طراحی آماری اقتصادی نمودار کنترلی برای مشاهدات انفرادی از توزیع نمایی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه آمار، دانشکده علوم ریاضی، دانشگاه تبریز

2 دانشگاه صنعتی بیرجند

چکیده

در این مقاله برای مشخصه‌های کیفی انفرادی که دارای توزیع نمایی هستند، یک نمودار کنترلی با طراحی آماری اقتصادی ارائه شده است. بدین منظور ابتدا با استفاده از تقریبی که توسط نلسون پیشنهاد شده است، توزیع نمایی مشاهدات انفرادی را به توزیع نرمال تبدیل کرده‌ایم. سپس با استفاده از مدل اقتصادی کاستا و رحیم یک طرح آماری اقتصادی را برای مشاهدات تبدیل یافته به دست آورده‌ایم. به منظور بهینه‌سازی پارامترهای مدل که بر اساس پارامترهای طرح محاسبه می‌شوند، مقادیر بهینه پارامترهای طرح را با استفاده از الگوریتم زنبور عسل بدست آورده‌ایم. در پایان، نتایج پارامترهای آماری اقتصادی نمودار کنترلی بیان شده با طرح اقتصادی مقایسه شده و عملکرد مثبت طرح آماری اقتصادی در مقایسه با طرح اقتصادی نشان داده شده است. همچنین به‌وسیله داده‌های شبیه‌سازی شده از توزیع نمایی، کارایی و عملکرد نمودار کنترلی معرفی شده در مقایسه با حالتی که توزیع مشخصه کیفی نرمال فرض می‌شود، بررسی شده است

کلیدواژه‌ها


عنوان مقاله [English]

Economic statistical design of control chart for individual observations of exponential distribution 

نویسندگان [English]

  • Ali Akbar Heydari 1
  • Masoud Tavakoli 2
1   Assistant Professor, Department of Statistics, University of Tabriz    
2 Assistant Professor, Department of Basic Sciences, Birjand University of Technology  
چکیده [English]

In this paper, an economic statistical design of control chart is presented for individual qualitative characteristics that have an exponential distribution. For this purpose, we first convert the exponential distribution of individual observations to the normal distribution using the approximation proposed by Nelson. Then, using Costa and Rahim economic model, we have obtained an economic statistical design for the transformed observations. In order to optimize the model parameters that are calculated based on the design parameters, we have obtained the optimal values of the design parameters using the honey bee algorithm. Finally, the results of the economic statistical design of the control chart are compared with the economic design and the positive performance of the economic statistical design compared to the economic design is shown. Also, by simulated data from the exponential distribution, the efficiency and performance of the introduced control chart in comparison with the case that the distribution of the qualitative characteristics is normal, has been investigated. 
 
 

کلیدواژه‌ها [English]

  • Control chart
  • Quality characteristic
  • Exponential Distribution
  • Economic statistical design
  • Costa and Rahim economic model  
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