Methods for Determining a Limit of a Tolerance Interval, Method for Evaluating a Production Process and Corresponding Calculation Device

Abstract

Disclosed is a method for determining a limit, comprising: providing a plurality of sample values, wherein the sample values define a sample value distribution, the sample values being values of a technical parameter related to a sample, wherein the sample items are parts of drug delivery devices, wherein the sample items are of the same construction, and wherein the technical parameter is limited by at least one technical limit value, depending on the technical parameter and/or the sample values, choosing a probability distribution function, using the technical limit value to determine a cutoff value for the probability distribution function, specifying a probability content for the tolerance interval, and providing the limit of the tolerance interval for the technical parameter based on a transformed probability content, wherein said transformed probability content is based on the cutoff value and based on the specified probability content.

Claims

1-15. (canceled)

16. A method for determining a limit of a tolerance interval, the method comprising: providing a plurality of sample values, wherein the sample values fluctuate and define a sample value distribution, the sample values being values of a technical parameter related to sample items of a sample, wherein the sample items are parts of drug delivery devices, assemblies for drug delivery devices, or drug delivery devices, wherein the sample items are of the same construction, and wherein the technical parameter is limited by at least one technical limit value, depending on the technical parameter and/or the sample values, choosing a probability distribution function, using the technical limit value to determine a cutoff value for the probability distribution function, specifying a probability content for the tolerance interval, and providing the limit of the tolerance interval for the technical parameter based on a transformed probability content, wherein said transformed probability content is based on the cutoff value and based on the specified probability content.

17. The method according to claim 16, wherein the specified probability content refers to a proportion or percentage of an overall amount of production items, wherein the production items are parts of drug delivery devices, assemblies for drug delivery devices, or drug delivery devices of the same construction as the sample items, wherein the amount of production items has been produced or will be produced and is greater than the size of the sample from which the sample values have been taken by at least a factor of 10, of 100 or of 1000.

18. The method according to claim 16, wherein at least one descriptive parameter or at least two descriptive parameters of the sample values are calculated, wherein the at least one descriptive parameter is used or wherein the at least two descriptive parameters are used to calculate the cutoff value of the probability distribution function.

19. The method according to claim 16, wherein the technical parameter is one of the following drug delivery device parameters: dose accuracy, dial torque, dispense force, cap attachment force, cap removal force, needle shield removal force, injection time, activation force, blocking distance of a needle cover, needle extension, expelled volume, assembly force.

20. The method according to claim 16, wherein the at least one limit of the tolerance interval is an upper limit that is compared with an upper specification limit for the sample items in order to evaluate a production process, or wherein the at least one limit is a lower limit that is compared with a lower specification limit for the sample items in order to evaluate a production process.

21. The method according to claim 16, wherein the transformed probability content is calculated using the specified probability content and a value that is determined by or equal to the area of a truncated part of the probability distribution function or determined by or equal to the value of a cumulative distribution function of the probability distribution function considering the cutoff value, wherein the truncated part is within a range that starts at minus infinity or at a corresponding value and that ends at the cutoff value or within a range that begins at the cutoff value and that ends at plus infinity or at a corresponding value.

22. The method according to claim 21, wherein an actual probability content is calculated using the specified probability content, the cumulative distribution function of the probability distribution function, and the cutoff value.

23. The method according to claim 22, wherein the transformed probability content is calculated by calculating the sum of the specified probability content and of the difference between the specified probability content and the actual probability content.

24. The method according to claim 22, wherein the transformed probability content is calculated using the specified probability content and the actual probability content.

25. The method according to claim 24, wherein the transformed probability content is used to calculate a tolerance limit factor that is used to calculate the at least one limit of the tolerance interval by using also at least one of the descriptive parameters of the probability distribution function.

26. The method according to claim 25, wherein the tolerance limit factor is calculated for a one sided setting.

27. The method according to claim 26, wherein the tolerance limit factor is calculated according to:
K_hat=1/sqrt(n)t*_n−1;1-alpha (sqrt(n) zP), wherein n is a natural number indicating the sample size, t*_n−1; 1−alpha is the (1−α)-th quantile of a non-central t distribution with d degrees of freedom and non-centrality parameter delta, and zP is the P-th percentile of the standard normal distribution, wherein the transformed probability content is used for P, and sqrt( )is the square root function.

28. The method according to claim 16, wherein ISO 11608-1 Needle based injection systems for medical use—Requirements and test methods—Part 1 Needle based injection systems, 2014 or an earlier or later version thereof is met with regard to the calculation of the at least one limit of the tolerance interval.

29. A method for determining a limit of a tolerance interval, wherein a test is performed whether it is necessary to calculate a transformed probability content, and wherein the method according to claim 16 is performed if a test equation is fulfilled, and wherein the specified probability content is used for the calculation of the at least one limit of the tolerance interval but not the transformed probability content if the test equation is not fulfilled.

30. A method for evaluating a production process, comprising the steps according to claim 16, wherein the at least one limit of the tolerance interval is compared with a limit of a specification interval for production items that have the same construction as the sample items.

31. A computer program product having computer readable program code portions which when executed on a controller or on a processor carry out at least one of, an arbitrarily selected plurality of, or all of the following method steps: providing a plurality of sample values, wherein the sample values fluctuate and define a sample value distribution, the sample values being values of a technical parameter related to sample items of a sample, wherein the sample items are parts of drug delivery devices, assemblies for drug delivery devices, or drug delivery devices, wherein the sample items are of the same construction, and wherein the technical parameter is limited by at least one technical limit value, depending on the technical parameter and/or the sample values, choosing a probability distribution function, using the technical limit value to determine a cutoff value for the probability distribution function, specifying a probability content for the tolerance interval, and providing the limit of the tolerance interval for the technical parameter based on a transformed probability content, wherein said transformed probability content is based on the cutoff value and based on the specified probability content.

32. The computer program product of claim 31, wherein the transformed probability content is calculated using the specified probability content and a value that is determined by or equal to the area of a truncated part of the probability distribution function or determined by or equal to the value of a cumulative distribution function of the probability distribution function considering the cutoff value, wherein the truncated part is within a range that starts at minus infinity or at a corresponding value and that ends at the cutoff value or within a range that begins at the cutoff value and that ends at plus infinity or at a corresponding value.

