Chi-square control chart for detection of linear trends in process mean

Hesham Fahmy, Elsayed A. Elsayed

Research output: Contribution to conferencePaperpeer-review


In this research, we develop a new process control approach based on Chi-square distribution to detect linear trends in the process mean. The new approach is described and its performance is compared to the well-known Cumulative Sum (CUSUM) and Shewhart charts in detecting shifts (linear trends) in the process mean. The results indicate that new approach is effective in detecting both moderate and large shifts over a large range. The run length properties of the proposed control chart under linear trends are investigated and compared with simulation results. We consider a process in which individual observations are collected at fixed intervals of time. A moving window of size n is used to calculate the value of the new statistic. There is an overlap in the moving windows by n-1 observations. When the process is in the state of statistical control, observations are assumed to be normally and independently distributed with mean m and standard deviation s. In the out-of-control state, the mean of the process is subjected to a linear shift. The amount of shift is Ks/unit time. The observations collected from the out-of-control process follow a normal distribution at time t (where t is measured after the shift) with a time-dependent mean and constant variance. The value for the proposed statistic is calculated for each window of size n along the data set. The proposed chart signals out-of-control when the chart value reaches a certain threshold.

Original languageEnglish (US)
Number of pages2
StatePublished - 2004
EventIIE Annual Conference and Exhibition 2004 - Houston, TX, United States
Duration: May 15 2004May 19 2004


OtherIIE Annual Conference and Exhibition 2004
Country/TerritoryUnited States
CityHouston, TX

All Science Journal Classification (ASJC) codes

  • Engineering(all)


Dive into the research topics of 'Chi-square control chart for detection of linear trends in process mean'. Together they form a unique fingerprint.

Cite this