THE ANOVA METHOD IN QUALITY AUDIT

Transcription

1 Annals of the Universit of Petroşani, Mechanical Engineering, 8 (006), THE ANOVA METHOD IN QUALITY AUDIT CODRUŢA DURA, CLAUDIA ISAC Abstract: Qualit audit eans a ssteatic, independent exaination of a qualit sste in order to deterine whether activities regarding qualit copl with applicable regulations or standards and also to assess whether these regulations are ipleented efficientl and serve their purpose The practical analsis which is presented further on was done in a ediu size copan fro the engineering industr The statistical ANOVA ethod has appeared recentl in the econoic theor and practice, and it proved its usefulness in obtaining rapidl and with advantageous costs, soe inforation that was necessar for the fundaental activities and anageent decisions Kewords: qualit audit, qualit anageent, statistical ANOVA ethod, total qualit anageent INTRODUCTION Qualit anageent is not an independent activit, it is part of the copan anageent and it has the role to organize, control and direct the resources in order to fulfill the qualit objectives In essence, qualit anageent represents a set of general anageent activities, which deterines the polic regarding qualit, objectives and responsibilities and it ipleents the within the qualit sste through eans like planning, control, insurance and qualit iproveent The iportance that was paid ore and ore to qualit, has deterined the foring of total qualit anageent as an all-ebracing concept which offers a wide field of activit and which induces a continuous process iproveent b extending qualit requireents fro products to processes and fro here to the level of relations, attitudes and convictions, thus laing the foundations for a new industrial culture, an integration and qualit culture In essence, total qualit anageent is the concept of continuous iproveent of products, processes and anageent in all aspects and phases of its Lecturer Ec PhD at the Universit of Petrosani, Roania, codrutadura@ahooco Lecturer Ec PhD at the Universit of Petrosani, Roania

2 4 Dura, C, Isac, C existence and activit, based on the participation of all factors fro all levels of the organization within an iproved organizational and operational sste, which is characterized b clear relations based on convictions aiing at qualit iproveent, reliabilit and the iproveent of costs through innovation and increasing the capacit and business efficienc, in order to fulfill the clients needs and even go beond their expectations APPLYING ANOVA METHOD IN ENERGETIC INDUSTRY For a long ter, the strategies to ipleent total qualit anageent in energetic industr break the preises towards a new anageent concept, that is to sa the qualit anageent sste auditing Qualit audit eans a ssteatic, independent exaination of a qualit sste in order to deterine whether activities regarding qualit copl with applicable regulations or standards and also to assess whether these regulations are ipleented efficientl and serve their purpose During the first phase of the audit the teas which identif the processes are fored, the list of the identified processes is approved, processes are grouped according to tpes and task anagers are being designated for inter-departent processes According to the activities perfored in a certain departent, the process identification tea centralizes the incoing data, the outgoing data, its beneficiar and it fills out the Process For In case the analzed process is copletel perfored within a service, sector or departent, the anager has to designate a process anager; in case the identified process is perfored inter-departentall, process anagers can be designated for each departent After the Process For has been filled out, a centralized report regarding the processes within the qualit anageent sste, is being ade out; this will be analzed b a qualit coittee (it is iportant to set up a qualit insurance office) that can decide to reanalze the situation appeared in one departent and/or to fill out the data in the Process For for that certain departent Following the analsis of the situations resulted fro internal qualit audits, following the evolution of the qualit of products and supplied services, as well as following the clients coplaints, the anageent tea will elaborate, together with the people fro the copan who are in charge with qualit anageent, a progra for the iproveent of the qualit sste, iplicitl of the qualit audit process Thus, the audit proves to be a necessar instruent, within the processes that ipl the analsis and evaluation of the copan s activities, for the anageent tea On the verge of the European integration, there are still several copanies, aong the sall and ediu size enterprises, which could not ipleent efficientl the qualit anageent sste, ainl because the polic and the objectives regarding qualit are abiguous and unquantized, and the are not regarded as a coponent of the copan s anageent strateg; the responsibilities and copetences of the people in charge with qualit anageent are not clearl defined, thus the do not have sufficient authorit; the anageent tea does not receive sufficient inforation and does not react towards the probles regarding qualit; and

