project progresses other paths may become critical Furthermore major risk events may not be on the critical path Critical Chain Project Management Managers need to be aware of to better manage projects 1 Time estimates are often pessimistic and with attention can be made more realistic 2 When activities are nished ahead of schedule that fact may go unreported so managers may be unaware of resources that could potentially be used to shorten the critical path Critical chain approach takes into account not only sequential task relationships but also resource constraints that can result in tasks being delayed when they must wait for a resource that is being used on another task Feeding time buffers are positioned at points in the network where noncritical sections of the network feed into the critical chain path to reduce the risk of delaying critical chain activities A project time buffer at the end of the project is used to reduce the risk that time variations on the critical chain will interfere with timely project completion Capacity buffers are used when multiple projects are ongoing to help manage the impact of variation of resource requirements among projects Virtual project teams some or all of the team members are geographically separated Advantages to using a project management software package It imposes a methodology and a common project management terminology It provides a logical planning structure It can enhance communication among team members It can ag the occurrence of constraint violations It automatically formats reports It can generate multiple levels of summary reports and detailed reports It enables what if scenarios It can generate various chart types including basic Gantt charts Don t focust too much on the critical path 1 As the project progresses other paths may become critical 2 Key risk events may not be on the critical path Even so if they occur they can have a major impact on the project Cost associated with risk events tend to be lowest near the beginning of a project and highest near the end Good risk mgmt identify as many potential risks as possible analyzing and assessing those risks working to minimizing the probability of their occurrence and establishing contingency plans for dealing with any that do occur 1 Identify risks 2 Evaluate to determine probability of occurrence and the potential consequences if it does occur Risk reduction redundant backup system frequent monitoring transferred risk sharing OPTMGMT301 Notes 129 Chl2 Inventory Management Inventory stock or store of goods Independent demand items items that are ready to be sold o r used Dependent demand items components of nished products Typical rm probably has about 30 of its CA and perhaps as much as 90 of Working capital invested in inventory ROI Widely used measure of managerial performance Different kinds of inventories 0 Raw materials and purchased parts 0 Partially completed goods WIP 0 Finished goods inventories or merchandise 0 Tools and supplies 0 Maintenance and repairs MRO inventory 0 Goods in transit to Warehouses distributors or customers pipleline inventory Functions of inventory 1 To meet anticipated customer demand anticipation stocks 2 To smooth production requirements seasonal inventories build up inventories during preseason periods to meet overly high requirements during seasonal periods To decouple operations buffers in case of disruption events 4 To protect against stockouts delayed deliveries and unexpected increases in demand increase the risk of shortages hold safety stocks stocks in excess of avg demand to compensate for variabilities in demand and lead time 5 To take advantage of order cycles inventory storage enables a rm to buy and produce in economic lot sizes period orders or order cycles Resulting stock cycle stock To hedge against price increase 7 To permit operations pipeline inventories 77 Little s law the avg amount of inventory in a system is equal to the product of the average demand rate and the average time a unit is in the system 8 To take advantage of quantity discounts Inventory mgmt has 2 concerns 1 Level of customer service 2 Costs of ordering and carrying inventories Must make 2 fundamental decisions timing and size of orders Inventory turnover ratio of avg COGS to avg inventory investment Requirement for effective Inventory mgmt A system to keep track of the inventory on hand and on order A reliable forecast of demand that includes an indication of possible forecast error Knowledge of lead times and lad time variability Reasonable estimates of inventory holding costs ordering costs and shortage costs A classi cation system for inventory items Periodic system physical count of inventory made at periodic intervals Perpetual inventory system system that keeps track of removals from inventory continuously thus monitoring current levels of each item EX bank transaction Twobin system two containers of inventory reorder When the rst is empty Perpetual system either batch or online Universal product code bar code printed on a label that has information about the item to which it is L 0 U1I L Jgt t attached RFID tags are also used to keep track of inventory in certain application used for identi cation inventory and product ow tracking Demand forecast and lead time information Lead time time interval between ordering and receiving order Point of Sale POS systems record items at time of sale 3 basic costs associated with inventories holding transaction ordering and shortage costs Holding or carrying costs cost to carry an item in inventory for a length of time usually a year Stated in 2 ways of unit price or as a dollar amount per unit Ordering costs costs of ordering and receiving inventory Expressed as a xed dollar amount per order regardless of order size