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MA30118: Management Statistics |
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Timetable: |
lectures are Monday |
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problem
classes are Monday |
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Lecturer: |
Simon Shaw; s.c.shaw at maths.bath.ac.uk |
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Credits: |
6 |
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Level: |
Honours |
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Semester: |
2 |
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Assessment: |
EX60CW40 |
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Requisites: |
Before taking this unit you must take MA20097 or take MA20035 or take EC20019 |
Aims & Learning Objectives:
This unit is designed primarily for DBA Final Year students who have
taken the First and Second Year management statistics units but is also
available for Final Year Statistics students from the Department of
Mathematical Sciences. Well qualified students from the IMML course
would also be considered. It introduces three statistical topics which
are particularly relevant to Management Science, namely quality control,
forecasting and decision theory.
Aims: To introduce some statistical topics which are
particularly relevant to Management Science.
Objectives: On completing the unit, students should be able to
implement some quality control procedures, and some univariate
forecasting procedures. They should also understand the ideas of
decision theory.
Content:
Introduction to decision analysis for discrete
events: Revision of Bayes' Theorem,
admissibility, Bayes' decisions, minimax. Decision trees, expected value of
perfect information.Utility, subjective
probability and its measurement.
Quality Control: Acceptance sampling, single and
double schemes, SPRT applied to sequential scheme. Process control, Shewhart charts for mean and range, operating
characteristics, ideas of cusum charts.
Practical
forecasting: Time plot.
Trend-and-seasonalmodels. Exponential smoothing. Holt's linear trend model and
Holt-Winters seasonal forecasting. Autoregressive models. Box-Jenkins ARIMA forecasting.
Introduction to decision analysis for discrete events
We won't follow a book as such but useful references include:
The interested student may find more mathematical treatments (and more breadth than this course) at the shelfmark 512.794. Two such are:
2005/06 schedule:
Lecture 1 (6 Feb 06): §1 Introduction: §1.1
Actions, §1.2 States of nature, §1.3 Worked example: Duff beer, §1.4 Payoff.
Lecture 2 (7 Feb 06): §1.5 Admissibility, §1.6 Minimax regret, §2 Decision making with
probabilities: §2.1 Maximising expected monetary value.
Lecture 3 (13 Feb 06): §2.2 Decision trees, §2.3 Value of perfect information.
Lecture 4 (14 Feb 06): §2.4 A brief review of some probability
theory. §2.5 An example with sequential decisions.
Homework -
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Question Sheet One: pdf or postscript |
Solution Sheet One: pdf or postscript |
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Question Sheet Two: pdf or postscript |
Solution Sheet Two:pdf or postscript |
Quality Control (Acceptance Sampling and Process Control)
We won't follow a book as such but the library shelfmark 512.766 contains plenty of examples. Books I consulted include:
2005/06 schedule:
Lecture 9 (6 Mar 06): Introduction to Acceptance Sampling.
Lecture 10 (7 Mar 06): Single sampling schemes, operating characteristic (OC) curve, AQL and producer's risk.
Lecture 11 (13 Mar 06): LTPD and consumer's risk, worked example of calculating single sampling scheme.
Lecture 12 (14 Mar 06): Rectifying schemes, average outgoing quality (AOQ), average outgoing quality limit (AOQL), double sampling schemes, construction of the OC-curve for double sampling.
Lecture 13 (20 Mar 06): Worked example of construction of the OC-curve for double sampling, average sample number (ASN), sequential probability ratio test (SPRT).
Lecture 14 (21 Mar 06): Continuation rule in the SPRT, worked example of construction of the continuation rule. Introduction to Process Control and its objectives.
Lecture 15 (27 Mar 06): Introduction to Process Control and its objectives. Description of control chart and general model, mean and range charts.
Lecture 16 (28 Mar 06): mean and range charts when µ and σ are unknown, worked example of construction of mean and range chart in this case, interpretation of control charts.
Lecture notes: pdf or postscript
(Lectures 9-16)
Homework -
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Question Sheet Three: pdf or postscript |
Solution Sheet Three: pdf or postscript |
| Question Sheet Four: pdf or postscript | Solution Sheet Four: pdf or postscript |
2005/06 schedule:
Lecture 17 (24 Apr 06): Introduction, time series models. Components of a time series: trend, seasonality, cyclical variation, irregular variation
Lecture 18 (25 Apr 06): Exponential smoothing, worked example of forecasting using exponential smoothing (Handout: pdf or postscript).
Lecture 19 (2 May 06): Criterion for determining the smoothing constant α, mean square deviation (MSD)
Lecture 20 (8 May 06): Holt's linear trend method, Holt-Winter's multiplicative model.
Lecture 21 (8 May 06): Introduction to Box-Jenkins methodology, autoregressive models of order p, AR(p), moving average models of order q, MA(q), mixture of autoregressive and moving average models, ARMA(p, q).
Lecture 22 (9 May 06): Achieving stationarity through differencing, autoregressive
integrated moving average models, ARIMA(p,
d, q), forecasting with ARIMA(p, d, q) models with worked example.
Lecture notes: pdf or postscript
(Lectures 17-22). These notes include a brief mention of Box-Jenkins
model identification via the autocorrelation function (ACF) and partial
autocorrelation function (PACF). This is for interest only and will not
be examined.
Homework -
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Question Sheet Five: pdf or postscript |
Solution Sheet Five: pdf or postscript |
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Last revision: |