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QMS 102 (186)

QMS Chapter 9 (Fall 2012)

13 Pages

Quantitative Methods
Course Code
QMS 102
Jason Chin- Tiong Chan

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Business StatisticsI-QMS102 Chapter9 Chapter9 Statistical Applications in Quality and Productivity Managements Outcomes: 1. Discuss the theory of Control Chart 2. Construct various control chart 3. Determine the X-bar and R chart control limits Total Quality Management (TQM) 1. An approach that focuses on continuous improvement of products and services through an increased emphasis on statistics, process improvement and optimization of the total system. 2. TQM is characterized by the following themes: a. the primary focus is on process improvement b. most of the variation in a process is due to the system and not the individual c. teamwork is an integral part of a quality management organization. d. Customer satisfaction is a primary organization. e. Organizational transformation must occur in order to implement quality management. f. Fear must be removed from organizations. g. Higher quality costs less not more, but requires an investment in training. Six Sigma Management 1. a quality improvement system. The Theory of Control Charts 1. Both TQM and Six Sigma Management use the control chart to analyze process data collected sequentially over time. 2. The control chart monitors variation in a characteristic of a product or service over time. Constructing Control Limits Process mean ± 3 standard deviation So that Upper control limit(UCL) = Process mean + 3 standard deviation Lower control limit(LCL) = Process mean - 3 standard deviation Fall2012 Page#1 Business StatisticsI-QMS102 Chapter9 The Control chart for the range (R chart) Control Limits for the Range d3 R ±3R d2 d d UCL = R +3R 3 LCL = R −3R 3 d2 d2 k R where ∑i=1 i , R = k d2factor = the relationship between the standard deviation and the range for varying sample sizes d 3factor = the relationship between the standard deviation and the standard error of the range for varying sample sizes Calculating Control Limits for The Range UCL = D R4 LCL = D 3 where D 3actor =1−3(d /3 ) 2 , D 4actor =1+3(d /d3) 2 The Control Chart for the X Control Limits for the X Chart R X ±3 d 2 n R R UCL = X +3 LCL = X −3 d2 n d2 n k k X R Where ∑ i ∑ i X = i=1 R = i=1 k k X = sample mean of n observations at time i i R i range of n observations at time i k = number of subgroups Calculating Control limits for the Mean using The A2 factor UCL = X + A R2 LCL = X − A 2 where A factor = 3/d n 2 2 Fall2012 Page#2 Business StatisticsI-QMS102 Chapter9 Fall2012 Page#3 Control Chart Factors Business StatisticsI-QMS102s Chapter9 In Sample d 2 d3 D3 D 4 A 2 2 1.12 0.85 0 3.26 1.880 8 3 7 3 1.69 0.88 0 2.57 1.023 3 8 5 4 2.05 0.88 0 2.28 0.729 9 0 2 5 2.32 0.86 0 2.11 0.577 6 4 4 6 2.53 0.84 0 2.00 0.483 4 8 4 7 2.70 0.83 0.07 1.92 0.419 4 3 6 4 8 2.84 0.82 0.13 1.86 0.373 7 0 6 4 9
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