33. The computer program product of claim 31, wherein at least one descriptive parameter or at least two descriptive parameters of the sample values are calculated, wherein the at least one descriptive parameter is used or wherein the at least two descriptive parameters are used to calculate the cutoff value of the probability distribution function.

34. The computer program product of claim 31, wherein the at least one limit of the tolerance interval is an upper limit that is compared with an upper specification limit for the sample items in order to evaluate a production process, or wherein the at least one limit is a lower limit that is compared with a lower specification limit for the sample items in order to evaluate a production process.

35. A calculation device, comprising: a processor configured to execute instructions, a memory that is configured to store the instructions and to store data that is used or generated during the execution of the instructions, and a computer program product according to claim 31 or a computer program product that calculates a transformed probability content based on a truncation of a probability distribution function that is used to calculate at least one limit of a tolerance interval.

Description

BRIEF DESCRIPTION OF FIGURES

[0102] For a more complete understanding of the presently disclosed concepts and the advantages thereof, reference is now made to the following description in conjunction with the accompanying drawings. The drawings are not drawn to scale. In the following drawings:

[0103] FIG. 1 illustrates a drug delivery device,

[0104] FIG. 2 illustrates a test setup device for drug delivery devices,

[0105] FIG. 3 illustrates empirical values measured with the test setup device,

[0106] FIG. 4 illustrates a calculation device (computer) for calculating transformed tolerance band limits,

[0107] FIG. 5 illustrates the plot of a density function of a given distribution, and p FIG. 6 illustrates the plot of the density function of a given distribution with left truncation.

DETAILED DESCRIPTION

[0108] FIG. 1 illustrates a drug delivery device 100 that may comprise a container retaining member 101. The drug delivery device 100 may comprise a main housing part 102 that houses the container retaining member 101 completely or partially and that comprises further parts of the drug delivery device 100. Alternatively the main housing part 102 may be connected to the container retaining member 101 but may not surround it and even may not surround a part of the container retaining member 101, see dashed line in FIG. 1.

[0109] Within the main housing part 102 the following may be arranged: [0110] a piston rod 104 that is adapted to move the piston of the container that is within container retaining member 101, [0111] a driving mechanism 106 for the piston rod 104. The driving mechanism 106 may comprise an energy storing element, for instance a spring, that is loaded manually or automatically, for instance during assembling of drug delivery device 100 or before each use, [0112] for instance at an proximal end P, an actuating element 108 that is used for the initiation of a movement of the piston rod 104 into the container retaining member 101, whereby the driving mechanism 106 is used. Alternatively, an autoinjector device may be used that is actuated by an axial movement of a movable needle shield. [0113] a cap 112 that may be attached to main housing part 102 or to another part of drug delivery device 100. Cap 112 may be an outer cap that may include a smaller inner cap that protects needle 110 directly.

[0114] Drug delivery device 100 may be a single use or a multiple use device. Actuating element 108 may be part of a trigger mechanism that is triggered from the distal end, for instance if drug delivery device 100 is an auto injecting device.

[0115] The drug may be dispensed from the container through a needle 110 or through a nozzle that is connectable and/or connected to the distal end D of drug delivery device 100. Needle 110 may be changed before each use or may be used several times.

[0116] The terms “drug” or “medicament” are used synonymously herein and describe a pharmaceutical formulation containing one or more active pharmaceutical ingredients or pharmaceutically acceptable salts or solvates thereof, and optionally a pharmaceutically acceptable carrier. An active pharmaceutical ingredient (“API”), in the broadest terms, is a chemical structure that has a biological effect on humans or animals. In pharmacology, a drug or medicament is used in the treatment, cure, prevention, or diagnosis of disease or used to otherwise enhance physical or mental well-being. A drug or medicament may be used for a limited duration, or on a regular basis for chronic disorders.

[0117] As described below, a drug or medicament can include at least one API, or combinations thereof, in various types of formulations, for the treatment of one or more diseases. Examples of API may include small molecules having a molecular weight of 500 Da or less; polypeptides, peptides and proteins (e.g., hormones, growth factors, antibodies, antibody fragments, and enzymes); carbohydrates and polysaccharides; and nucleic acids, double or single stranded DNA (including naked and cDNA), RNA, antisense nucleic acids such as antisense DNA and RNA, small interfering RNA (siRNA), ribozymes, genes, and oligonucleotides. Nucleic acids may be incorporated into molecular delivery systems such as vectors, plasmids, or liposomes. Mixtures of one or more drugs are also contemplated.

[0118] The drug or medicament may be contained in a primary package or “drug container” adapted for use with a drug delivery device. The drug container may be, e.g., a cartridge, syringe, reservoir, or other solid or flexible vessel configured to provide a suitable chamber for storage (e.g., short- or long-term storage) of one or more drugs. For example, in some instances, the chamber may be designed to store a drug for at least one day (e.g., 1 to at least 30 days). In some instances, the chamber may be designed to store a drug for about 1 month to about 2 years. Storage may occur at room temperature (e.g., about 20° C.), or refrigerated temperatures (e.g., from about −4° C. to about 4° C.). In some instances, the drug container may be or may include a dual-chamber cartridge configured to store two or more components of the pharmaceutical formulation to-be-administered (e.g., an API and a diluent, or two different drugs) separately, one in each chamber. In such instances, the two chambers of the dual-chamber cartridge may be configured to allow mixing between the two or more components prior to and/or during dispensing into the human or animal body. For example, the two chambers may be configured such that they are in fluid communication with each other (e.g., by way of a conduit between the two chambers) and allow mixing of the two components when desired by a user prior to dispensing. Alternatively or in addition, the two chambers may be configured to allow mixing as the components are being dispensed into the human or animal body.

[0119] The drugs or medicaments contained in the drug delivery devices as described herein can be used for the treatment and/or prophylaxis of many different types of medical disorders. Examples of disorders include, e.g., diabetes mellitus or complications associated with diabetes mellitus such as diabetic retinopathy, thromboembolism disorders such as deep vein or pulmonary thromboembolism. Further examples of disorders are acute coronary syndrome (ACS), angina, myocardial infarction, cancer, macular degeneration, inflammation, hay fever, atherosclerosis and/or rheumatoid arthritis. Examples of APIs and drugs are those as described in handbooks such as Rote Liste 2014, for example, without limitation, main groups 12 (anti-diabetic drugs) or 86 (oncology drugs), and Merck Index, 15th edition.

