First of all I must congratulate you for raising a very good & relevant question , which is in fact is relevant for the entire / over all  Global Education System. I mean whats you asked that is applicable for every country i.e. to make an assessment related with efficiency & quality of Education !!

In my views it starts from measuring the level of Knowledge which is the very basis objective of any education , second is the level of exposure , third one is the utility in terms of contribution towards the society , nation & economy as well.

As for as the question of efficiency & quality is concerned with a little difference both have different meaning.

Quality has to do with Standards, content,delivery and products of education,while efficiency refers to functionality ie how relevant is the education to economic,social and psychological development of the society.There are two types of efficiency.INTERNAL &  EXTERNAL EFFICIENCY.Internal efficiency has to do with level of  the productivity measured by wastage level(how many pupils/students budgeted were really catered for in a given year.It measures shortages/wastages using a type of  cohort analysis..While external efficiency measure usablilty or employability of University products.so efficiency same as quality.But if quality is functional,the efficiency is implied

Quality education may not be efficient but effective

Fathy:

You've received very good responses to your question. I would only add that quality is also about "fit for purpose" so that you would have to determine what is best for your education system in Egypt, then tailor your processes and products to towards this end. When your measuring quality and efficiency, it would be against your set standards in keeping with your mission and vision for your education system. Here's what is available in ResearchGate on your topic:

https://www.researchgate.net/publicliterature.PublicLiterature.search.html?type=keyword&search-keyword=quality+and+efficiency+in+education&search-abstract=&search-journal=&search=Search

I hope this helps.

Debra

Thanks to all, these answers very helpful for me, I want to add that to assessment the education system, we can use many indicators, i. e. the quantity and quality of stock of human capital in the country, what extent use the stock of human capital ( to measure the external efficiency for example unemployment between tertiary education graduates), and what extent improvement in stock of human capital (to measure the internal efficiency).

Efficiency is :  output/input

The input for various countries may be different (LDC's vs HDC's etc). For the differential inputs, at same efficiency, the outputs will be different.

However "quality of education" i.e. Juran's  "fitness for purpose" remains sacrosanct. Because different countries may expect similar outputs from the education.

you would need to know what the "purpose" of the education was before you could define effectiveness - this is a very difficult question to answer. Determining efficiency on the other hand is much less contentious

efficiency may refer to the process

while quality refers to the product of the process and yet to certain extent efficient process does not ensure quality production as there are many element s involved in the process in order to produce a good product

understanding the entirety of the process and product to be produced would be able to ensure the required quality 

back to the question

in assessing the efficiency of education which stage are you referring to?

teaching, system, content or syllabus development etc

focusing on one element at a time will build up the complete the whole process

teaching for instance may look at the delivery process of the content and so on

Yes "efficient process does not ensure quality production as there are many element s involved in the process in order to produce a good product"  as Azman says.

The rider is that of reliability@capability:  Thus  An efficient process (which is capable), will sure produce QUALITY. This aspect is design (system, content or syllabus development ).

To expand on Michael's answer>

For me, quality in education is a relative concept. It depends on such things as the aims of education, views of learning and local values. For example, Jin Li makes a distinction between the mind model of learning (claimed to be largely Western) in which education aims to cultivate minds that understand the world and the virtue model of learning focussing more upon perfection of the self in moral and social terms (claimed to be largely Eastern). Then there are the debates around the sorts of learning we need for changing societies (the so called "knowledge society, for example), good citizenship (again something that different countries might see in different ways). That is possibly too simplistic, but it gives a flavour of the sort of issues. The purpose of education is constantly debated and, as Michael, notes very difficult to answer definitively and so always in contention. Quality of education is a complex concept, even within a national boundary.

Efficiency would then be the degree to which education meets its aims, view of learning, values, and whatever other components go into local conceptions of quality. That might be measured (or at least some indication obtained) as noted above by such things as student dropouts (high dropout rate equals low efficiency/effectiveness), assessment results (assuming the assessments, syllabus and the teaching methodology are aligned properly with the concept of quality being applied and that is a big if), opinions of employers, students' opinions of their experiences, and so on. However, even if these do align with a concept of quality, they are probably not complete either as these are most likely measures made at the point of exit of education.The missing measure is the long lasting (or otherwise) effects of education (How much influence does it have 10, 20, 30 years later? How much of that influence is beneficial in changing circumstances and how much hinders adaptation to those changing circumstances?) 

So, unlike Michael, i am not sure that even  determining efficiency is less contentious.

@Colin,  the stated definition of " Efficiency would then be the degree to which education meets its aims, view of learning, values,." gels well with that of 'quality' defined as per ISO 9000:  the degree to which stated or implied needs of something are met. or ASQ's definition: Quality is the degree to which an object (entity) [e.g., process, product ] [confers]. on its ability to satisfy stated or implied needs; 

But since educational objectives are defined for short term and measurable ones, the quality issue continues to remains subjective.