Shortage costs costs resulting when demand exceeds the supply of inventory often unrealized pro t per unit ABC approach classifying inventory according to some measure of importance and allocating control efforts accordingly Cycle counting a physical count of items in inventory Key questions for cycle counting for mgmt 1 How much accuracy is needed 2 When should cycle counting be performed 3 Who should do it Economic order quantity EOQ model the order size that minimizes total annual cost 1 Basic economic order quantity model 2 The economic production quantity model 3 The quantity discount model Basic economic order quantity Model Used to identify a xed order size Assumptions Only one product is involved Annual demand requirements are known Demand is spread evenly throughout the year so that the demand rate is reasonably constant Lead time does not vary Each order is received in a single delivery There are no quantity discounts Ideal solution order size that causes neither a few very large orders nor many small orders but one that lies somewhere between Annual carrying cost Q2 H Unlike carrying costs ordering costs are relatively insensitive to ordersize Annual ordering cost DQ S D demand S ordering cost TC annual carrying cost annual ordering cost Q2 H DQS It reaches its minimum at the qty where carrying and ordering costs are equal Qsquareroot 2DSH Length of order cycle 2 QD Totally alright to round EOQ comes from estimates relatively at area around the EOQ 8 exibility to modify the order qty a bit from the EOQ OU1I bJgt t Economic Production Quantity EOQ Assumptions 1 Only one item is involved 2 Annual demand is known 3 The usage rate is constant 4 Usage occurs continually but production occurs periodically 5 The production rate is constant 6 Lead time does not vary 7 There are no quantity discounts Ordering costs y setup costs independent of the lot run size Quantity discounts price reductions for large orders TC Carrying Cost Ordering Cost Purchasing cost No one curve applies to the entire range of quantities a When carrying costs are constant P all curves have their minimum points at the same quantity b When carrying costs are stated as a percentage of unit price the minimum points do not line up Reorder point ROP When the quantity on hand of an item drops to this amount the item is reordered 4 determinants of the reorder point quantity 1 The rate of demand usually based on a forecast 2 The lead time 3 The extent of demand andor lead time variability 4 The degree of stockout risk acceptable to management Safety stock stock that is held in excess of expected demand due to variable demand andor lead time Service level probability that demand will not exceed supply during lead time The amount of safety stock that is appropriate for a given situation depends on the following factors 1 The avg demand rate and avg lead time 2 Demand and lead time variability 3 The desired service level Fill rate the percentage of demand lled by the stock on hand Fixed order interval FOI model orders are placed at xed time intervals Reasons for using Fixed Order Interval model Supplier s policy produce savings by grouping orders for items from the same supplier some situations do not readily lend themselves to continuous monitoring of inventory levels Bene ts and Disadvantages Results I tight control Grouping orders can yield savings in ordering packing and shipping costs When multiple items come from the same supplier May be the only practical approach if inventory Withdrawals cannot be closely monitored Negative Necessitates a larger amount of safety stock for a given risk of stockout bc need to protect against shortages during an entire order interval lead time increase carrying cost Single period model model for ordering of perishables and other items With limited useful lives Period for spare parts life of the equipment 2 costs shortage and excess Shortage cost generally the unrealized pro t per unit Excess cost difference between purchase cost and salvage value of items left over at the end of a period Cost associated with disposing of excess items XY cost per unit Continuous stocking levels Service level probability that demand will not exceed the stocking level Discrete stocking levels increase the excess Solution is to stock at the next higher level If the computed service level is EXACTLY equal to the cumulative probability associated with one of the stocking levels there are 2 equivalent stocking levels in terms of minimizing long run cost a One w equal probability b Next higher one Operations Strategy Record keeping estimates of holding ordering and setup costs as well as demand and lead times should be reviewed periodically and updated when necessary Variation reduction lead time variations and forecast errors are 2 key factors that impact inventory mgmt and variation reduction in these areas can yield signi cant improvement in inventory mgmt Lean operation demand driven feature smaller lot sizes than more traditional systems Decrease in avg inventory on hand Ho lower carrying costs Fewer disruptions of work ow reduction in space needs enhanced ability to spot problems and increased feasibility to place machines and workers closer together j more opportunities for socialization communication and cooperation Supply chain mgmt collaboration w suppliers g reduce size and frequency of stockouts while lowering inventory carrying costs Consignment cross docking pg 586 OPTMGMT301 Notes 218 Ch6 Process Selection and Facility Layout Process selection a Operational equipment and labor requirements operations costs and both the ability to meet demand and the ability to respond to variations in demand b Volume and variety of inputs and outputs and the degree of exibility that is required Technology often a