An examination of the performance of a natural truncation point and acceptance rule for a curtailed Wald sequential sampling plan with Bernoulli parameters.

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by  Lewis, Cameron J.;Lindsay, Glenn F.

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THE
SIS
AN EXAMINATION OF THE PERFORMANCE
OF A NATURAL TRUNCATION POINT AND
ACCEPTANCE RULE FOR A CURTAILED WALD
SEQUENTIAL SAMPLING PLAN WITH
BERNOULLI PARAMETERS
by
Cameron Lewis
J.
September 1992
Thesis Advisor Prof. Glenn F. Lindsay
Approved for public release; distribution is unlimited.

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NavalPostgraduate School (IfApplicable) Naval Postgraduate School
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11 TITLE(IncludeSecurityClassification)
ANEXAMINATION OFTHEPERFORMANCE OFANATURALTRUNCATIONPOINT AND ACCEPTANCERULE
FOR ACURTAILED WALDSEQUENTIAL SAMPLINGPLANWITHBERNOULLI PARAMETERS (U)
12. PERSONALAUTHOR(S)
Lewis, Cameron J,
13a. TYPEOFREPORT 13b. TIMECOVERED 14. DATEOFREPORT(year,monthday) 15. PAGECOUNT
Master'sThesis FROM TO 1992September 128
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Theviewsexpressed inthisthesis arethose oftheauthoranddo notreflect theofficialpolicyorposition oftheDepartmentof
Defense ortheU.S. Government.
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FIELD GROUP SUBGROUP
19. ABSTRACT(Continueonreverse ifnecessaryandidentifybyblocknumber)
This paperexamines the performance ofaproposed truncation and acceptance rule for the Wald Sequential
Probability Ratio test for Bernoulli parameters and the rules influence on errors of the first and second kind
as well as the average number ofitems sampled for inspection. The proposed truncation and acceptance rule
suggest that there exists a natural truncation point for every Sequential Probability Ratio testsuch that the
desired error probabilities are not exceeded or that one ofthe true errors is smaller then desired and the other
A
will be exceeded by an insignificant amount. computerprogram is used to simulate the sampling process
and provide estimates ofthe true values ofaplan's Operating Characteristic curve, its average sample number
as well as the probability ofimplementing the truncation and acceptance rule. Results suggestthat truncation
,
andrejection ofa lot at the natural truncation point will maintain aplan's desiredOperating Characteristic
curve. The cases examined also suggest that any modifications to the natural truncation point truncation and
acceptancerule may cause an unacceptable deviation from the desiredOperating Characteristic curve. Finally,
a linearequation was developed whichprovides an estimate ofthe upper limit on the probability of
implementing a truncation and acceptance rule and that in most cases, this upper limit is less than 0.15.
20. DISTRIBUTION/AVAILABILITYOFABSTRACT 21. ABSTRACTSECURITYCLASSIFICATION
X UNOASSIFIED/UNLIMrrED D SAMEASRPT. DTICUSERS Unclassified
22a. NAMEOFRESPONSIBLEINDIVIDUAL 22b. TELEPHONE(IncludeAreaCode) 22c. OFFICESYMBOL
G. F. Lindsay [phone] CodeOR/RL
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Approved for public release; distribution is unlimited.
AN EXAMINATION OF THE PERFORMANCE OF A NATURAL
TRUNCATION POINT AND ACCEPTANCE RULE FOR A
CURTAILED WALD SEQUENTIAL SAMPLING PLAN WITH
BERNOULLI PARAMETERS
by
Cameron Lewis
J.
n
Lieutenant, United States Coast Guard
B.S., UnitedStates Coast Guard Academy, 1985
Submitted in partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE IN OPERATIONS RESEARCH
from the
NAVAL POSTGRADUATE SCHOOL
September 1992
u
ABSTRACT
This paper examines the performance of a proposed truncation and acceptance
rule for the Wald Sequential Probability Ratio test for Bernoulli parameters, and
the rule's influence on errors of the first and second kind as well as the average
number of items sampled for inspection. The proposed truncation and acceptance
rule suggests that there exists a natural truncation point for every sequential
probability ratio test such that the desired error probabilities are not exceeded or
that one of the true errors is smaller then desired and the other will be exceeded by
an insignificant amount. A computer program is used to simulate the sampling
process and provide estimates of the true values of a plan's Operating
Characteristic curve, its average sample number, as well as the probability of
implementing the truncation and acceptance rule. Results suggest that truncation
and rejection of a lot at the natural truncation point will maintain a plan's
desired Operating Characteristic curve. The cases examined also suggest that any
modification to the natural truncation point truncation and acceptance rule may
cause an unacceptable deviation from the desired Operating Characteristic curve.
Finally a linear equation was developed which provides an estimate of the upper
,
limit on the probability of implementing a truncation and acceptance rule, and
that in most cases, this upper limit is less than 0.15.
111
TABLE OF CONTENTS
INTRODUCTION
I.. 1
WALDS SEQUENTIAL PROBABILITY RATIO TEST 3
II.
BERNOULLI PARAMETERS AND ERRORS OF
A.
THE FIRST AND SECOND KIND 3
SEQUENTIAL PROBABILITY RATIO
B. 5
SEQUENTIAL SAMPLING CHART
C. 6
D. THE OC CURVE FOR A SPR SAMPLING PLAN 9
THE AVERAGE SAMPLE NUMBER CURVE
E. 10
III. NATURAL TRUNCATION POINT AND ACCEPTANCE RULE - 12
A. THE NATURAL TRUNCATION POINT 12
ACCEPTANCE RULES
B. 16
EXPERIMENTAL PROCEDURES
IV. 19
A. PARAMETER SPECIFICATION 19
B. DEFINITION OF CONFORMING AND NONCONFORMING - 20
C. COMPUTER SIMULATION 22
V. RESULTS AND CONCLUSIONS 25
A. NATURAL TRUNCATION POINT 25
THE m ACCEPTANCE RULE
B. (hi - ) 27
C. THE EXTENDED (hi - m) ACCEPTANCE RULE 29
D. PROBABILITY OF IMPLEMENTING THE
ACCEPTANCE RULE
(hl-1) 30
AREAS FOR FURTHER STUDY
E. 31
LIST OF REFERENCES 122
INITIAL DISTRIBUTION LIST 123
IV