Optimal policies for machine repairmen problems

1993 ◽  
Vol 30 (3) ◽  
pp. 703-715 ◽  
Author(s):  
Esther Frostig
Keyword(s):  
Failure Rate ◽  
Optimal Policy ◽  
Repair Time ◽  
Increasing Failure Rate ◽  
Rate Distribution ◽  
Unreliable Machines ◽  
Optimal Policies

n unreliable machines are maintained by m repairmen. Assuming exponentially distributed up-time and repair time we find the optimal policy to allocate the repairmen to the failed machines in order to stochastically minimize the time until all machines work. Considering only one repairman, we find the optimal policy to maximize the expected total discount time that machines work. We find the optimal policy for the cases where the up-time and repair time are exponentially distributed or identically arbitrarily distributed up-times and increasing failure rate distribution repair times.

Optimal policies for machine repairmen problems

1993 ◽  
Vol 30 (03) ◽  
pp. 703-715 ◽  
Author(s):  
Esther Frostig
Keyword(s):  
Failure Rate ◽  
Optimal Policy ◽  
Repair Time ◽  
Increasing Failure Rate ◽  
Rate Distribution ◽  
Unreliable Machines ◽  
Optimal Policies

n unreliable machines are maintained by m repairmen. Assuming exponentially distributed up-time and repair time we find the optimal policy to allocate the repairmen to the failed machines in order to stochastically minimize the time until all machines work. Considering only one repairman, we find the optimal policy to maximize the expected total discount time that machines work. We find the optimal policy for the cases where the up-time and repair time are exponentially distributed or identically arbitrarily distributed up-times and increasing failure rate distribution repair times.

A multivariate IFR class

1985 ◽  
Vol 22 (01) ◽  
pp. 197-204 ◽  
Author(s):  
Thomas H. Savits
Keyword(s):  
Exponential Distribution ◽  
Failure Rate ◽  
Random Vector ◽  
Increasing Failure Rate ◽  
Rate Distribution ◽  
Weak Limits ◽  
Multivariate Exponential Distribution ◽  
Multivariate Exponential

A non-negative random vector T is said to have a multivariate increasing failure rate distribution (MIFR) if and only if E[h(x, T)] is log concave in x for all functions h(x, t) which are log concave in (x, t) and are non-decreasing and continuous in t for each fixed x. This class of distributions is closed under deletion, conjunction, convolution and weak limits. It contains the multivariate exponential distribution of Marshall and Olkin and those distributions having a log concave density. Also, it follows that if T is MIFR and ψ is non-decreasing, non-negative and concave then ψ (T) is IFR.

A multivariate IFR class

1985 ◽  
Vol 22 (1) ◽  
pp. 197-204 ◽  
Author(s):  
Thomas H. Savits
Keyword(s):  
Exponential Distribution ◽  
Failure Rate ◽  
Random Vector ◽  
Increasing Failure Rate ◽  
Rate Distribution ◽  
Weak Limits ◽  
Multivariate Exponential Distribution ◽  
Multivariate Exponential

A non-negative random vector T is said to have a multivariate increasing failure rate distribution (MIFR) if and only if E[h(x, T)] is log concave in x for all functions h(x, t) which are log concave in (x, t) and are non-decreasing and continuous in t for each fixed x. This class of distributions is closed under deletion, conjunction, convolution and weak limits. It contains the multivariate exponential distribution of Marshall and Olkin and those distributions having a log concave density. Also, it follows that if T is MIFR and ψ is non-decreasing, non-negative and concave then ψ (T) is IFR.

Optimality of the round-robin routing policy

1994 ◽  
Vol 31 (2) ◽  
pp. 466-475 ◽  
Author(s):  
Zhen Liu ◽  
Don Towsley
Keyword(s):  
Failure Rate ◽  
Response Times ◽  
Random Variables ◽  
Round Robin ◽  
State Information ◽  
Convex Ordering ◽  
Increasing Failure Rate ◽  
Rate Distribution ◽  
Routing Policy ◽  
Increasing Convex Ordering

In this paper we consider the problem of routing customers to identical servers, each with its own infinite-capacity queue. Under the assumptions that (i) the service times form a sequence of independent and identically distributed random variables with increasing failure rate distribution and (ii) state information is not available, we establish that the round-robin policy minimizes, in the sense of a separable increasing convex ordering, the customer response times and the numbers of customers in the queues.

