Annals of the University of Petroşani, Mechanical Engineering, 8 (2006), 23-30

23

THE ANOVA METHOD IN QUALITY AUDIT CODRUŢA DURA 1, CLAUDIA ISAC 2

Abstract: Quality audit means a systematic, independent examination of a quality system in order to determine whether activities regarding quality comply with applicable regulations or standards and also to assess whether these regulations are implemented efficiently and serve their purpose. The practical analysis which is presented further on was done in a medium size company from the engineering industry. The statistical ANOVA method has appeared recently in the economic theory and practice, and it proved its usefulness in obtaining rapidly and with advantageous costs, some information that was necessary for the fundamental activities and management decisions.

Keywords: quality audit, quality management, statistical ANOVA method, total

quality management

1. INTRODUCTION Quality management is not an independent activity, it is part of the company management and it has the role to organize, control and direct the resources in order to fulfill the quality objectives. In essence, quality management represents a set of general management activities, which determines the policy regarding quality, objectives and responsibilities and it implements them within the quality system through means like planning, control, insurance and quality improvement. The importance that was paid more and more to quality, has determined the forming of total quality management as an all-embracing concept which offers a wide field of activity and which induces a continuous process improvement by extending quality requirements from products to processes and from here to the level of relations, attitudes and convictions, thus laying the foundations for a new industrial culture, an integration and quality culture. In essence, total quality management is the concept of continuous improvement of products, processes and management in all aspects and phases of its 1 2

Lecturer Ec. PhD. at the University of Petrosani, Romania, [email protected] Lecturer Ec. PhD. at the University of Petrosani, Romania

24

Dura, C., Isac, C.

existence and activity, based on the participation of all factors from all levels of the organization within an improved organizational and operational system, which is characterized by clear relations based on convictions aiming at quality improvement, reliability and the improvement of costs through innovation and increasing the capacity and business efficiency, in order to fulfill the clients’ needs and even go beyond their expectations. 2. APPLYING ANOVA METHOD IN ENERGETIC INDUSTRY For a long term, the strategies to implement total quality management in energetic industry break the premises towards a new management concept, that is to say the quality management system auditing. Quality audit means a systematic, independent examination of a quality system in order to determine whether activities regarding quality comply with applicable regulations or standards and also to assess whether these regulations are implemented efficiently and serve their purpose. During the first phase of the audit the teams which identify the processes are formed, the list of the identified processes is approved, processes are grouped according to types and task managers are being designated for inter-department processes. According to the activities performed in a certain department, the process identification team centralizes the incoming data, the outgoing data, its beneficiary and it fills out the “Process Form”. In case the analyzed process is completely performed within a service, sector or department, the manager has to designate a process manager; in case the identified process is performed inter-departmentally, process managers can be designated for each department. After the Process Form has been filled out, a centralized report regarding the processes within the quality management system, is being made out; this will be analyzed by a quality committee (it is important to set up a quality insurance office) that can decide to reanalyze the situation appeared in one department and/or to fill out the data in the Process Form for that certain department. Following the analysis of the situations resulted from internal quality audits, following the evolution of the quality of products and supplied services, as well as following the clients’ complaints, the management team will elaborate, together with the people from the company who are in charge with quality management, a program for the improvement of the quality system, implicitly of the quality audit process. Thus, the audit proves to be a necessary instrument, within the processes that imply the analysis and evaluation of the company’s activities, for the management team. On the verge of the European integration, there are still several companies, among the small and medium size enterprises, which could not implement efficiently the quality management system, mainly because the policy and the objectives regarding quality are ambiguous and unquantized, and they are not regarded as a component of the company’s management strategy; the responsibilities and competences of the people in charge with quality management are not clearly defined, thus they do not have sufficient authority; the management team does not receive sufficient information and does not react towards the problems regarding quality; and

The ANOVA Method in Quality Audit

25

last but not least, the costs implied by the assimilation of a recognized quality standard. As far as the internal quality audit is concerned, if it exists, it is determined that the scheduling of internal audits is incomplete and it is not approved by the company management, the audit reports are not made public to all the parties concerned and remedial measures are also incomplete; sometimes these measures are not finalized and the necessary resources for their completion are not allotted. The practical analysis which is presented further on was done in a medium size company from the engineering industry. One of the few sectors that reacted to the responsibilities and the importance of the quality audit and of the quality management system, in general, was the mechanical working department, which keeps a precise record of all the audit files and reports from the last six trimesters. Registering and processing the data from internal audits can be easily done using the statistical ANOVA method, a special statistical method also known as the dispertional analysis method or the analysis of variance. This method has appeared recently in the economic theory and practice, and it proved its usefulness in obtaining rapidly and with advantageous costs, some information that was necessary for the fundamental activities and management decisions. The Romanian specialized literature outlines two variants of the ANOVA method: the first one, called one-way ANOVA, is used where a single factor is being studied, and the second one, called two-way ANOVA is used where there are two factors being considered, also called multifactor dispertional analysis. The analysis of variance is a method that studies the influence applied by one or more factors that act simultaneously upon a certain characteristic, which is studied as a dependent variable. It has to be a quantitative variable and it must be measured on an interval or report scale. In contrast with the dependent variable, the factor or the factors which act as independent variable or variables can be qualitative variables. Each possible value of a factor is called level or treatment. The dispertional analysis is used to verify the hypothesis which states that the factor or factors have no influence upon the dependent variable, that is to say that the average values of the dependent variable are equal in all the cases/ for all the population included in the study. On principle, the ANOVA method is a family of methods used in analyzing statistical data, data that depends on several factors with simultaneous effects, in order to establish the most important ones and to estimate their effects. In order to be able to apply this method, one has to draw up a centralizing table (Table 1 and 2) which outlines, for each of the audit reports, the targeted operations (c 1 , c 2, …, c m ). The application of this method implies several steps: a) Delimitation of the requirements that must be met as far as the quality of the product or service is concerned. This phase coincides with the preliminary phase of implementing the integrated quality management system; b) The actual internal audit and partially filling out the forms for the Audit report of the company; c) Systematization of the internal audit results from departments in the

