Ockham's Razor Applied on Pharmaceutical Powder Compaction Models

Published:November 30, 2020DOI:


      This investigation contains a critical survey of a collection of five well-known and often used standard models in pharmaceutical technology. The basic idea is to use the recognised Ockham's razor as a tool in search for simpler methods or explanations for these models. The study includes the indirect tensile strength of tablets, Pitt's equation for tensile strength of biconvex tablets, Adams' model for strength of agglomerates, Weibull's distribution for variability of strength measurements and Heckel's equation for compressibility. In all these cases simpler and equally valid solutions and explanations are presented and subsequently preferred rather than the original.


      To read this article in full you will need to make a payment
      APhA Member Login
      APhA Members, full access to the journal is a member benefit. Use your society credentials to access all journal content and features.
      One-time access price info
      • For academic or personal research use, select 'Academic and Personal'
      • For corporate R&D use, select 'Corporate R&D Professionals'

      Purchase one-time access:

      Already a print subscriber? Claim online access
      Already an online subscriber? Sign in
      Institutional Access: Sign in to ScienceDirect


        • Hoffman R.
        • Minkin V.I.
        • Carpenter B.K.
        Ockham's Razor and chemistry.
        An Int J Philos Chem. 1997; 3: 3-28
        • Spitzer A.L.
        • Barcia A.M.
        • Schell M.T.
        • et al.
        Applying Ockham's razor to pancreatitis prognostication: a four-variable predictive model.
        Ann Surg. 2006; 243: 380-388
        • Jefferys W.H.
        • Berger J.O.
        Ockham's razor and Bayesian analysis.
        Am Sci. 1992; 80: 64-72
        • Paronen P.
        • Ilkka J.
        Porosity–pressure functions.
        in: Alderborn G. Nyström C. Pharmaceutical Powder Compaction Technology. Marcel Dekker, New York1996: 55-75
        • Shapiro I.
        Compaction of powders X. Development of a general compaction equation.
        Adv Powder Mettall Part Mater. 1993; 3: 229-243
        • Leuenberger H.
        The compressibility and compactibility of powder systems.
        Int J Pharm. 1982; 12: 41-55
        • Joiris E.
        • Martino P.D.
        • Berneron C.
        • Guyot-Hermann A.M.
        • Guyot J.C.
        Compression behavior of orthorhombic paracetamol.
        Pharm Res (N Y). 1998; 15: 1122-1130
        • ICH Harmonised Tripartite Guideline
        Validation of analytical procedures: text and methodology Q2(R1), (CPMP/ICH/381/95).
      1. USP advisory panel on physical test methods, new general test chapter “tablet breaking force” proposed by the USP advisory panel on physical test methods.
        Pharmacop Forum. 2000; 26: 513-516
        • Claesson J.
        • Bohloli B.
        Brazilian test: stress field and tensile strength of anisotropic rocks using an analytical solution.
        Int J Rock Mech Min Sci. 2002; 39: 991-1004
        • Sonnergaard J.
        Quantification of the compactibility of pharmaceutical powders.
        Eur J Pharm Biopharm. 2006; 63: 270-277
        • Hilden J.
        • Polizzi M.
        • Zettler A.
        Note on the use of diametrical compression to determine tablet tensile strength.
        J Pharm Sci. 2017; 106: 418-421
        • Podczeck F.
        Methods for the practical determination of the mechanical strength of tablets - from empiricism to science.
        Int J Pharm. 2012; 436: 214-232
        • Rees J.E.
        • Rue P.J.
        Work required to cause failure of tablets in diametral compression.
        Drug Dev Ind Pharm. 1978; 4: 131-156
        • Sonnergaard J.
        A new brittleness index for compacted tablets.
        J Pharm Sci. 2013; 102: 4347-4352
        • de Jong J.A.H.
        Tablet properties as a function of the properties of granules made in a fluidized bed process.
        Powder Technol. 1991; 65: 293-303
        • Sonnergaard J.
        • Jensen C.G.
        • Poulsen L.
        • Lokind K.B.
        Comparative investigations of tablet crushing force testers.
        Pharm Ind (Pharmind). 2005; 67: 109-115
        • Sonnergaard J.M.
        Distribution of crushing strength of tablets.
        Eur J Pharm Biopharm. 2002; 53: 353-359
        • Stanley P.
        • Newton J.M.