[0120] Examples of APIs for the treatment and/or prophylaxis of type 1 or type 2 diabetes mellitus or complications associated with type 1 or type 2 diabetes mellitus include an insulin, e.g., human insulin, or a human insulin analogue or derivative, a glucagon-like peptide (GLP-1), GLP-1 analogues or GLP-1 receptor agonists, or an analogue or derivative thereof, a dipeptidyl peptidase-4 (DPP4) inhibitor, or a pharmaceutically acceptable salt or solvate thereof, or any mixture thereof. As used herein, the terms “analogue” and “derivative” refers to a polypeptide which has a molecular structure which formally can be derived from the structure of a naturally occurring peptide, for example that of human insulin, by deleting and/or exchanging at least one amino acid residue occurring in the naturally occurring peptide and/or by adding at least one amino acid residue. The added and/or exchanged amino acid residue can either be codable amino acid residues or other naturally occurring residues or purely synthetic amino acid residues. Insulin analogues are also referred to as “insulin receptor ligands”. In particular, the term “derivative” refers to a polypeptide which has a molecular structure which formally can be derived from the structure of a naturally occurring peptide, for example that of human insulin, in which one or more organic substituent (e.g. a fatty acid) is bound to one or more of the amino acids. Optionally, one or more amino acids occurring in the naturally occurring peptide may have been deleted and/or replaced by other amino acids, including non-codeable amino acids, or amino acids, including non-codeable, have been added to the naturally occurring peptide.

[0121] Examples of insulin analogues are Gly(A21), Arg(B31), Arg(B32) human insulin (insulin glargine); Lys(B3), Glu(B29) human insulin (insulin glulisine); Lys(B28), Pro(B29) human insulin (insulin lispro); Asp(B28) human insulin (insulin aspart); human insulin, wherein proline in position B28 is replaced by Asp, Lys, Leu, Val or Ala and wherein in position B29 Lys may be replaced by Pro; Ala(B26) human insulin; Des(B28-B30) human insulin; Des(B27) human insulin and Des(B30) human insulin.

[0122] Examples of insulin derivatives are, for example, B29-N-myristoyl-des(B30) human insulin, Lys(B29) (N-tetradecanoyl)-des(B30) human insulin (insulin detemir, Levemir®); B29-N-palmitoyl-des(B30) human insulin; B29-N-myristoyl human insulin; B29-N-palmitoyl human insulin; B28-N-myristoyl LysB28ProB29 human insulin; B28-N-palmitoyl-LysB28ProB29 human insulin; B30-N-myristoyl-ThrB29LysB30 human insulin; B30-N-palmitoyl-ThrB29LysB30 human insulin; B29-N-(N-palmitoyl-gamma-glutamyl)-des(B30) human insulin, B29-N-omega-carboxypentadecanoyl-gamma-L-glutamyl-des(B30) human insulin (insulin degludec, Tresiba®); B29-N-(N-lithocholyl-gamma-glutamyl)-des(B30) human insulin; B29-N-(ω-carboxyheptadecanoyl)-des(B30) human insulin and B29-N-(ω-carboxyheptadecanoyl) human insulin.

[0123] Examples of GLP-1, GLP-1 analogues and GLP-1 receptor agonists are, for example, Lixisenatide (Lyxumia®), Exenatide (Exendin-4, Byetta®, Bydureon®, a 39 amino acid peptide which is produced by the salivary glands of the Gila monster), Liraglutide (Victoza®), Semaglutide, Taspoglutide, Albiglutide (Syncria®), Dulaglutide (Trulicity®), rExendin-4, CJC-1134-PC, PB-1023, TTP-054, Langlenatide/HM-11260C, CM-3, GLP-1 Eligen, ORMD-0901, NN-9924, NN-9926, NN-9927, Nodexen, Viador-GLP-1, CVX-096, ZYOG-1, ZYD-1, GSK-2374697, DA-3091, MAR-701, MAR709, ZP-2929, ZP-3022, TT-401, BHM-034. MOD-6030, CAM-2036, DA-15864, ARI-2651, ARI-2255, Exenatide-XTEN and Glucagon-Xten.

[0124] An examples of an oligonucleotide is, for example: mipomersen sodium (Kynamro®), a cholesterol-reducing antisense therapeutic for the treatment of familial hypercholesterolemia.

[0125] Examples of DPP4 inhibitors are Vildagliptin, Sitagliptin, Denagliptin, Saxagliptin, Berberine.

[0126] Examples of hormones include hypophysis hormones or hypothalamus hormones or regulatory active peptides and their antagonists, such as Gonadotropine (Follitropin, Lutropin, Choriongonadotropin, Menotropin), Somatropine (Somatropin), Desmopressin, Terlipressin, Gonadorelin, Triptorelin, Leuprorelin, Buserelin, Nafarelin, and Goserelin.

[0127] Examples of polysaccharides include a glucosaminoglycane, a hyaluronic acid, a heparin, a low molecular weight heparin or an ultra-low molecular weight heparin or a derivative thereof, or a sulphated polysaccharide, e.g. a poly-sulphated form of the above-mentioned polysaccharides, and/or a pharmaceutically acceptable salt thereof. An example of a pharmaceutically acceptable salt of a poly-sulphated low molecular weight heparin is enoxaparin sodium. An example of a hyaluronic acid derivative is Hylan G-F 20 (Synvisc®), a sodium hyaluronate.

[0128] The term “antibody”, as used herein, refers to an immunoglobulin molecule or an antigen-binding portion thereof. Examples of antigen-binding portions of immunoglobulin molecules include F(ab) and F(ab′)2 fragments, which retain the ability to bind antigen. The antibody can be polyclonal, monoclonal, recombinant, chimeric, de-immunized or humanized, fully human, non-human, (e.g., murine), or single chain antibody. In some embodiments, the antibody has effector function and can fix complement. In some embodiments, the antibody has reduced or no ability to bind an Fc receptor. For example, the antibody can be an isotype or subtype, an antibody fragment or mutant, which does not support binding to an Fc receptor, e.g., it has a mutagenized or deleted Fc receptor binding region. The term antibody also includes an antigen-binding molecule based on tetravalent bispecific tandem immunoglobulins (TBTI) and/or a dual variable region antibody-like binding protein having cross-over binding region orientation (CODV).