factor in process selection and layout 1 Product technology 2 Processing technology 3 Information technology Process selection refers to deciding on the way production of goods or services will be organized Process strategy a Capital intensity the mix of equipment and labor that will be used by the organization b Process exibility the degree to which the system can be adjusted to changes in processing requirements due to such factors as changes in product or service design changes in volume processed and changes in technology Technological innovation discovery and development of new or improved products services or processes for producing or providing them Technology application of scienti c discoveries to the development and improvement of products and services and operations processes 3 technology opt mgmt is concerned 1 Product and service technology discovery and development of new products and services 2 Process technology methods procedures and equipment used to produce goods and provide 3 Information technology the science and use of computer and other electronic equipment to store process and send information Processing technologies often come through acquisitions rather than through internal efforts of an organization Process selection 1 How much variety in products or services will the system need to handle 2 What degree of equipment exibility will be needed 3 What is the expected volume of output 5 basic process types 1 Job shop usually operates on a relatively small scale Used when a low volume of high variety goods or service will be needed Ex Veterinarian s of ce 2 Batch used when a moderate volume of goods or services is desired and it can handle a moderate variety in products or services Ex Bakery 3 Repetitive when higher volumes of more standardized goods or services are needed Ex production lines 4 Continuous very high volume of nondiscrete highly standardized output is desired Ex Petroleum products steel sugar flour and salt Services air monitoring supplying electricity Internet Some situations are not ongoing but instead are of limited durations project Project a nonrepetitive set of activities directed toward a unique goal within a limited time frame Product or service pro ling linking key product or service requirements to process capabilities Automation machinery that has sensing and control devices that enable it to operate automatically 3 kind of automation Fixed automation most rigid uses high cost specialized equipment for a xed sequence of operations Low cost and high volume Programmable automation use of high cost general purpose equipment controlled by a computer program that provides both the sequence of operations and speci c details about each operation Computer aided manufacturing use of computers in process control Numerically controlled machines perform operations by following mathematical processing instructions Robot machine consisting of mechanical arm a power supply and a controller Flexible automation evolved from programmable automation uses equipment that is more customized than that of programmable automation Decision makers choose exible systems for either 2 reasons Demand variety or uncertainty exists about demand Layout decisions important 1 Require substantial investments of money and effort 2 Involve long term commitments which makes mistakes dif cult to overcome 3 Have signi cant impact on the cost and ef ciency of operations Product layout layout that uses standardized processing operations to achieve smooth rapid high volume ow Production line Assembly line standardized layout arranged according to a xed sequence of assembly tasks Process layouts layouts that can handle varied processing requirements Intermittent processing nonrepetitive processing Fixed position layout layout in which the product or project remains stationary and workers materials and equipment are moved as needed Cellular production layout in which workstations are grouped into a cell that can process items that have similar processing requirements Group technology the grouping into part families of items with similar design or manufacturing characteristics Flexible manufacturing system group of machines designed to handle intermittent processing requirements and produce a variety of similar products Computer integrated manufacturing a system for linking a broad range of manufacturing activities through an integrating computing system Line balancing the process of assigning tasks to workstations in such a way that the workstations have approximately equal time requirements Cycle time the maximum time allowed at each workstation to complete its set of tasks on a unit Precedence diagram a diagram that shows elemental tasks and their precedence requirements Balance delay percentage of idle time of a line Lines that involve human tasks are more of an ideal than a reality No algorithms exist to identify the best layout arrangement under all circumstances Richard Muther more general approach to the problem which allows for subjective input from analysis or managers to indicate the relative importance p275 summary OPTMGMT301 Notes 13 Linear Programming Linear programming problem 2 constrained optimization problems Graphical linear programming amp computer solutions Graphical linear programming provides a visual portrayal of many of the important concepts of linear programming limited to problems With only 2 variables Computers in practice used to obtain solutions for problems some of which involve a large number of variables Characteristics components amp assumptions Components 1 Objective function 2 Decision variables 3 Constraints 4 Parameters LP algorithms require that a single goalobjective such as the maximization of pro ts be speci ed Objective function mathematical expression