26

Dura, C., Isac, C.

ANOVA file. Table 1. The ANOVA File Model Target operations c1 c2 c3 …

Number of the audit report

∑j ∑ y1 j ∑ y2 j ∑ y3 j

cm

Audit report 1/year N

y 11

y 12

y 13

…

y 1m

Audit report 2/year N

y 21

y 22

y 23

…

y 2m

Audit report 1/year N+1

y 31

y 32

y 33

…

y 3m

. .

. .

. .

. .

. .

. .

Audit report n/year N+i

y n1

y n2

y n3

…

y nm

. . ∑ yn j

∑i

∑ yi1

∑ yi 2

∑ yi 3

∑ yi m

∑∑ yi j

n

i =1 j =1

Table 2. Audit File for the Mechanical Working Department Tasks / Score y 2j ∑yj C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 0 0 2 1 0 2 0 1 0 2 0 10 18 0 1 1 1 1 1 0 1 0 2 0 9 11 0 1 1 0 1 0 1 1 0 1 0 6 6 0 0 2 0 1 0 0 1 0 1 0 5 7 0 1 0 1 0 0 0 0 0 1 0 4 4

∑

AUDIT NR. AUDIT 1 AUDIT 2 AUDIT 3 AUDIT 4 AUDIT 5 ∑ yi

C1 2 1 0 0 1 4

0

3

6

3

3

3

1

4

0

7

0

34

-

∑y

6

0

3

10

3

3

5

1

4

0

11

0

-

-

36

0

9

100

9

9

25

1

16

0

121

0

2 i

m

324 121 36 49 16

546 326

The audit file that was filled out for this department presents the built-in data received following the analysis of two factors:  The first factor, m, is represented by the targeted criteria within the mechanical working department, which were put down in the file c j , j = 1…12 and which refer to the following activities: c 1 – longitudinal interior and exterior turning; c 2 – face turning and hole/canal turning; c 3 – abrasive wheel grinding; c 4 – boring operation; c 5 – thread cutting through plastic deformation or using threading dies; c 6 – thread cutting through chipping with profiling cutters; c 7 – cutting with an automatic saw; c 8 – form planning on blanks / half-finished products made of gray cast iron; c 9 form planning on blanks / half-finished products made of steel and crown metal; c 10 – milling flat surfaces with face cylindrical cutters; c 11 – cutting bars and shoulders with rounding mills; c 12 – slotting of flat surfaces and canals.

The ANOVA Method in Quality Audit

27

 The second factor, n, is represented by the number the audits performed within this department, i = 1…5 and it is called treatment. A term t ij, which is registered in the ANOVA file, shows the points given when there are deviations from the initial quality standards, tat is to say: 0 points when there is no deficiency regarding the parameters established in “The Annual Internal Quality Audit”; 1 point, in case there was traced a minor inaccuracy / unconformity according to the remarks that were made; 2 points when there are major inaccuracies / unconformities for which one must establish the causes and the measures that are taken must be written / recorded in the “Remedial Action File”; d) Carrying out calculations involving the dispersion analysis or the ANOVA method, in several phases:  The sum of all the values registered in the ANOVA file can be calculated as follows:

S=

n

m

∑∑ y

ij

= 34

(1)

i =1 j =1

 formula:

The corrective coefficient, C c, is calculated using the following

Cc =

S2 = 19,266 , n⋅m

(2)

where: S2 – the square of the sum of the values registered in the ANOVA file.  The average values on a line are calculated next using the following formula: m

y i* =

∑y j =1

m

ij

,

(3)

where, y i* - the average value on line i. The sum of the values registered in the ANOVA file, the average values on lines and columns can be easily calculated using a calculating sheet within the Microsoft Excel. The average values for the five lines in the ANOVA audit file, which was set as example, are:

y1* = 0,83

y 2* = 0,75

y 3* = 0,50

y 4* = 5 = 0,41

y 5* = 0,33

 The average values on columns are calculated according to the following formula:

28

Dura, C., Isac, C. m

∑y

ij

y* j =

i =1

m

,

(4)

where, y *j – the average value on line j. The average values for the twelve columns in the ANOVA audit file, which was set as example, are:

y *1 = 0,8

y *2 = 0

y *3 = 0,6

y *4 = 1,2

y *5 = 0,6

y *6 = 0,6

y *7 = 0,6

y *8 = 0,2

y *9 = 0,8

y *10 = 0

y *11 = 1,4

y *12 = 0

These calculations of the average values on lines and columns are carried out in order to offer a visual comparison of the estimated values, as well as in order to make an ulterior supposition referring to the evidence of the values which help tracing down the factors that overrule / disallow / deny / dismiss the hypothesis. In this case, the average values on columns are decreasing (from 0.83 to 0.33) and they show that after each audit of the criterion, established by the implemented quality management system, remedial measures have been taken, measures that improved the quality indicators. The average values on lines vary according to the targeted operations, from 0 – which indicates a high quality level for all the time periods that are analyzed and registered in the audit reports with proper values (0.2; 0.6; 0.8) for criteria no.1, 3, 5, 6, 7, 8, 9 – this indicates the existence of some minor inaccuracies / unconformities, which were generally eliminated (due to evolution, it can be observed that, in all the cases, the tendency is to find only minor deficiencies or no deficiencies at all) and of some improper values, which prove that there still are some inaccuracies / unconformities that need to be eliminated. These inaccuracies / unconformities are mainly related to thread cutting through plastic deformation and chipping, to cutting with an automatic saw and to profile cutting of half-finished products made of different materials.  The STT indicator (the sum of the square of values) can be calculated using the following formula:

STT =

n

m

∑∑ y

− Cc = 26,734 ,

2 ij

(5)

i =1 j =1

where, STT - the sum of the square of the values registered in the file;  The sum of the square of treatments is then determined:

SS (Tr ) =

1 ⋅ m

n

∑T

2 i*

i =1

− Cc = 2,233

(6)

The ANOVA Method in Quality Audit

29

where Ti*2 represents the square of the total of the row i.  The average of the sum between treatments is calculated next:

MS (Tt ) = 

SS (Tr ) = 0,56 n −1

(7)

The sum of the square of / between requirements can be determined:

SS ( Bc ) =

1 ⋅ n

m

∑T

2 *j

− Cc = 11,533

(8)

j =1

where T*2j represents the square of the total of the column j. 

The average of the sum between requirements is figured out:

MS ( Bc ) = 

SS ( Bc ) = 1,05 m −1

Let us calculate the sum of the square of errors:

SSE = STT − SS (Tr ) − SS ( Bc ) = 12,967 

(10)

Next, let us figure out the MSE indicator:

MSE = 

(9)

SSE = 0,29 (n − 1) ⋅ (m − 1)

(11)

The F type decisional tests can be applied further on:

FTr =

MS (Tr ) = 1,93 MSE

(12)

FBi =

MS ( Bi ) = 3,62 MSE

(13)

Considering the elements / numbers which were calculated using formulae (9) and (10) and referring to the statistical tables for the F type test, in the case of an imposed risk α = 0.05, the freedom degrees corresponding to a factorial analysis can be calculated:

Gll = [(n − 1); (n − 1)(m − 1)]

(14)

Glc = [(m − 1); (n − 1)(m − 1)]

(15)

30

Dura, C., Isac, C.

F0,5; 4; 44 = 2,58 F0,5;11; 44 = 2,02  The homogeneity of the lines can be determined by comparing the calculated values with those from the tables. If the decisional F type test is smaller than the corresponding freedom degree, we can assert that there exists homogeneity between treatments (lines or audits); if not, then this hypothesis cannot be accounted for. In the case presented above, this homogeneity is obvious because F T1 < F 0.5;4;44 (1.93 < 2.58). The hypothesis of the homogeneity between columns cannot be admitted because F B1 > F 0.5;11;44 (3.62 > 2.02) 3. CONCLUSION According to previous calculations that were made, we can notice that: the homogeneity of the lines lends at least 95% credit to the results of the quality auditors, considering the risk imposed, that is α = 5%, which proves the efficiency of implementing the quality management system; observing the variations of the average values on lines, we find that there is a reasonable degree of dispersion, which demonstrates that the results are pretty close although the audits were performed by several people; the overruling of the hypothesis referring to the homogeneity of columns proves that there are some problems, thus, the efficiency of the system is affected within these requirements and therefore, they indicate the directions for future actions. Defining these directions is the main goal of the ANOVA method. It can be applied in all departments, so that the activities registered in the long run can form the basis of the improving analysis of the audit activity. BIBLIOGRAPHY [1] [2] [3]

Noye, D., Practical Guide to Quality Control. Principles. Methods. Means., Technical Pb. House, Bucharest, 2000 Olaru, M., Quality Management, Economic Pb. House, Bucharest, 1999 ***, Evaluating the Efficiency of the Internal Audit using the Statistical ANOVA method, Quality Tribune, no.11-12 / 2002