3 The ANOVA Method in Qualit Audit 5 last but not least, the costs iplied b the assiilation of a recognized qualit standard As far as the internal qualit audit is concerned, if it exists, it is deterined that the scheduling of internal audits is incoplete and it is not approved b the copan anageent, the audit reports are not ade public to all the parties concerned and reedial easures are also incoplete; soeties these easures are not finalized and the necessar resources for their copletion are not allotted The practical analsis which is presented further on was done in a ediu size copan fro the engineering industr One of the few sectors that reacted to the responsibilities and the iportance of the qualit audit and of the qualit anageent sste, in general, was the echanical working departent, which keeps a precise record of all the audit files and reports fro the last six triesters Registering and processing the data fro internal audits can be easil done using the statistical ANOVA ethod, a special statistical ethod also known as the dispertional analsis ethod or the analsis of variance This ethod has appeared recentl in the econoic theor and practice, and it proved its usefulness in obtaining rapidl and with advantageous costs, soe inforation that was necessar for the fundaental activities and anageent decisions The Roanian specialized literature outlines two variants of the ANOVA ethod: the first one, called one-wa ANOVA, is used where a single factor is being studied, and the second one, called two-wa ANOVA is used where there are two factors being considered, also called ultifactor dispertional analsis The analsis of variance is a ethod that studies the influence applied b one or ore factors that act siultaneousl upon a certain characteristic, which is studied as a dependent variable It has to be a quantitative variable and it ust be easured 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 treatent The dispertional analsis is used to verif the hpothesis which states that the factor or factors have no influence upon the dependent variable, that is to sa that the average values of the dependent variable are equal in all the cases/ for all the population included in the stud On principle, the ANOVA ethod is a fail of ethods used in analzing statistical data, data that depends on several factors with siultaneous effects, in order to establish the ost iportant ones and to estiate their effects In order to be able to appl this ethod, one has to draw up a centralizing table (Table and ) which outlines, for each of the audit reports, the targeted operations (c, c,, c ) The application of this ethod iplies several steps: a) Deliitation of the requireents that ust be et as far as the qualit of the product or service is concerned This phase coincides with the preliinar phase of ipleenting the integrated qualit anageent sste; b) The actual internal audit and partiall filling out the fors for the Audit report of the copan; c) Ssteatization of the internal audit results fro departents in the

4 6 Dura, C, Isac, C ANOVA file Nuber of the audit report Audit report /ear N Audit report /ear N Audit report /ear N+ Audit report n/ear N+i n Table The ANOVA File Model Target operations c c c3 c 3 3 n j 3 j 3 j j n n3 n j i i i i3 i n i j i= j= Table Audit File for the Mechanical Working Departent AUDIT Tasks / Score NR C C C3 C4 C5 C6 C7 C8 C9 C0 C C j j AUDIT AUDIT AUDIT AUDIT AUDIT i i The audit file that was filled out for this departent presents the built-in data received following the analsis of two factors: The first factor,, is represented b the targeted criteria within the echanical working departent, which were put down in the file c j, j = and which refer to the following activities: c longitudinal interior and exterior turning; c face turning and hole/canal turning; c 3 abrasive wheel grinding; c 4 boring operation; c 5 thread cutting through plastic deforation or using threading dies; c 6 thread cutting through chipping with profiling cutters; c 7 cutting with an autoatic saw; c 8 for planning on blanks / half-finished products ade of gra cast iron; c 9 - for planning on blanks / half-finished products ade of steel and crown etal; c 0 illing flat surfaces with face clindrical cutters; c cutting bars and shoulders with rounding ills; c slotting of flat surfaces and canals

5 The ANOVA Method in Qualit Audit 7 The second factor, n, is represented b the nuber the audits perfored within this departent, i = 5 and it is called treatent A ter t ij, which is registered in the ANOVA file, shows the points given when there are deviations fro the initial qualit standards, tat is to sa: 0 points when there is no deficienc regarding the paraeters established in The Annual Internal Qualit Audit ; point, in case there was traced a inor inaccurac / unconforit according to the rearks that were ade; points when there are ajor inaccuracies / unconforities for which one ust establish the causes and the easures that are taken ust be written / recorded in the Reedial Action File ; d) Carring out calculations involving the dispersion analsis or the ANOVA ethod, in several phases: The su of all the values registered in the ANOVA file can be calculated as follows: S = n i j i= j= = 34 () The corrective coefficient, C c, is calculated using the following forula: S C c = = 9,66, () n where: S the square of the su of the values registered in the ANOVA file The average values on a line are calculated next using the following forula: i j j= i = *, (3) where, i* - the average value on line i The su of the values registered in the ANOVA file, the average values on lines and coluns can be easil 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 exaple, are: * = 0,83 * = 0,75 3* = 0,50 4* = 5 = 0,4 5 * = 0,33 The average values on coluns are calculated according to the following forula:

6 8 Dura, C, Isac, C = i j i= * j, (4) where, *j the average value on line j The average values for the twelve coluns in the ANOVA audit file, which was set as exaple, are: * *7 = 0,8 = 0,6 * *8 = 0 = 0, *3 *9 = 0,6 = 0,8 *4 *0 =, = 0 *5 * = 0,6 =,4 *6 * = 0,6 = 0 These calculations of the average values on lines and coluns are carried out in order to offer a visual coparison of the estiated values, as well as in order to ake an ulterior supposition referring to the evidence of the values which help tracing down the factors that overrule / disallow / den / disiss the hpothesis In this case, the average values on coluns are decreasing (fro 083 to 033) and the show that after each audit of the criterion, established b the ipleented qualit anageent sste, reedial easures have been taken, easures that iproved the qualit indicators The average values on lines var according to the targeted operations, fro 0 which indicates a high qualit level for all the tie periods that are analzed and registered in the audit reports with proper values (0; 06; 08) for criteria no, 3, 5, 6, 7, 8, 9 this indicates the existence of soe inor inaccuracies / unconforities, which were generall eliinated (due to evolution, it can be observed that, in all the cases, the tendenc is to find onl inor deficiencies or no deficiencies at all) and of soe iproper values, which prove that there still are soe inaccuracies / unconforities that need to be eliinated These inaccuracies / unconforities are ainl related to thread cutting through plastic deforation and chipping, to cutting with an autoatic saw and to profile cutting of half-finished products ade of different aterials The STT indicator (the su of the square of values) can be calculated using the following forula: n STT ij C c = 6,734, (5) = i= j= where, STT - the su of the square of the values registered in the file; The su of the square of treatents is then deterined: n SS ( Tr ) = Ti* Cc =,33 (6) i=

7 The ANOVA Method in Qualit Audit 9 where where T i* represents the square of the total of the row i The average of the su between treatents is calculated next: SS( Tr ) MS( Tt ) = = 0,56 (7) n The su of the square of / between requireents can be deterined: SS ( Bc ) = T* j Cc =,533 (8) n j= T * j represents the square of the total of the colun j The average of the su between requireents is figured out: SS( Bc ) MS( Bc ) = =,05 (9) Let us calculate the su of the square of errors: SSE STT SS( T ) SS( B ) =,967 (0) = r c Next, let us figure out the MSE indicator: SSE MSE = = 0,9 () ( n ) ( ) The F tpe decisional tests can be applied further on: MS( Tr ) FT r = =,93 () MSE MS( Bi ) FB i = = 3,6 (3) MSE Considering the eleents / nubers which were calculated using forulae (9) and (0) and referring to the statistical tables for the F tpe test, in the case of an iposed risk α = 005, the freedo degrees corresponding to a factorial analsis can be calculated: G l [( n ) ;( n )( ) ] l = (4) [( ) ;( n )( ) ] G lc = (5)

8 30 Dura, C, Isac, C F 0,5;4;44 = F 0,5;;44 =,58,0 The hoogeneit of the lines can be deterined b coparing the calculated values with those fro the tables If the decisional F tpe test is saller than the corresponding freedo degree, we can assert that there exists hoogeneit between treatents (lines or audits); if not, then this hpothesis cannot be accounted for In the case presented above, this hoogeneit is obvious because F T < F 05;4;44 (93 < 58) The hpothesis of the hoogeneit between coluns cannot be aditted because F B > F 05;;44 (36 > 0) 3 CONCLUSION According to previous calculations that were ade, we can notice that: the hoogeneit of the lines lends at least 95% credit to the results of the qualit auditors, considering the risk iposed, that is α = 5%, which proves the efficienc of ipleenting the qualit anageent sste; observing the variations of the average values on lines, we find that there is a reasonable degree of dispersion, which deonstrates that the results are prett close although the audits were perfored b several people; the overruling of the hpothesis referring to the hoogeneit of coluns proves that there are soe probles, thus, the efficienc of the sste is affected within these requireents and therefore, the indicate the directions for future actions Defining these directions is the ain goal of the ANOVA ethod It can be applied in all departents, so that the activities registered in the long run can for the basis of the iproving analsis of the audit activit BIBLIOGRAPHY [] Noe, D, Practical Guide to Qualit Control Principles Methods Means, Technical Pb House, Bucharest, 000 [] Olaru, M, Qualit Manageent, Econoic Pb House, Bucharest, 999 [3] ***, Evaluating the Efficienc of the Internal Audit using the Statistical ANOVA ethod, Qualit Tribune, no- / 00