that can be used to determine the total pro t for a given solution Decision Variables represent choices available to the decision maker in terms of amounts of either inputs or outputs Constraints limitations that restrict the alternatives available to decision makers less than or equal to greater than or equal to simply equal to Feasible solution set of all feasible combinations of decision variables as de ned by the constraints Parameters numerical constants xed values the model is solved given those values 1 Linearity the impact of decision variables is linear in constraints and the objective function 2 Divisibility noninteger values of decision variables are acceptable 3 Certainty values of parameters are known and constant 4 Nonnegativity negative values of decision variables are unacceptable Graphical linear programming method for nding optimal solutions to 2 variable problems Set up the objective function and the constraints in mathematical format Plot the constraints Identify the feasible solution space Plot the objective function Determine the optimal solution U1I bJgt t Procedure for nding the optimal solution using the objective function approach 1 Graph the constraints 2 Identify the feasible solution space 3 Set the objective function equal to some amount that is divisible by each of the objective function coef cients This Will yield integer values for the x1 and x2 intercepts and simplify the plotting line 4 After identifying the optimal point determine Which 2 constraints intersect there Solve their equations simultaneously to obtain the values of the decision variables at the optimum 5 Substitute the values obtained in the previous step into the objective function to determine the value of the objective function at the optimum Redundant constraint a constraint that does not form a unique boundary of the feasible solution space Constraint is redundant if it meets the following test its removal would not alter the feasible solution space Enumeration approach substituting the coordinates of each corner point into the objective function to determine which corner point is optimal Binding constraint a constraint that forms the optimal corner point of the feasible solution space Surplus when the values of decision variables are substituted into a gt2 constraint the amount by which the resulting value exceeds the right side value Slack when the values of decision variables are substituted into a lt2 constraint the amount by which the resulting value is less than the right side value Simplex method a linear programming algorithm that can solve problems having more than 2 decision variables Sensitivity analysis assessing the impact of potential changes to the numerical values of an LP model 3 types of potential changes 1 Objective function coef cients 2 Right hand values of constraints 3 Constraint coef cients Range of optimality range of values over which the solution quantities of all the decision variables remain the same If a change extends beyond the range of optimality the solution will change Even for change that are within the range of optimality the optimal value of the objective function WILL change Shadow price amount by which the value of the objective function would change with a one unit change in the RHS value of a constraint If constraint is nonbinding shadow price is ZERO Range of feasibility range of values for the RHS of a constraint over which the shadow price remains the same OPTMGMT301 Notes 124 Ch1O Quality Control Quality control a process that evaluates output relative to a standard and takes corrective action when output doesn t meet standards Acceptance sampling inspection of lots beforeafter production Process control inspection and corrective action during production Continous improvement quality built into the process Inspection appraisal activity that compares goods services to a standard Basic issues 1 How much to inspect and how often 2 At What points in the process inspection should occur 3 Whether to inspect in a centralized or on site location 4 Whether to inspect attributes count the number of times something occurs or variables measure the value of a characteristic Low cost high volume items require little inspection because 1 The cost associated W passing defective items is quite low 2 The processes that produce these items are usually highly reliable High volume system automated inspection is one option Where to inspect in the Process Raw materials and purchased parts Finished products Before a costly operation Before an irreversible process Before a covering process Centralized vs On site Inspection Is it Worth it to use the lab Some rely on self inspection by operators if errors can be traced back to speci c operators quality at the source Quality of conformance a product or service conforms to speci cations Statistical process control SPC statistical evaluation of the output of a process Process Variability 1Are the variations random if not unstable corrective action 3 Given a stable process is the inherent variability of process output Within a range that conforms to performance criteria Random Variation natural variation in the output of a process created by countless minor factors common variability Assignable Variation in process output a variation Whose cause can be identi ed A nonrandom variation special variation Sampling distribution a theoretical distribution of sample statistics mostly used normal distribution Central limit theorm the distribution of sample averages tends to be normal regardless of the shape of the process distribution Value of sample statistics fall outside of the limit H randomness suggest nonrandomness Control Process 1 De ne de ne in suf cient detail What is to be controlled 2 Measure only those characteristics