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Introduction to Operations Management Quality Assurance (Quality Control)

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Introduction to Operations Management Phases of Quality Assurance Acceptance sampling Process control Continuous improvement Inspection before/after production Corrective action during production Quality built into the process The least progressive The most progressive

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Introduction to Operations Management Inspection §How Much/How Often §Where/When §Centralized vs. On-site InputsTransformationOutputs Acceptance sampling Process control Acceptance sampling

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Introduction to Operations Management Inspection Costs Optimal Cost Amount of Inspection Cost of inspection Cost of passing defectives Total Cost

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Introduction to Operations Management 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

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Introduction to Operations Management Examples of Inspection Points

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Introduction to Operations Management Statistical Process Control §The Control Process l Define l Measure l Compare to a standard l Evaluate l Take corrective action l Evaluate corrective action

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Introduction to Operations Management Statistical Process Control §Variations and Control l Random variation: Natural variations in the output of process, created by countless minor factors l Assignable variation: A variation whose source can be identified

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Introduction to Operations Management Sampling Distribution Sampling distribution Process distribution Mean

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Introduction to Operations Management Normal Distribution Mean 95.5% 99.7% Standard deviation

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Introduction to Operations Management Control Limits (Type I Error) Mean LCLUCL /2 Probability of Type I error

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Introduction to Operations Management Control Limits Sampling distribution Process distribution Mean Lower control limit Upper control limit

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Introduction to Operations Management Mean Charts §Two approaches: If the process standard deviation is available (x l If the process standard deviation is not available (use sample range to approximate the process variability)

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Introduction to Operations Management Mean charts ( SD of process available ) §Upper control limit (UCL) = average sample mean + z (S.D. of sample mean) §Lower control limit (LCL) = average sample mean - z (S.D. of sample mean)

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Introduction to Operations Management Mean charts ( SD of process not available ) §UCL = average of sample mean + A 2 (average of sample range) §LCL = average of sample mean - A 2 (average of sample range) §A 2 is a parameter depending on the sample size and is obtainable from table.

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Introduction to Operations Management Example §Means of sample taken from a process for making aluminum rods is 2 cm and the SD of the process is 0.1cm (assuming a normal distribution). Find the 3-sigma (99.7%) control limits assuming sample size of 16 are taken.

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Introduction to Operations Management Example (solution) § x = SD of sample mean distribution l = SD of process / (sample size) l = 0.1 / (16) = §z = 3 §UCL = 2 + 3(0.025) = §LCL = = 1.925

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Introduction to Operations Management Example(p.427) §Twenty samples of size 8 have been taken from a process. The average sample range of the 20 samples is 0.016cm and the average mean is 3cm. Determine the 3- sigma control limits.

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Introduction to Operations Management Example §Average sample mean = 3cm §Average sample range = 0.016cm §Sample size = 8 §A 2 = 0.37 (From Table 9-2) §UCL = (0.016) = §LCL = (0.016) = 2.994

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Introduction to Operations Management Control Chart UCL LCL Sample number Mean Out of control Normal variation due to chance Abnormal variation due to assignable sources

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Introduction to Operations Management Observations from Sample Distribution Sample number UCL LCL 1234

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Introduction to Operations Management Mean and Range Charts UCL LCL UCL LCL R-chart x-Chart Detects shift Does not detect shift

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Introduction to Operations Management Mean and Range Charts UCL LCL UCL LCL x-Chart UCL LCL R-chart Detects shift Does not detect shift

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Introduction to Operations Management Control Chart for Attributes §p-Chart - Control chart used to monitor the proportion of defectives in a process §c-Chart - Control chart used to monitor the number of defects per unit

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Introduction to Operations Management Use of p-Charts §When observations can be placed into two categories. l Good or bad l Pass or fail l Operate or do not operate §When the data consists of multiple samples of several observations each

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Introduction to Operations Management p-chart §The center line is the average fraction (defective) p in the population if p is known, or it can be estimated from samples is it is unknown. § p = SD of sample distribution = {p(1-p)/n} §UCL p = p + z p §LCL p = p - z p

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Introduction to Operations Management Example (p.431) §The following table indicates the defective items in 20 samples, each of size 100. Construct a control chart that will describe 95.5% of the chance variations of the process

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Introduction to Operations Management Example §The following table indicates the defective items in 20 samples, each of size 100. Construct a control chart that will describe 95.5% of the chance variations of the process §No. of defective items

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Introduction to Operations Management Example (solution) §Population mean not available, to be estimated from sample mean §Total No. of defective items = 220 §Estimate sample mean = 220/{20(100)}=.11 §SD of sample = {.11(1-.11)/100}= 0.03 §z = 2 (2-sigma) §UCL p = (.03) = 0.17 §LCL p = (.03) = 0.05 §Thus a control chart can be plotted (p.431)

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Introduction to Operations Management Use of c-Charts §Use only when the number of occurrences per unit of measure can be counted; nonoccurrences cannot be counted. l Scratches, chips, dents, or errors per item l Cracks or faults per unit of distance l Calls, complaints, failures per unit of time

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Introduction to Operations Management Process Capability Lower Specification Upper Specification Process variability matches specifications Lower Specification Upper Specification Process variability well within specifications Lower Specification Upper Specification Process variability exceeds specifications

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