[0129] The terms “fragment” or “antibody fragment” refer to a polypeptide derived from an antibody polypeptide molecule (e.g., an antibody heavy and/or light chain polypeptide) that does not comprise a full-length antibody polypeptide, but that still comprises at least a portion of a full-length antibody polypeptide that is capable of binding to an antigen. Antibody fragments can comprise a cleaved portion of a full length antibody polypeptide, although the term is not limited to such cleaved fragments. Antibody fragments that are useful in the present invention include, for example, Fab fragments, F(ab′)2 fragments, scFv (single-chain Fv) fragments, linear antibodies, monospecific or multispecific antibody fragments such as bispecific, trispecific, tetraspecific and multispecific antibodies (e.g., diabodies, triabodies, tetrabodies), monovalent or multivalent antibody fragments such as bivalent, trivalent, tetravalent and multivalent antibodies, minibodies, chelating recombinant antibodies, tribodies or bibodies, intrabodies, nanobodies, small modular immunopharmaceuticals (SMIP), binding-domain immunoglobulin fusion proteins, camelized antibodies, and VHH containing antibodies. Additional examples of antigen-binding antibody fragments are known in the art.

[0130] The terms “Complementarity-determining region” or “CDR” refer to short polypeptide sequences within the variable region of both heavy and light chain polypeptides that are primarily responsible for mediating specific antigen recognition. The term “framework region” refers to amino acid sequences within the variable region of both heavy and light chain polypeptides that are not CDR sequences, and are primarily responsible for maintaining correct positioning of the CDR sequences to permit antigen binding. Although the framework regions themselves typically do not directly participate in antigen binding, as is known in the art, certain residues within the framework regions of certain antibodies can directly participate in antigen binding or can affect the ability of one or more amino acids in CDRs to interact with antigen.

[0131] Examples of antibodies are anti PCSK-9 mAb (e.g., Alirocumab), anti IL-6 mAb (e.g., Sarilumab), and anti IL-4 mAb (e.g., Dupilumab).

[0132] Pharmaceutically acceptable salts of any API described herein are also contemplated for use in a drug or medicament in a drug delivery device. Pharmaceutically acceptable salts are for example acid addition salts and basic salts.

[0133] Those of skill in the art will understand that modifications (additions and/or removals) of various components of the APIs, formulations, apparatuses, methods, systems and embodiments described herein may be made without departing from the full scope and spirit of the present invention, which encompass such modifications and any and all equivalents thereof.

[0134] FIG. 2 illustrates a test setup device 200 for testing at least one parameter of drug delivery devices, especially of drug delivery devices 100. Test setup device 200 may comprise: [0135] a mounting arrangement 201 that allows vertical movement of some parts of test setup device 200, [0136] a motor M that generates a torque for the movement of the movable parts, [0137] an upper clamp device 202 that may clamp the distal end or the proximal end of a device under test, [0138] a lower clamp device 204 that may clamp the other end of the device under test, [0139] a control device 206 that may control the movement that is generated by motor M, and [0140] a measurement reporting device 208 that is connected for instance to a force sensor.

[0141] Other parts of test setup device 200 are not shown, for instance an optional scale, an electrical power supply unit, etc.

[0142] Upper clamp device 202 and/or lower clamping device 204 may be movable relative to each other in order to generate or exert a force that is applied onto the device under test (DUT).

[0143] Test setup device 200 may be used to measure forces that are relevant for drug delivery devices 100 or for other devices. In the following, it is assumed that test setup device 200 is used to measure the force of cap attachment of cap 112, see item d) that is mentioned within the introduction part of the description. The drug delivery devices 100 under test may be devices of device type U300max that is produced by the applicant of this application. However, other device types may also be tested.

[0144] A completely assembled drug delivery device 100 may be clamped into test setup device 200. Cap 112 may be held by lower clamp device 204. The proximal end P of drug delivery device 100 may be held by upper clamp device 202. However, it is also possible that cap 112 is hold in upper clamp device 204 and that the proximal end of drug delivery device 100 is held in lower clamp device 204.

[0145] It is assumed that the cap attachment force of 19 drug delivery devices 100 is measured. These drug delivery devices 100 may be prototypes or part of a small series production process. Alternatively the devices may be taken out of a large series production process. One example of test measurements is shown in FIG. 3.

[0146] FIG. 3 illustrates empirical values measured with test setup device 200 for the cap attachment force of 19 drug delivery devices 100. A horizontal x-axis 300 is used to classify the sampled values x of the cap attachment force of cap 112 into classes that have a width of for instance 1 N (Newton). There may be classes with class ranges of 0.5 N to 1.5 N (class 1), 1.5 N to 2.5 N, of 2.5 N to 3.5 N, of 3.5 to 4.5 N etc. The sample values are located within 7 classes: [0147] class 2 from 1.5 N to 2.5 N: 4 sample values, [0148] class 3 from 2.5 N to 3.5 N: 2 sample values, [0149] class 4 from 3.5 N to 4.5 N: 3 sample values, [0150] class 5 from 4.5 N to 5.5 N: 5 sample values, [0151] class 6 from 5.5 N to 6.5 N: 1 sample value, [0152] class 7 from 6.5 N to 7.5 N: 2 sample values, [0153] class 8 from 7.5 N to 8.5 N: 3 sample values.

[0154] A vertical y-axis 302 shows the number of samples within a respective class. Columns 304 represent the frequency of force values of cap attachment force. The mean value x is determined and in the example the mean value x may have a value of about 6 N. Furthermore, the standard deviation s is calculated for all of the 19 sample values x.

[0155] Based on the mean value x and on the standard deviation s a normal probability distribution function 306 (density function, PDF) may be calculated and mapped over the histogram that shows the classes 2 to 8.

[0156] There is a truncation threshold 308, i.e., a technical limit TL, under which the cap attachment force may not occur. The value of the threshold 308 is 0 N.

[0157] FIG. 3 shows an upper tolerance band limit 310, UTBL for the case in which a truncation due to the technical limit TL is not considered. Furthermore, a calculated lower tolerance band limit 312, LTBL is shown for the case in which a truncation due to the technical limit TL is not considered. Upper tolerance band limit 310, UTBL and lower tolerance band limit 312, LTBL define a tolerance interval TI. Lower tolerance band limit LTBL is located left from technical limit 308, i.e., it has a value that is smaller than the technical limit 308.

