نمودارهای کنترل پذیرش برای پایش فرآیند خودبرگشتی مرتبه اول

نوع مقاله : پژوهشی

نویسندگان

1 گروه مهندسی صنایع. دانشگاه یزد

2 گروه مهندسی صنایع، دانشگاه یزد

3 دانشکده مهندسی صنایع، دانشکدگان فنی، دانشگاه تهران

4 گروه مهندسی صنایع دانشگاه قم

چکیده

اگر فرآیند به قابلیت بالایی رسیده باشد می‌توان، با در نظر گرفتن سطح انتظارات، تا حدودی تغییرات در میانگین را مجاز دانست. برای چنین وضعیتی نمودار کنترل پذیرش (ACC) ایجاد شده است که از مهمترین مفروضات آن می‎توان به نرمال بودن و استقلال داده‌های مورد پایش اشاره کرد. با این وجود، تحت شرایطی در عمل، الگوهای همبستگی خاصی از میان اطلاعات نمونه‌ای قابل استخراج است که نقض فرض استقلال را در پی دارد. هدف اصلی این پژوهش معطوف به توسعه نمودار کنترل پذیرش در شرایطی است که داده‌های پرکاربردترین فرآیند خودهمبسته، یعنی فرآیند خودبرگشتی مرتبه اول AR(1)، مورد پایش قرار می‌گیرند. پس از ارزیابی عملکرد روش‌های پایش با استفاده از معیار متوسط طول دنباله (ARL)، مشخص می‌شود که نمودار پیشنهادی EWMA نتایج بهتری دارد. علاوه بر این، طراحی اقتصادی-آماری نمودار مذکور با هزینه کمتری میسر می‌شود.

کلیدواژه‌ها


عنوان مقاله [English]

Acceptance control charts for monitoring first-order autoregressive process

نویسندگان [English]

  • Samrad Jafarian-Namin 1
  • Mohammad Saber Fallahnezhad 2
  • Reza Tavakkoli-Moghaddam 3
  • Ali Salmasnia 4
1 Department of Industrial Engineering, Faculty of Engineering, Yazd University
2 Department of Industrial Engineering, Faculty of Engineering, Yazd University
3 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran
4 Department of Industrial Engineering,, University of Qom
چکیده [English]

Thinking that any deviation should be recognized as soon as possible will often be impractical. Despite the existence of numerous assignable causes in the process, their effects may be so small and minor against the permissible tolerance. Identifying them seems uneconomical from practical sights. If the process reaches a high level of capability, the production may be acceptable even though assignable causes befall. Since customers’ expectations will not be affected in this case, it is not economical to stop the process. By considering the level of specifications, some changes in the average can be allowed. Dividing the conditions of the monitored process into just black and white can be simplistic. In such cases, traditional control charts with two zones are not applicable. By defining the zone of indifference, permissible deviations can be tolerated. For such a situation, Acceptance Control Chart (ACC) is developed based on three zones. Suppose that a statistically assignable cause is detected using the traditional control charts; however, no signal is observed by the ACC. Thus, this change does not result in a nonconforming output, and there is no need to stop production since no operational loss occurs. The most important assumptions of the ACC are the normality and independence of the monitored data. In some industrial/non-industrial processes (e.g., continuous production processes, financial processes, network monitoring, and environmental phenomena), serial correlation can be extracted among samples, which violates the assumption of independence. Autocorrelation reduces the performance of traditional control charts by producing frequent false signals in the in-control state or makes them respond slowly to the detection of the out-of-control state. The main purpose of this study is to develop an ACC for monitoring the data of the most widely used autocorrelated process, namely the first-order autoregressive process AR(1). In this regard, two types of ACC are extended for the residuals of AR(1) processes. After evaluating the performance of monitoring methods using the average run length (ARL), it is found that the proposed EWMA chart has better results. Moreover, the economic-statistical design of the proposed chart is carried out at a lower cost.

کلیدواژه‌ها [English]

  • Acceptance control chart
  • Autoregressive process
  • Average run length
  • Economic-statistical design