AQL and LQ Schemes – their use and limitations in pharmaceutical quality assurance 1 Introduction Paolo – as a prelude to answering the supplementary questions you asked (and I apologise in advance if I repeat myself), myself), it is worthwhile re-visiting some key facts about a bout AQL and and LQ schemes !here " refer to a #lide by number, it is one in the slide set to which " provided the link
2 Issues 1.1 Issue 1- the perceive perceived d ‘magical ‘magical proper properties ties o! o! IS" 2#$% 2#$% schemes $he AQL schemes schemes of "#% &'()–* and the LQ schemes of "#% &'()-& possess no +magical properties which provide a level of protection beyond beyond that statistically calculable from the inomial.Poisson statistics which underpin them for a given combination of sample si/e and acceptance number $he $he standards merely provide a convenient, standard, sub-set of the infinite possible sample si/e.acceptance number permutations, together with tabulated details on the level of protection they supply for particular sample si/e.acceptance number combinations
1.2 Issue 2 – the the perception perception that that the AQL AQL value is is the percenta percentage ge o! de!ects &ithin a single 'atch &ith a high pro'a'ility o! re(ection $he clue to the first problem with this fallacy of this perception lies in the name (Acceptable Quality Level) that the acronym AQL represents Average Level of Defects across a Composited Series of $he stated AQL value is the Average Batches which you would be happy to have an appro0imately 95 cha!ce of Accepti!g An An individual batch can have a significantly higher proportion of defects 1up to *& times the stated AQL2 present Average $he second problem comes from the words Composited Series of Batches and Average Level of Defects which are critical, since they imply two things which are not acceptable for many 34P purposes5 •
6ompositing, eliminating batch based track and trace during the manufacture chain
•
6ompositing of batches deliberately using the better batches which are part of the composite to average out the effect of batches which are substantially worse than the composite average
1.) Issue ) – using IS" IS" 2#$%-1 scheme schemes s !or outgoi outgoing ng product product assessment $his standard is designed for incoming inspection As is e0plicit in the background Average Level of information provided within the standard, they are designed for giving an Average "rotectio! as measured over a Composited Bul# as as a Series of $!comi!g batches batches $hey are identified as Specifically %ot Desig!ed to to provide $!dividual Batch "rotectio! on Si!gle &utgoi!g Batches An understanding of how %perating 6haracteristic curves 1%6 curves2 work allows the tabulated probabilities in the different code letter tables of "#% &'()-* to be used to
determine the level of defects which would give a high probability of re7ection on a single batch – effectively, you are then looking at the performance of an LQ (Limiting Quality Scheme) but when used in this way, the tabulated AQL value is meaningless (see 1.5 later) $his is why, for single batches, the Limiti!g Quality schemes of "#% &'()-& are intuitively clearer in the level of single batch protection they offer since, to paraphrase use the words from a 89 advert for wood protection paint which have passed into common 89 usage ‘.they do exactly hat it says on the la!el"..#
1.* Issue * – using AQLs in the 'elie! that they can control critical de!ects or can deliver the ‘mythical +, AQL 6ritical defects, by definition cannot be controlled by any form of sampling – AQL schemes do not possess any +magic properties which allow control of critical defects A fundamental condition of the use of any sa mpling scheme, including these schemes, is that there is a finite permissible level of defects which can be present in a batch $he level may be very low but use of a sample requires it to be finite !hen the :; AQL appears in a specification, in m y e0perience, one or both of the following is happening5 •
$he author of the scheme is using :;AQL to describe what is in reality a 6ritical
•
An acceptance number of : is being confused with an assumption that : defects found in the sample = : defects in the batch
) our specic questions 1.$ /roperties o! "perating 0haracteristic "0 curves. $he answers to the questions are so dependent on the properties of %6 curves that " will deal with this issue first, before answering the questions *( – code 4
"n diagram & below, " have focussed on one of these curves – sample >*( – accept on : or * defects -re7ect on & or more
An %6 curve (the !lue line) is a graphical representation of the probability (vertical axis) of accepting of a batch with a given percentage of defects (hori$ontal axis) and it is derived
directly from the percent nonconforming = &(; column of table *:-4-* of diagram * Acceptance schemes technically follow inomial statistics, though for large samples with low percentages of defects e0pected, sampling schemes such as the "#% &'() series use the Poisson appro0imation to the inomial distribution $he shape of the curve produced by either distribution is solely dictated by two parameters – the # ample #i/e and the 4a0imum Acceptable ?umber of defects @or *( and the ma0imum acceptable number of defects is * $he shape of the curve is the unaffected, whether the curve is being used to predict the effect of an AQL scheme or a LQ s cheme $he curves in "#% &'()-& are, in effect a sub-set of the curves in "#% &'()-* and " have chosen in ti mes higher than the stated value of the AQL $his is the origin of my comment in slide *& of the presentation that the common belief that the AQL value is the level of defects with a high chance of re7ection is wrong and leads to a vast overestimate of the protection offered As
1.3 Question 1 I &onder i! you could indicate ho& a company should in general select4dene appropriate AQL values. As " hope " have made clear in previous answers, AQLs, as defined in the "#% &'()-* standard, with their focus on the average properties of a composited bulk where batch identity is lost are typically inappropriate for batch related pharmaceutical 34P controls A focus on preventing acceptance of individual batches whose defect level e0ceeds a certain percentage is, by its nature, an LQ scheme $o legitimately use such schemes, one precondition must be met and three key decisions have to be made5 •
$he precondition for using LQ sampling is that within a batch, there must be a finite tolerable level of any defect selected for control by sampling – the level may !e small !ut it cannot !e $ero.
