One-Sided Cumulative Sum (CUSUM) Control Charts for the Zero-Truncated Binomial Distribution

Abstract

One-sided cumulative sum control charts are constructed for controlling the parameters of a random variable with zero-truncated binomial distribution. It is observed that the Average Run Length (ARL) of the resulting control charts change considerably for a slight shift in the parameters of the distribution under study.

One-Sided Cumulative Sum (CUSUM) Control Charts for the Erlang-Truncated Exponential Distribution

“…If we assume that X 1 , X 2 , ...X m be i.i.d. random variables taken from ETE distribution with the probability density function (1). The likelihood ratio to test the null hypothesis H 0 : λ = λ 0 against the alternative hypothesis…”

Measurement error effect on the power of control chart for Zero truncated Negative Binomial Distribution (ZTNBD)

“…Zero-truncated models are those where the number of individuals falling into zero class cannot be defined, or the observational apparatus becomes operational only when at least one event happens. Chakraborty and Kakoty [3] and Chakraborty and Bhattacharya [1,2] have constructed CUSUM charts for zero-truncated Poisson distribution, doubly truncated geometric distribution, and doubly truncated binomial distribution, respectively. Chakraborty and Singh [8] constructed Shewhart control charts for zero-truncated Poisson distribution where average length and operating characteristic function were obtained.…”

“…Chakraborty and Singh [8] constructed Shewhart control charts for zero-truncated Poisson distribution where average length and operating characteristic function were obtained. Chakraborty and Khurshid [4,5] have constructed CUSUM charts for zero-truncated binomial distribution and doubly truncated binomial distribution, respectively. Recently, Khurshid and Chakraborty [16,18] have constructed CUSUM, and Shewhart control charts for ZTNBD, respectively.…”

Control Charts for Doubly Truncated Binomial Distributions

“…Suppose that r defective units are inevitable and that not less than m non-defective units are always contained in a manufactured lot of n items (m < n); then the number of defective items X may adopt a value between r and m, i.e., X follows a doubly truncated binomial distribution which is dealt with in this paper. Recently, Chakraborty and Khurshid [2] used zero-truncated binomial distributions to construct a cumulative sum (CUSUM) control chart. Examples of practical applications of truncated binomial distribution can be found in Johnson et al [4].…”