Acceptance criteria fr prcess capability indexes generated frm statistical tlerance intervals as per Backgrund Justificatin fr sampling plans and statistical analysis f results is a requirement fr prcess validatin in medical devices. Current standards [1] and regulatins [2] hwever, give limited advice r guidance regarding this tpic. Several appraches where therefre adpted by the medical device industry. Purpse This statement intends t evaluate, if acceptance criteria fr prcess capability indexes [3] culd be generated frm statistical tlerance intervals calculated as per [4]. It is nt intending t questin r challenge the appraches as such. Discussin Statistical tlerance intervals The use f statistical tlerance intervals as described in can be fund in different regulatry surces like ISO 11608-1 [5] and FDA Guidance fr stents [6]. The basic idea behind the statistical tlerance intervals is t use the average and standard deviatin bserved within a sample grup in rder t calculate a tlerance interval. The apprach is recmmended fr validatin as it makes use f the LTPD (cnsumer s risk), instead f AQL (prducer s risk). Usually this is accmplished by a calculatin f average +/- k*standard deviatin, where the k-value is derived frm tables within the standard. The k-value cnsiders sample size used as well as the cnfidence and the prbability levels chsen. Selectin f adequate levels is the respnsibility f the manufacturer and must be justified. Sme regulatry requirements fr applicable cnfidence and the prbability levels are given within the relevant dcuments [5, 6]. Michael Schaefer Quality Management and Regulatry Affairs in Medical Devices Fr mre infrmatin visit www.quality-n-site.cm r cntact michael@quality-n-site.cm
Acceptance criteria fr prcess capability indexes generated frm statistical tlerance intervals as per The calculated statistical tlerance interval shall then be cmpared t the given specificatin f the prduct under cnsideratin. It is essential t understand, that the individual results must als meet specificatin. Statistical tlerance intervals are therefre a well-accepted way f fulfilling the requirements t justify sampling plans and t analyze results f prcess validatin activities. Prcess Capability Indexes Anther apprach chsen t justify sampling plans and t analyze results is the calculatin f prcess capability indexes (like Cp r Cpk). This apprach was discussed within the annex A t GHTF Guidance n prcess validatin [7]. Prcess capability indexes are calculated by relatin f the specified tlerance t the standard deviatin bserved within the sample grup(s). The Cp-Index is established by dividing the specified tlerance by 6 standard deviatins and shws if the prcess is stable (simplified calculatin fr nrmal distributin). The Cp-Index as such des nt cnsider the average f the prcess and cnsequently it des nt prvide infrmatin if the prcess is capable. Therefre it shuld nt be used as the nly acceptance criteria in prcess validatin. It is essential t understand, that the individual results must als meet specificatin. Fr these reasns anther prcess capability index may be used, which is the Cpk. The Cpk-Index is calculated using the average and the standard deviatin bserved. Calculatin is made by dividing the difference f the average critical (lwer r upper) spec limit by 3 standard deviatins (simplified calculatin fr nrmal distributin). The index will prvide infrmatin n capability and stability f the prcess. Michael Schaefer Quality Management and Regulatry Affairs in Medical Devices Fr mre infrmatin visit www.quality-n-site.cm r cntact michael@quality-n-site.cm