•
!hat is the tolerable percentage for each defect where a proportion of such defects can be allowed in the batch
•
!hat constraints are there on sample si/e Larger samples give better discrimination and schemes with an acceptance number of /ero have particularly poor discrimination (slides %& and %5 of the presentation)
•
"s there a defined scheme meeting the need in "#% &'()-& or is it necessary to interpolate the %6 curves of "#% &'() to find a more appropriate combination of sample si/e, acceptance number and LQ
B0amples of things which may be amenable to LQ sampling include, but are not limited to, black specks on white tablets, smudged print on printed capsules, misaligned labels or nonfunctional defects in plastic components such as mould lines 6ritical defects such as non-sterile in7ection vials, rogue labels or components or incorrect print on labels cannot be controlled by any sampling scheme
1.5 2 In one particular e6ample7 a company is using !or many years a unique AQL 82.$,. 9o'ody :no&s ho& this AQL &as selected7 and the company &ould li:e to (usti!y this value retrospectively. ;o& &ould you proceed to provide a rationale sho&ing the pertinence o! the a!orementioned value< Is a retrospective data analysis possi'le< =hat :ind o! data sets &ould have in this case to 'e analy>ed< Any 7ustification would have to start with understanding the protection the e0isting scheme has been delivering, and in assessing this protection, an AQL value in isolation i s inadequate – the number of samples and the acceptance numbers are also needed as illustrated in diagram > below
oth the curves are for an AQL of :C(, but the sample si/e and permissible number of defects produce very different LQ values - D>; for the >*( sample and D*(; for the &: sample $he first stage of any analysis and 7ustification starts with this understanding of the level of protection which has been present $his then needs to be sub7ected to the analysis of outlined in section *C to confirm whether the attributes allegedly controlled by the sampling are appropriate for control by sampling and whether the actual level of protection delivered by the sample si/e and acceptance number meet the identified control need As regards retrospective data analysis, if the average re7ect rate over large a sample of batches, then using the sample si/e and acceptance number, it would be possible to use Poisson statistics to estimate the probable LQ achieved and determine whether it was possible to develop a rationale based, for e0ample, on the basis of process performance, customer complaints etc that this LQ delivered an acceptable outcome
1.# ) I thin: I got con!used &ith the di?erence 'et&een IS" 2#$%-1 and 2#$%-2. @he rst is intended !or lot-'y-lotB inspection and the second !or isolated lotB inspection. In my current understanding lot-'y-lotB is applica'le to a continuous production and the second one !or a discontinuous production at supplier – am I correct < Coes the continuous production re!er to a single production equipment including7 !or e6ample7 one single mold<
As " hope " was able to make clear in section *(, the difference between "#% &'()-* and &'()-& is not the type of production process it is applied to – it is the fact that "#% &'()-* focusses on the assumption that recipient wishes to composite individual batches into a pooled bulk, and you wish to manage the average properties of this pooled bulk as you add new batches "n most pharmaceutical applications where batches are being assessed on receipt, the focus is typically on ensuring that the properties of individual batches are unlikely to be worse than a stated percentage of defects of a type where a finite level of such defects is permissible – ie, an LQ based sampling scheme of the type specifically described in "#% &'()-& or using the more comprehensive set of %6 curves in "#% &'()-* to find an acceptance number.sample si/e combination whose LQ fits the need 1.% * Is it correct to indicate that a 0riticalB component is a component having at least one criticalB quality attri'ute out o! the various quality attri'utes it can have – &ith the di?erent criticality degrees< "m not sure of the properties implied by +different criticality degrees so " would answer the question in this way5 •
Proposition * - A +6ritical
•
Proposition & - #uch defects cannot be controlled by any form of sampling $hey can only be controlled by a manufacturing process designed to eliminate the possibility of such defects
•
Proposition > – the detection of an instance of the type of defect defined in proposition * affects not 7ust the batch in which it was found – it indicates the system defined in proposition & has failed and calls into question other batches from the sa me source – even if sampling has not disclosed any instances of the defect
Peter Murray – *E.).&:*( #c, 4PhA, 66hem, @F#6