        Variability in the strength of powder compacts.
        J Powder Bulk Solids Technol. 1997; 1: 13-19
        • Pitt K.G.
        • Newton J.M.
        • Stanley P.
        Tensile fracture of doubly-convex cylindrical disks under diametral loading.
        J Mater Sci. 1988; 23: 2723-2728
        • Schmidt P.C.
        • Römpp H.
        Resistance to crushing of tablets. Do we need a more precise description of the method in the European Pharmacopoeia?.
        Pharmeurope. 2000; 12: 573-583
        • Schwartz J.B.
        • Flamholz J.R.
        • Press R.H.
        Computer optimization of pharmaceutical formulations I: general procedure.
        J Pharm Sci. 1973; 62: 1165-1170
        • Podczeck F.
        • Drake K.R.
        • Newton J.M.
        Investigations into the tensile failure of doubly-convex cylindrical tablets under diametral loading using finite element methodology.
        Int J Pharm. 2013; 454: 412-424
        • Adams M.J.
        • Mullier M.A.
        • Seville J.P.K.
        Agglomerate strength measurement using a uniaxial confined compression test.
        Powder Technol. 1994; 78: 5-13
        • Machaka R.
        • Chikwanda H.K.
        Analysis of the cold compaction behavior of titanium powders: a comprehensive inter-model comparison study of compaction equations.
        Metall Mater Trans. 2015; 46: 4286-4297
        • Sonnergaard J.
        Impact of particle density and initial volume on mathematical compression models.
        Eur J Pharm Sci. 2000; 11: 307-315
        • Heckel R.W.
        Density-pressure relationships in powder compaction.
        Trans Metall Soc AIME. 1961; 221: 671-675
        • Kawakita K.
        • Lüdde K.-H.
        Some considerations on powder compression equations.
        Powder Technol. 1970; 4: 61-68
        • Nordström J.
        • Welch K.
        • Frenning G.
        • Alderborn G.
        On the physical interpretation of the Kawakita and Adams parameters derived from confined compression of granular solids.
        Powder Technol. 2008; 182: 424-435
        • Weibull W.A.
        A statistical distribution function of wide applicability.
        J Appl Mech. 1951; 18: 293-297
        • Torres J.L.
        • García A.
        • Prieto E.
        • de Francisco A.
        Characterization of wind speed data according to wind direction.
        Sol Energy. 1999; 66: 57-64
        • Lambrecht B.
        • Perraudin W.
        • Satchell S.
        Time to default in the UK mortgage market.
        Econ Model. 1997; 14: 485-499
        • Hutchinson T.P.
        Graphing the death of Escherichia coli.
        Int J Food Microbiol. 2000; 62: 77-81
        • Stanley P.
        Mechanical strength testing of compacted powders.
        Int J Pharm. 2001; 227: 27-38
        • Pitchumani R.
        • Zhupanska O.
        • Meesters G.M.H.
        • Scarlett B.
        Measurement and characterization of particle strength using a new robotic compression tester.
        Powder Technol. 2004; 143–144: 56-64
        • Daniels H.E.
        The statistical theory of the strength of bundles and threads.
        Proc R Soc Lond. 1945; 183: 405-435
        • Hassanpour A.
        • Ghadiri M.
        Distinct element analysis and experimental evaluation of the Heckel analysis of bulk powder compression.
        Powder Technol. 2004; 141: 251-261
        • Sonnergaard J.
        A critical evaluation of the Heckel equation.
        Int J Pharm. 1999; 193: 63-71
        • Hooper D.
        • Clarke F.C.
        • Mitchell J.C.
        • Snowden M.J.
        A modern approach to the Heckel Equation: the effect of compaction pressure on the yield pressure of ibuprofen and its sodium salt.
        J Nanomed Nanotech. 2016; 7: 381
        • Patel S.
        • Kaushal A.M.
        • Bansal A.K.
        Mechanistic investigation on pressure dependency of Heckel parameter.
        Int J Pharm. 2010; 389: 66-73
        • Rowe R.C.
        • Roberts R.J.
        Mechanical properties.
        in: Alderborn G. Nyström C. Pharmaceutical Powder Compaction Technology. Marcel Dekker, New York1996: 283-322
        • Sun C.
        • Grant D.J.
        Influence of elastic deformation of particles on Heckel analysis.
        Pharm Dev Technol. 2001; 6: 193-200
        • Holman L.E.
        The compaction behaviour of particulate materials. An elucidation based on percolation theory.
        Powder Technol. 1991; 66: 265-280