Page 179 - Special Topic Session (STS) - Volume 3

STS539 Chenglong Li

Modeling and optimization of the SPRT control
chart for individual observations
Chenglong Li
School of Management, Northwestern Polytechnical University, Xi'an-710072, China

Abstract
In many practical situations, it may not be feasible to take samples larger than
one for various reasons, so control charts must be based on individual
observations ( = 1) rather than larger samples of > 1. The sequential
probability ratio test (SPRT) chart is particularly suitable for monitoring
individual observations. The existing research conducts the design or
optimization algorithm for a SPRT chart from a statistical point of view only.
This paper uses a Markov chain approach and proposes an economic model
for designing the SPRT chart. The results based on an extensive performance
comparison, indicate that under various scenarios the SPRT chart uniformly
outperforms some other competing charts on a cost basis.

Keywords
Control chart; Economic modeling; Individual observation; Optimization; SPRT;
Markov chain.

1. Introduction
The use of most control charts requires sample sizes larger than one
(known as rational subgroups). However, in some applications, only a single
item can be sampled at each point in time. This usually happens when
sampling and testing are time-consuming, expensive and even destructive.
Many traditional (Shewhart-type) control charts perform poorly in such
situations. Instead, memory-type control charts, say, the CUSUM chart or the
EWMA chart, are often recommended in order to make efficient use of all the
information in the sequence of individual data points.
Actually the SPRT chart is also an alternative choice for monitoring
processes with individual observations. The SPRT chart is normally defined as
a sequence of SPRT’s, each separated by a fixed sampling interval. By
inspecting sequentially one observation at a time, the SPRT chart allows the
sampling rate used at each sampling point or SPRT to vary based on the data
observed at the current SPRT, with the possibility of a decision about the
process after each observation.
Stoumbos and Reynolds (1996, 1997) made the early efforts on the
research of SPRT charts. In recent years, a number of research has been
devoted to the development and improvement of SPRT-based schemes; see

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