[0158] The histogram that is shown in FIG. 3 may be an accurate representation of the distribution of numerical data. It may be an estimate of the probability distribution of a continuous variable. The probability distribution function 306 may be truncated in order to consider the technical limit 308 for the calculation of the upper tolerance band limit 310. It is supposed that even if the truncation is considered the lower tolerance band limit LTBL will not move over the technical limit 308. Therefore, the tolerance interval TI is a one sided tolerance band or tolerance interval TI that has only an upper tolerance band limit UTBL. For example, the tolerance interval TI is calculated as one-sided. However, when the distribution is truncated at ξ.sub.L the value of ξ.sub.L can be interpreted as a lower tolerance band limit.

[0159] In order to consider the technical limit 308 for the calculation of upper tolerance band limit UTBL a cutoff value ξ.sub.L has to be determined. This can be done graphically or by simple arithmetic calculations. In the example, a further coordinate system may be used that has an x-axis 300*. The x-value zero is where the maximum of the probability distribution function 306 is located, i.e., this corresponds to the location of mean value x on x-axis 300. The value of ξ.sub.L corresponds to the negative of the mean value x.

[0160] Further optional steps may be necessary, for instance normalization of probability distribution function 306 and/or of value before further calculations are made or standard statistical software packages or modified standard statistical software packages may be used. The purpose of the normalization is to make the area that is contained below probability distribution function 306 to have the value 1. This may require a compression or an expansion in x-direction and/or a scaling in y-direction. These steps may be done automatically by performing a corresponding script for a statistical software package. FIG. 6 shows a probability distribution function 602 that is truncated. The steps that are performed to calculate a transformed upper tolerance band limit UTBL* considering the technical limit 308 are described with regard to FIG. 6 below.

[0161] FIG. 4 illustrates a calculation device 400 (computer) for calculating transformed tolerance band limits. Calculating device 400 may comprise: [0162] a processor (Pr) configured to execute instructions, especially for performing the disclosed calculations, [0163] a memory (Mem) that is configured to store the instructions and to store data that is used or generated during the execution of the instructions, [0164] an optional input device (In), for instance a keyboard, that is configured to input data that will be stored in the memory (Mem), especially to enter the sample values x, [0165] an optional output device (Out), for instance a display device, that is configured to output data that is generated during the execution of the instructions, and [0166] a computer program product that calculates a transformed probability content () based on a truncation of a probability distribution function (306, 602) that is used to calculate at least one limit (UTBL, LTBL) of a tolerance interval (TI), especially transformed upper or lower tolerance band limit UTBL* or LTBL*.

[0167] There may be a connection/bus 410 between processor Pr and memory Mem. Further units of calculation unit 400 are not shown but are known to the person skilled in the art, for instance a power supply unit, an optional internet connection, etc. Alternatively, a server solution may be used that uses calculation power and/or memory space available on the internet supplied by other service providers or on an intranet of a company.

[0168] FIG. 5 illustrates the plot of a density function 502 of a given distribution with upper tolerance band limit UTBL and upper specification limit USL. X-axis 500 shows the value of sample values x. A y-axis is not shown but is used for displaying the frequency of the respective sample values x. In the example that is shown in FIG. 5 a normal probability distribution function 502 (density function) is used, i.e., a bell curve or a Gauss curve. The area below probability distribution function 502 is one. This is illustrated by a reference to the cumulate distribution function F(x, p), CDF of the normal probability distribution function 502, PDF. FIG. 5 shows an upper tolerance band limit 504, UTBL. A truncation is not considered for the calculation of upper tolerance band limit 504, UTBL using a confidence level of 1−α, a probability content or proportion pc and the vector p that contains the descriptive parameters of normal probability distribution function 502. This calculation is known to the person skilled in the art. Upper tolerance band limit 504 is below upper specification limit 506, USL. Thus, a decision could be made to start the production process of drug delivery devices 100. However, this decision may be wrong because a technical limit 308 has not been considered appropriately.

[0169] FIG. 6 illustrates the plot of the probability distribution function (density function) 602, for instance 306, of a given distribution with left truncation at The upper tolerance band limit UTBL is transformed to a transformed upper tolerance band limit UTBL* if a transformed probability content is used for the calculations. In the example transformed probability content is still smaller than upper specification limit USL. However, the distance between transformed upper tolerance band limit UTBL* and upper specification limit is reduced due to a shift of the transformed upper tolerance band limit UTBL* to the right if compared with upper tolerance band limit UTBL of FIG. 5, see delta 612. This is due to the consideration of the left truncation ξ.sub.L. The decision to produce the drug delivery devices 100 is more reliable compared to the decision that is made based on FIG. 5.

[0170] FIG. 6 shows an x-axis 600 for the sample values x. A y-axis is not shown but relates to the frequency of the respective sample values. Normal probability distribution function 602 (density function), PDF approximates the histogram of a sample of drug delivery devices 100 a mentioned in the description of FIG. 3 or of other devices. A truncation threshold 604 corresponds to a technical limit TL, for instance to value zero, see also FIG. 3. An area 606 corresponds to a value of cumulative distribution function F at cutoff value ξ.sub.L or truncation value ξ.sub.L. An area 608 corresponds to the remainder of cumulative distribution function F if the truncated area 606 is subtracted, i.e., to the value 1−F(ξ.sub.L, p).

[0171] Line 610 shows the location of a transformed upper tolerance band limit 610, UTBL* for the case in which a truncation of the probability distribution function 602 by a technical limit 308, i.e., at cutoff value ξ.sub.L is considered. A delta value 612 is shown especially large to make the displacement visible. Note that the displacement may also take place in the other direction, e.g., UTBL* may be smaller than UTBL, depending on the value of the cutoff value ξ.sub.L. Line 614 shows an example of upper specification limit USL.

[0172] The transformed upper tolerance band limit 610, UTBL* is calculated based on a confidence level 1−α, a transformed probability content and the descriptive parameter vector of probability density function 602. Transformed probability content is calculated according to formulas (1) and (2) that are also described below. An intermediate step for the calculation of transformed upper tolerance band limit 610, UTBL* is the calculation of a transformed tolerance limit factor {circumflex over (k)} according to formula (5) that is described below.