Michael's perceived difficulty in defining effectiveness -  is thus right, because of the complexity involved in the education process itself..  Determining efficiency will  be though straight forward, measured over chosen metrics. Howsoever efficiently the learning task has been undertaken., the effectiveness is relative to the fulfillment of the objectives?, - the question which sustains in case of education. Is it teaching and learning or inculcation of citizenry and societal values?  Is it in handling of a class of students assigned in general, or developing a single meritorious product of unprecedented quality what Chanakya did - in transforming two kings.  His meeting of  the  stated or implied needs of developing common, un-oriented lads into Chandragupt and Ashoka - rulers with wisdom and efficacy are notable. How efficient was he (Chanakya) appears to take a back seat.

Arguably , the concept of quality, is most likely evidenced at the point of exit of education., but the phenomenon does not escape the planning of the inputs of efficiency of process, which enabled the ultimate effectiveness a reality.

The concept of efficiency applies to a number of fields, including education. It is based on presuming a transition of some kind. Initially, there was a human case  before transformation (call it A). Finally, there was the same case  after transformation (call it B) and the transition from A to B occurred by process. The initial elements may be referred to as ingredients, inputs, or resources while the final elements are denoted as results, outputs, or outcomes. When the transitional process proceeds more smoothly, then the efficiency is higher. Obviously, a lower efficiency is indicative of more difficulties in the educational process.

Efficiency is not a "yes/no" kind of observable but is better thought of in relative or comparative terms in such that one process may be more or less efficient than another. 

As for quality in education, there is no consensus on defining it & some educational authorities even escape from adopting a particular definition. Those who dared to define it say & I quote: ‘Academic quality is a way of describing how well the learning opportunities available to students help them to achieve their award. It is about making sure that appropriate and effective teaching, support, assessment and learning opportunities are provided for them.’

At once, this definition will be criticized from different angles: Is quality a way of describing ? Who sets the award of the students? Is the whole issue dependent on one of the ingredients of the input (i.e. the teachers)? How about the recipient's interaction; is it just sitting idle to be served?  What about the resources that are made available to ensure high quality? And quality, itself, is targeted to what level?

Many universities claim that they offer high quality education but what is the standard point of reference or this quality is compared to what ?

Internal efficiency concerns operation parameters such as curricula, teacher qualifications, student standardized tests, textbook quality and infrastructure. All these may be measured using both qualitative and quantitative research.  External efficiency concerns the value added offered by graduates to national economy and society. Collecting evidence on various indicators such as matched employment, rate of returns etc. is one way to assess external efficiency.  Related methodologies could be longitudinal panel, tracer study, retrospective tracer study, household survey and firm survey.  Clearly, quality assurance is an issue explored in all methodologies.

@ Stamatis, Rightly quality assurance is the Mantra related to maintenance of efficiency- of all kinds. You have well knit the requirements/ end objectives of education, though there could be no scope of being complacent in any. These (parameters to achieve) all are subject to right design and capability, and their performance a stipulated pre-condition of success (of quality assurance), confirmed by .measurement (s)..

@ Nizar maintains herein efficiency is comparable. And thus when can use it for benchmarking. It sure is improveable.- by transformation -  say of contributors (or  process, or by Design ).

As says Nizar, , " there is no consensus on defining Quality- And Education, being complex, there is more to this non-conensus. It is very elusive as many authors on education have maintained. The biggest Gap is that 'Teaching' is the cause, and Learning should be the Impact. One wants to improve upon the cause - 'Teaching'  wanting to maximising the affect, and expect great outcome () in terms of 'learning'.

That is how Rightly quality assurance is the Mantra related to outcome. It is a subset of effectiveness and not efficiency. Efficiency was defined by Colin as  quote 'Efficiency would then be the degree to which education meets its aims, view of learning, values" ..."How much of that influence is beneficial in changing [or] adaptation to [applied /needed stimulus ]?). (applied is Teaching , and needed is outcome/ expected learning). Important it is that how do we connect them??

Quality relates to the distribution of student outcomes measured by test scores, or preferably by Rasch measures. Tipically the mean of the distribution is a point of reference.

Efficiency relates to how much you spent to get that level of outcome.

The input is given based on the experience at al-Azhar University, Cairo, Egypt only.

For me, it was a tiring learning experience, students have to understand and apply what has been learned. Students are taught to understand deeply about the subjects matter, the same classes is repeated for few times, after several session, students have to have group discussion.

Assessment based on final examination only, however the examination not determine whether the student pass or fail. Rather the lecturer looked at the students achievement through the knowledge that students have acquired. This is demonstrate through student's ability to analyze and synthesis the knowledge that they acquired. The students and lecturers alike are not so much concerned with examination but more focusing the deep understanding of the knowledge.. happy Ramadhan    

@ Nor, The initiatives are appreciable. Focus on Outcome is the most preached measure. Exams need be properly designed, as these act as a co-processor for ascertaining outcomes.