OPTIMAL MAINTENANCE AND OPERATION OF A SYSTEM WITH BACKUP COMPONENTS

2002 ◽  
Vol 16 (3) ◽  
pp. 339-349 ◽  
Author(s):  
Rhonda Righter
Keyword(s):  
Failure Rate ◽  
Closed System ◽  
Optimal Policy ◽  
Idle Time ◽  
Repair Time ◽  
Single Server ◽  
System Availability ◽  
Turn On ◽  
Single Server Queues ◽  
Optimal Maintenance

We consider a system with heterogeneous unreliable components that requires only one component to be turned on in order for it to operate. Repair workers may have different skills and may be unavailable for random periods of time. The problem is to determine a usage and repair policy to maximize system availability. We give conditions under which the optimal usage policy is to always use, or turn on, the component with the shortest repair time, and the optimal repair policy is to always repair the most reliable component (with the smallest failure rate). We fully characterize the optimal policy when there are only two components. Our system is equivalent to a closed system with multiple single-server queues, where the objective is to minimize server idle time at one of the queues.

When Is a Renewal Process Convexly Parameterized in Its Mean Parameterization?

1997 ◽  
Vol 11 (1) ◽  
pp. 43-48
Author(s):  
James D. Lynch
Keyword(s):  
Failure Rate ◽  
Renewal Process ◽  
Survival Functions ◽  
Increasing Failure Rate ◽  
Rate Distribution

The convex (concave) parameterization of a generalized renewal process is considered in this paper. It is shown that if the interrenewal times have log concave distributions or have log concave survival functions (i.e., an increasing failure rate distribution), then the renewal process is convexly (concavely) parameterized in its mean parameterization.

Optimality of the round-robin routing policy

1994 ◽  
Vol 31 (02) ◽  
pp. 466-475 ◽  
Author(s):  
Zhen Liu ◽  
Don Towsley
Keyword(s):  
Failure Rate ◽  
Response Times ◽  
Random Variables ◽  
Round Robin ◽  
State Information ◽  
Convex Ordering ◽  
Increasing Failure Rate ◽  
Rate Distribution ◽  
Routing Policy ◽  
Increasing Convex Ordering

In this paper we consider the problem of routing customers to identical servers, each with its own infinite-capacity queue. Under the assumptions that (i) the service times form a sequence of independent and identically distributed random variables with increasing failure rate distribution and (ii) state information is not available, we establish that the round-robin policy minimizes, in the sense of a separable increasing convex ordering, the customer response times and the numbers of customers in the queues.

إيجاد أفضل مقدر لمعلمات التوزيع الخطي العام لمعدلات الفشل باستخدام المحاكاة

2012 ◽  
Vol 18 (69) ◽  
pp. 237
Author(s):  
فاتن فاروق البدري ◽  
علا علي فرج
Keyword(s):  
Failure Rate ◽  
Rate Distribution

تهدف دراسة التوزيعات الإحصائية إلى الحصول على التوصيفات الأفضل لمجموعة المتغيرات والظواهر والتي كل منها يمكن أن يسلك سلوك واحد من هذه التوزيعات. وتعد دراسة عمليات التقدير لمعلمات هذه  التوزيعات من الأمور المهمة والتي لا غنى عنها في دراسة سلوك هذه المتغيرات ونتيجة لذلك جاء هذا البحث محاولة للوصول إلى أفضل طريقة تقدير معلمات توزيع هو واحد من أهم التوزيعات الإحصائية وهو التوزيع الخطي العام لمعدلات الفشل، (Generalized Linear Failure Rate Distribution) وذلك من خلال دراسة الجوانب النظرية بالاعتماد على طرق الاستدلال الإحصائي مثل طريقة الإمكان الأعظم وطريقة المربعات الصغرى وبالإضافة إلى الطريقة المختلطة(طريقة مقترحة) . وتضمن البحث إجراء المقارنات بين طرائق التقدير الثلاثة لمعلمات التوزيع الخطي العام لمعدلات الفشل (GLFRD)، بالاعتماد على مقياسين إحصائيين مهمين هما متوسط مربعات الخطأ (MSE)، ومتوسط الخطأ النسبي المطلق (MAPE)، للحصول على طريقة التقدير الأفضل.

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