[0173] The transformed upper tolerance band limit UTBL* may be calculated according to:

UTBL*=x+{circumflex over (k)}*s,

where x is the mean value of sample values x and s is the standard deviation of the sample values s. The calculation of the mean value and of the standard deviation is known from basic statistics books.

[0174] Corresponding calculations may be made if there is a right side truncation of a probability distribution function. In this case, a transformed lower tolerance band limit LTBL* may be calculated according to:

LTBL*=x+{circumflex over (k)}*s,

[0175] where x is the mean value of sample values x and s is the standard deviation of the sample values s. The calculation of the mean value and of the standard deviation is known from basic statistics books.

[0176] Spoken with other words and in addition to the description of FIGS. 1 to 6 above, in statistics, a truncated distribution is a conditional distribution that results from restricting the domain of some other probability distribution. Truncated distributions arise in practical statistics in cases, where for some reason, the range of values is limited to values which lie above or below a given threshold or within a specified range. For example, if the force of removing the cap 112 of a device 100 is measured, this would be subject to truncation because the force can only be positive.

[0177] Thus, several device-related features have to be evaluated, which are subject to truncation.

[0178] For example the expelled volume of a pen device 100 is always non-negative. Thus, the dose accuracy distribution is left-truncated at threshold ξ.sub.L0. In practice the truncation of features can often be neglected as actually considered values are sufficiently far away from the according truncation threshold, such that the influence on derived statistics is not significant. However in some cases a significance may arise.

[0179] It may be defined that in verification testing a statistical tolerance interval TI shall be calculated according to ISO 16269-6 (statistical Interpretation of data—Part 6: Determination of statistical tolerance intervals, 2014 (E), or an earlier or later version thereof) and compared to the specification range S, where truncation due to physical limits may be treated as one limit of the specification range. The acceptance criterion is that the tolerance interval TI is part or is identical to the specification range S. A plot of the density function of the normal distribution or of another given distribution with upper tolerance band limit UTBL and upper specification limit USL (Upper Specification Limit) is diagrammatically shown in FIG. 5. In that case we have UTBL USL, i.e., tolerance interval TI is part or is identical to specification limit S. Thus the acceptance criterion is met.

[0180] In certain cases it may occur that one tolerance band limit may exceed the according physical limit, though it is known that the physical limit can never be exceeded in practice. In that case that violation may be rated as being practically not existent. However, there may be an impact on the other side of the tolerance band and this impact may be treated adequately. It is noted that this case is different from the case that is named as censoring, i.e., in which values below or above a threshold cannot be observed due to technical or physical limits or properties of the measurement system although these values exist practically and theoretically. The proposed methods should not be applied to “censoring” because there may be other calculations applied.

[0181] The following formulas are given to ease the understanding of the invention. However, the invention should not be bound to this theory or to another theory. Values of a given feature may be statistically distributed with a given density function f or probability distribution function PDF that may be a mapping of real numbers, e.g., sample values x, to the interval of 0 to 1, especially comprising also the limits of the interval. This may be expressed as: f(⋅; p) : R->[0; 1] with parameter vector p element of R.sup.n, where n is the dimension of the parameter space. Typically we have n=2 for distributions used for instance for medical devices 100 or other types of devices. For example, in case of the normal distribution the parameter vector p is p=[μ; σ{circumflex over ( )}2].sup.T, where “μ” is the expected value (mean value) and σ{circumflex over ( )}2, i.e., the square of the standard deviation σ, is the variance σ{circumflex over ( )}2. T means the transposed of the vector.

[0182] The corresponding distribution function or cumulative distribution function CDF is:

f(⋅; p):R->[0; 1],

where “⋅” is a place holder,

[0183] with:

F(a, p)=∫.sub.−∞.sup.af(x, p)dx,

wherein “a” is a special value of a device feature.

[0184] Furthermore, it may be valid:

∫.sub.Rf(⋅,p)=1,

if integrated over the whole definition ranges of R.sup.n, i.e. the n dimensional space of real numbers, wherein n is a natural number greater or equal 1.

[0185] According to the standard ISO 16269-6:2014(E), introduction, first sentence: “A statistical tolerance interval is an estimated interval, based on a sample, which can be asserted with confidence level 1−α, for example 0.95, to contain at least a specified proportion p of the items in the population.” This definition of the statistical tolerance interval TI is also used in this application. The specified portion p is named as probability content pc in this application.

[0186] The standard ISO 16269-6:2014(E) discloses possibilities to calculate tolerance intervals TI, especially lower and upper tolerance interval limits. However, truncation is not considered.

[0187] Without loss of generality, in the following, the case of a left-truncation is considered, see FIG. 6 that illustrates a plot of the density of a given distribution function 602 with left truncation at ξ.sub.L. This means that a ξ.sub.L exists with ξ.sub.L element of R such that the probability content of F(ξ.sub.L,p)—this is the portion left to the truncation—does practically not exist. The upper tolerance band limit UTBL is transformed according to a transformed probability content to a transformed upper tolerance band limit UTBL*. Furthermore, an upper specification limit USL is shown.

[0188] This means that there exists a element of R such that a probability content pc of F(ξ.sub.L; p), i.e., the portion 606 left to the truncation ξ.sub.L, does practically not exist because there may be a technical limit 308 for the variable x under investigation as stated above.

[0189] The upper tolerance band limit UTBL indicates that a certain probability content pc lies within the according tolerance interval TI. In the case in which the portion F(ξ.sub.L; p) of practically not relevant probability content pc is however significant, the upper tolerance band limit UTBL may need some transformation to reflect that truncation of the cumulative density function CDF.

[0190] As described above, the required probability content pc may need to be transformed (=T.sub.L(pc)), as diagrammatically shown in FIG. 6, wherein T.sub.L is a transformation function that is valid for left truncation.

[0191] In a first step we may calculate an actual probability content pc.sub.act or an actual probability content pc.sub.act which is covered by the tolerance interval TI, e.g., it may be corrected by subtraction of the according portion 606 due to the truncation More specifically the actual probability content pc.sub.act may be computed by a linear transformation of the desired probability content. The truncated portion 606, see left part in FIG. 6, of the distribution function 602 may be subtracted from the desired probability content pc. A normalization may be made by dividing by the remaining portion 608 of the distribution, see right part in FIG. 6.

pc.sub.act=(pc−F(ξ.sub.L; p))/(1−F(ξ.sub.L; p))   formula (1)

However, other formulas may also be used to determine the actual probability content pc.sub.act.