that can be counted or measured are candidates for control U1I bJgt t P small probability that the value re ects 3 Compare there must be a standard of comparison that can be used to evaluate the measurements 4 Evaluate Mgmt must establish a de nition of out of control distinguish random from non random variability 5 Correct when a process is judged out of control Q corrective action must be taken Involves uncovering the cause of nonrandom variability and correcting it 6 Monitor results to ensure that corrective action is effective the output of a process must be monitored for a suf cient period of time to verify that the problem has been eliminated Control chart a time ordered plot of sample statistics used to distinguish between random and nonrandom variability a In controlstable all the data points fall between the upper and lower control limits b Essence is to assure that the output of a process is random so that future output will be random Control limits the dividing lines between random and nonrandom deviations from the mean of the distribution a Upper control limit UCL and lower control limit LCL Type I error concluding a process is not in control when it actually is a Producer s risk it places an unnecessary burden on the producer who must search for something that isn t there Alpha risk sum of the probabilities in the two tails Type II error concluding a process is in control when it is not a Consumer s risk producer doesn t realize something is wrong and passes it on to the consumer Variables generate data that are measured Attributes generate data that are counted Mean control chart control chart used to monitor the central tendency of a process Range control charts control charts used to monitor process dispersion Mean charts are sensitive to shifts in the process mean Range charts are sensitive to changes in process dispersion To determine initial control limits 1 Obtain 20 to 25 samples Compute the appropriate sample statistics for each sample 2 Establish preliminary control limits using the formulas 3 Determine if any points fall outside the control limits 4 If you nd no out of control signals assume that the process is in control If not investigate and correct assignable causes of variation Then resume the process and collect another set of observations upon which control limits can be based 5 Plot the data on the control chart and check for out of control signals Control Charts for Attributes Control charts for attributes are used when the process characteristic is counted rather than measured p chart and c chart p chart appropriate when data consist of 2 categories of items c chart appropriate when one cannot count the number of nonoccurences p chart control chart for attributes used to monitor the proportion of defective items in a process bc formula is approximation mD sometimes get negative LCL c chart control chart for attributes used to monitor the number of defects per unit a Goal is to control number of occurrences per unit Managerial Considerations Concerning Control Charts a At what points in the process to use control charts b What size samples to take c What type of control chart to use ie variables or attribute USC Z I39O Should focus on those aspects of the process that 1 Have a tendency to go out of control and 2 Are critical to the successful operation of the product or service Run Tests Run test a test for patterns in a sequence Trend sustained upward or downward movement Cycles a wave pattern Bias too many observations on one side of the center line Mean shift a shift in the average Too much dispersion the values are too spread out Run sequence of observations with a certain characteristic Z test Observed Number of runs Expected number of runs Standard deviation of number of runs Process Capability Speci cations a range of acceptable values established by engineering design or customer requirements tolerances Control limits statistical limits that reflect the extent to which sample statistics such as means and ranges can vary due to randomness alone Process Variability natural or inherent variability in process Process capability the inherent variability of process output relative to the variation allowed by the design speci cation Capability Analysis We must speci cally check whether a process is capable of meeting speci cations and not simply set up a control chart to monitor it A process should be in control and within speci cations before production beings Cp Process capability ratio Speci cation width Process width It must have a capability ratio of at least 100 aim for at least 133 Cpk Used if a process is not centered Cpk smaller of upper speci cation process mean 3 sigma And Process mean Lower speci cation 3 sigma Improving Process Capability Simplify eliminate steps reduce the number of parts use modular design Standardize use standard parts standard procedures Make mistake proof deign parts that can only be assembled the correct way have simple checks to verify a procedure has been performed correctly Upgrade equipment replace worn out equipment take advantage of technological improvements Automate substitute automated processing for manual processing Taguchi Cost function any deviation from the target value represents poor quality and that the farther away from target a deviation is the greater the cost Limitations of capability indexes 1 The process may not be stable in which case a capability index is meaningless 2 The process output may not be normally distributed in which case inferences about the fraction of output that isn t acceptable will be incorrect 3 The process is not centered but the Cp index is used giving a misleading result Case Bar codes might cut drug errors in hospitals
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