Acceptance criteria fr prcess capability indexes generated frm statistical tlerance intervals as per Fr bth, Cp and Cpk, there are n regulatry acceptance criteria published fr suitable values f these capability indexes. Mst ften it can be bserved, that industries just brrw values cmmnly accepted in autmtive industries withut further justificatin (e.g. Cpk equal r higher than 1.0). Cmparisn and evaluatin As a cnsequence f the frmulas used t calculate Cpk, an index f 1.0 wuld mean, that the difference between the critical spec limit and the average is exactly 3*stdev. It can be seen that the apprach used is similar t the statistical tlerance limits. This can be shwn by the fllwing calculatins (dne fr the example f the lwer spec limit): Cpk = (average lwer spec limit) / (3*stdev) Cpk*3*stdev = (average lwer spec limit) Cpk*3*stdev + lwer spec limit = average lwer spec limit = average - Cpk*3*stdev Fllwing the apprach fr statistical tlerance limits, the lwer spec limit must be Lwer spec limit <= average k*stdev (taken frm Annex B, Frm A, [4]) Cnsequently, ne culd use the relevant k-value frm as a measure fr an acceptable Cpk value: Cpk >= k/3 r k <= 3*Cpk r in wrds, Cpk must be equal r larger than the applicable k-value divided by 3, Cpk >= k(n, C,P) / 3, where n=sample size, C=Cnfidence level, P = Prbability level, selected frm applicable standard [4]. Michael Schaefer Quality Management and Regulatry Affairs in Medical Devices Fr mre infrmatin visit www.quality-n-site.cm r cntact michael@quality-n-site.cm
Acceptance criteria fr prcess capability indexes generated frm statistical tlerance intervals as per Plausibility Check A Cpk f >1 is cmmnly accepted in autmtive industries. It needs t be knwn, that this value shuld be calculated frm n>100 samples as a minimum [8]. Sme surces recmmend higher Cpk values (1.33 t 1.67) [9]. Using the frmula abve, a Cpk f 1 wuld require a k-value f less r equal than 3. When lking int (Annex D, Tw sided statistical tlerance limit factrs, 2-sided as wrst case) a k-value f 3.0, n=100, wuld satisfy a Cnfidence level 95,0 % and prprtin 99,0 % (Table D.6, k=2.9356, zer defects), which can ften be fund fr critical defects in medical device industries. Hwever, a sample size f n>100 is nt always used in prcess validatin. Repeating the abve with a mre cmmn sample size f n=30 wuld result in k-value (95/99, n=30, table D.6) = 3.3546 and wuld necessitate a Cpk f 1.12. n=15 wuld result in k-value (95/99, n=15, table D.6) = 3.8853 and wuld necessitate a Cpk f 1.30. Actually these values wuld fit t the cmmnly used interpretatin, that Cpk fr small sample sizes shuld be arund 1.33 (smetimes knwn as shrt term r machine capability). Rule-f-thumb Frm the abve, the fllwing rules f thumb culd be cncluded: Cpk>1.33 may satisfy a Cnfidence/Prbability level f 95/99% if the sample size is at least n=15 (in alignment t ). In ther cases, mre detailed calculatin wuld be needed: Cpk >= k/3, where k is a functin f n=sample size, and C=Cnfidence level, P = Prbability level, selected frm applicable standard. Michael Schaefer Quality Management and Regulatry Affairs in Medical Devices Fr mre infrmatin visit www.quality-n-site.cm r cntact michael@quality-n-site.cm
Acceptance criteria fr prcess capability indexes generated frm statistical tlerance intervals as per References: [1] ISO/FDIS 13485:2015 Medical devices Quality management systems Requirements fr regulatry purpses [2] 21CFR820, Quality system regulatin, FDA [3] ISO 3534-2:2006 Statistics Vcabulary and symbls Part 2: Applied statistics [4] :2014 Statistical interpretatin f data Part 6: Determinatin f statistical tlerance intervals [5] ISO 11608-1:2014 Needle-based injectin systems fr medical use Requirements and test methds Part 1: Needle-based injectin systems [6] Guidance fr Industry and FDA Staff: Nn-Clinical Engineering Tests and Recmmended Labeling fr Intravascular Stents and Assciated Delivery Systems, April 2010 [7] GHTF Study Grup 3 Quality Management Systems - Prcess validatin guidance, January 2004 [8] SPC 1 - Statistische Przesslenkung (DGQ-Schrift Nr.16 31) [9] Mntgmery, Duglas (2004). Intrductin t Statistical Quality Cntrl. New Yrk Michael Schaefer Quality Management and Regulatry Affairs in Medical Devices Fr mre infrmatin visit www.quality-n-site.cm r cntact michael@quality-n-site.cm