[0192] In a second step the difference between the specified/ required probability content pc and the actual probability content pc.sub.act may be added to the required probability content pc in order to get the transformed probability content :

[00001]$\begin{array}{cc}=T_L\left(\mathrm{pc}\right)=\mathrm{pc}+\left(pc-p{c}_{act}\right)& \mathrm{formula}\left(1b\right)\end{array}$

[0193] However, other formulas may also be used as transform function T.sub.L(pc). The following holds with the transform function T.sub.L(pc)=pc+(pc−pc.sub.act) using formula (1):

[00002]$\begin{array}{cc}=2\mathrm{pc}-\left(pc-F\left({\xi }_L,p\right)\right)/\left(1-F\left({\xi }_L,p\right)\right)=\left(2-\frac{1}{1-F\left({\xi }_L,p\right)}\right)*pc+\frac{F\left({\xi }_L,p\right)}{1-F\left({\xi }_L,p\right)}=(2-1/{\left(1-F\left({\xi }_L,p\right)\right)}^{*}pc+F\left({\xi }_L,p\right)/\left(1-F\left({\xi }_L,p\right)\right)& \mathrm{formula}\left(2\right)\end{array}$

[0194] Thus, the transformation of the desired probability content pc may be a linear function of the desired probability content pc and the truncated portion 606 of the distribution 602. The area of the truncated portion 606 may depend on the truncation threshold ξ.sub.L in a non-linear way.

[0195] In case of right truncation at ξ.sub.R element of R.sup.n the according transformation of the probability content is:

[00003]$\begin{array}{cc}=\left(2-\frac{1}{1-F\left({\xi }_R,p\right)}\right)*pc+\frac{1-F\left({\xi }_R,p\right)}{F\left({\xi }_R,p\right)}& \mathrm{formula}\left(3\right)\end{array}$$\begin{array}{cc}=T_R\left(pc\right)=pc(2-1/\left(1-F\left({\xi }_R,p\right)\right)+\left(1-F\left({\xi }_R,p\right)\right)/F\left({\xi }_R,p\right)& \mathrm{formula}\left(3\right)\end{array}$

[0196] Derivation of the formula for right truncation is a further term conversion and directly analogous to the case of left truncation, see formula for p.sub.act and right truncation in the introduction part of the description.

[0197] Example: Let's assume, a force feature of a pen device 100 is tested and the distribution of the sample values x is known to be normally distributed. For that feature a USL of 40 N (Newton) is defined. It is known that the force cannot be below ξ.sub.L=0 N due to physical properties. The acceptance criterion for testing may be that at least a probability content of pc=97.5% lies within the specification limits at a confidence level of 1−α=95%. A test of 20 samples results in a mean value of x=9.13 N and an estimated standard deviation of s=5.97 N. A two-sided tolerance interval without considering the truncation is calculated by x+/−k*s for getting the tolerance band limits, where k=3.154 is the tolerance limit factor for the given conditions. This leads to a tolerance interval of TI=[−9.70; 27.96] N. In that case the lower tolerance band limit LTBL is below the truncation threshold ξ.sub.L.

[0198] In order to treat that truncation issue correctly, the approach derived above may be used. Using formula (2) the required probability content is transformed to:

[00004]$\begin{array}{cc}=(2-1/\left(1-F\left({\xi }_L,p\right)\right)\mathrm{pc}+F\left({\xi }_L,p\right)/\left(1-F\left({\xi }_L,p\right)\right)=(2-1/\left(1-F\left({0;\left[9.13;5.972\right]}^T\right)\right)0\text{.975}+F\left({\left[9.13;5.972\right]}^T\right)/\left(1-F\left({\left[9.13;5.972\right]}^T\right)\right),\mathrm{with}F\left({0;\left[9.13;5.972\right]}^T\right)=\frac{1}{5.97*\sqrt{2*\mathrm{PI}}}{\int }_{-\infty }^0{e}^{-\frac{1}{2}{\left(\frac{x-9.13}{5.97}\right)}^2}\mathrm{dx}(1/(5.97*\mathrm{sqrt}\left(2*\mathrm{PI}\right)*\mathrm{integral}\mathrm{from}-\mathrm{infinity}\left(\infty \right)\mathrm{to}0\mathrm{over}\exp \left(-1/2*{\left(\left(x-9.13\right)/\left(5.97\right)\right)}^{.Math.}2\mathrm{dx}\right)=0.06& \mathrm{formula}\left(4\right)\end{array}$

[0199] wherein PI=3, 24 . . . , sqrt( )is the square root function and exp is the exponential function.

[0200] And furthermore using formula (2):

[00005]$=0.975*(2-1/\left(1-0.06\right)+0.06/\left(1-0.06\right)=0.977$

[0201] In a third step the according tolerance limit factor {circumflex over (k)} for is determined, i.e. {circumflex over (k)}=2.847. Standard statistical software packages may be used to calculate {circumflex over (k)}. However, transformed probability content has to be used instead of specified probability content pc that is suggested by standard statistical software packages.

[0202] In a fourth step the resulting tolerance interval is calculated, i.e. I=[0; 26.12] N. The upper limit is also below the upper specification limit USL of 40 N. Thus, the acceptance criterion is met.

[0203] {circumflex over (k)} may be calculated using software packages available on the market. It is possible to use the software R, especially the package tolerance intervals TI, see “An R package for Estimating Tolerance Intervals”, Derek S. Young, Journal of Statistical Software, August 2010, Volume 36, Issue 5, page 1 to 39, especially section 4.8. (Univariate) normal tolerance intervals. The relevant function may be:

[0204] K.factor(n, f=NULL, alpha=0.05, P=0.99, side=1, method=c(“HE”, “HE2”, “WBE”, “ELL”, “KM”, “EXACT”, “OCT”), m 32 50), However may be used instead pc for the value P of the function. A one side setting may be used, i.e. side=1.

[0205] The article of Derek S. Young mentions that there is an exact solution for k in the case of a one sided setting:

k=1/sqrt(n)t*.sub.n−1;1−alpha(sqrt(n)zp)   formula (5)

such that n is the sample size, t*.sub.n−1;1−alpha(delta) is the (1−α)-th quantile of a non-central t distribution with d degrees of freedom, e.g., n−1, and non-centrality parameter delta, and zp is the P-th percentile of the standard normal distribution. Alternatively, the exact solution may also be calculated by numerical integration. However, the numerical effort, i.e., processor power, may be much larger compared to the usage of the analytical exact solution.

[0206] The significance of the truncation may be evaluated for instance according to the following rule of Barbara Bredner in “Prozessfaehigkeit bewerten, Kennzahlen fuer nomalverteilte und nicht-normalverteilte Merkmale”, Jun. 11, 2014, http://www.drsteuer.de/vorlagen/Prozessfaehigkeit_bewerten_November_14.pdf (visited May 16, 2019) and “Prozessfaehigkeit bei technisch begrenzten Merkmalen, Faehigkeitskennzahlen und Berechnungsmethoden”, Jan. 15, 2015, URL: https://www.bb-sbl.de/wp-content/uploads/2018/08/BB-SBL-Prozessf%C3%A4higkeit-bewerten-V13-2015-01-15.pdf (visited May 20, 2013). It is proposed that a truncation is relevant in case |x−ξ| smaller or equal 3 s, where x is the samples mean, ξ is the truncation threshold ξ.sub.L or ξ.sub.R and “s” is the samples estimated standard deviation.

[0207] A further step may be the analysis of process capability for truncated distributions which is described for instance in Barbara Bredner, “Prozessfaehigkeit bei technisch begrenzten Merkmalen, Faehigkeitskennzahlen and Berechnungsmethoden”, Jan. 15, 2015, URL: https://www.bb-sbl.de/wp-content/uploads/2018/08/BB-SBL-Prozessf%C3%A4higkeit-bewerten-V13-2015-01-15.pdf (visited May 20, 2019).

[0208] In summary, a transformation of the required probability content in case of a truncated distribution is disclosed. In case of left-truncation the probability content should be transformed according to formula (2) or a similar/corresponding formula. In case of right-truncation the probability content should be transformed according to formula (3) or a similar/corresponding formula.

[0209] It is also possible to transfer the given technical teaching to other distributions than normal distributions, for instance to log normal, Weibull, Gumbel, Fréchet distribution functions, etc.

[0210] Although embodiments of the present disclosure and their advantages have been described in detail, it should be understood that various changes, substitutions and alterations can be made therein without departing from the spirit and scope of the disclosure as defined by the appended claims. For example, it will be readily understood by those skilled in the art that many of the features, functions, processes and methods described herein may be varied while remaining within the scope of the present disclosure. Moreover, the scope of the present application is not intended to be limited to the particular embodiments of the system, process, manufacture, method or steps described in the present disclosure. As one of ordinary skill in the art will readily appreciate from the disclosure of the present disclosure, systems, processes, manufacture, methods or steps presently existing or to be developed later that perform substantially the same function or achieve substantially the same result as the corresponding embodiments described herein may be utilized according to the present disclosure. Accordingly, the appended claims are intended to include within their scope such systems, processes, methods or steps. The embodiments mentioned in the first part of the description may be combined with each other. The embodiments of the description of FIGS. 1 to 6 may also be combined with each other. Further, it is possible to combine embodiments mentioned in the first part of the description with examples of the second part of the description which relates to FIGS. 1 to 6.

LIST OF REFERENCE NUMERALS

[0211] 100 drug delivery device

[0212] 101 container retaining member

[0213] 102 main housing part

[0214] 104 piston rod

[0215] 106 driving mechanism

[0216] 108 actuating element

[0217] 110 needle

[0218] 112 cap

[0219] 200 test setup device

[0220] 201 mounting arrangement

[0221] 202 upper clamp device

[0222] 204 lower clamp device

[0223] 206 control device

[0224] 208 measurement reporting device

[0225] 300 x-axis

[0226] 302 y-axis

[0227] 304 column representing one class of force values

[0228] 306 normal probability distribution function

[0229] 308 truncation threshold

[0230] 310 upper tolerance band limit UTBL

[0231] 312 calculated lower tolerance band limit LTBL

[0232] 400 calculating device

[0233] 410 connection

[0234] Pr processor

[0235] Mem memory

[0236] In input device

[0237] Out output device

[0238] 500 x-axis

[0239] 502 normal probability distribution function

[0240] 504 upper tolerance band limit UTBL

[0241] 506 upper specification limit USL

[0242] 600 x-axis

[0243] 602 normal probability distribution function

[0244] 604 truncation threshold

[0245] 606 area that corresponds to the value of cumulative distribution function F

[0246] 608 area that corresponds to the remainder of cumulative distribution function F

[0247] 610 upper tolerance band limit UTBL

[0248] 612 delta value

[0249] 614 upper specification limit USL

[0250] TL technical limit

[0251] CDF Cumulative Distribution Function

[0252] PDF Probability Distribution Function

[0253] x variable under test

[0254] X set of values for x

[0255] s, σ a standard deviation of X

[0256] σ{circumflex over ( )}2 variance (small Greek letter Sigma)

[0257] μexpected value (small Greek letter My)

[0258] S specification range

[0259] TI Tolerance Interval

[0260] DE Device Evaluation,

[0261] USL Upper Specification Limit

[0262] UTBL Upper Tolerance Band Limit

[0263] UTBL* transformed Upper Tolerance Band Limit

[0264] LSL Lower Specification Limit

[0265] LTBL Upper Tolerance Band Limit

[0266] 1−α confidence level (1−small Greek letter Alpha)

[0267] F(.Math.; p) cumulative distribution function with parameter vector p

[0268] f(.Math.; p) probability distribution function with parameter vector p (density function)

[0269] k tolerance limit factor

[0270] {circumflex over (k)} transformed tolerance limit factor

[0271] pc probability content

[0272] transformed probability content

[0273] R real Numbers

[0274] x.sup.T vector x transposed

[0275] x mean of x

[0276] ξ general truncation threshold (small Greek letter Ξ)

[0277] ξ.sub.L left truncation threshold

[0278] ξ.sub.R right truncation threshold

[0279] N newton, unit of force