Experience Curve Compared With Manufacturing Processes for TKA

Abstract

In the experience curve concept set forth by the National Aeronautics and Space Administration (NASA), production time falls by a set percentage every time cumulative production doubles. NASA has established benchmark figures for different manufacturing processes, and we have used these figures in analyzing our first 240 navigated total knee arthroplasties for varus knees. Our experience curve was 93% (P < .001), which is similar to the experience curve (90%) for processes consisting of 25% hand assembly and 75% machining. We suggest that the experience curve may provide a guide for comparing different surgical teams and navigation systems and for resource allocation.

In 1885, the German psychologist Hermann Ebbinghaus introduced the concept of the learning curve,¹ which arose from observations relating the efficiency of memorization with number of repetitions. This was supported by later studies published by Thorndike² in 1898 and by Thurstone³ in 1919, which showed how an individual’s performance improved with experience. In 1936, Theodore Paul Wright⁴ described the effect of learning on labor productivity in the aircraft industry and proposed a mathematical model of the learning curve. His work suggested that there was a constant percentage of improvement until productivity reached a plateau. The term experience curve is broader in scope and includes manufacturing and labor costs.

In a typical manufacturing assembly line, standardized preprocessed components are put together in a predetermined order. The experience in assembly and the time taken to do the assembly are therefore the only variables. Although the process of a total knee arthroplasty (TKA) can be analyzed as a series of component modules, the analysis is not as straightforward. Patients’ knees have different sizes and deformities. The deformities have to be corrected (preprocessed) before the components are assembled. The experience curve for TKAs therefore reflects both preprocessing and assembly of the components.

The learning curve of a surgeon new to navigated TKA has recently been described⁵; however, in that report, the equation of the curve is not mentioned, and the influence of deformity and patient morphology is not investigated.

We describe the statistical relationship between surgical experience, operative time, deformity, and patient morphology⁶; however, because only a simple multivariate linear analysis was done, the plateau effect seen in practice could not be described. Moreover, the experience curve was not described and the relationship to other experience curves was not investigated.

The study reported here was done to provide a mathematical model that more closely reflects what is found in practice and to compare those findings with data in other manufacturing industries.

Materials and Methods

This prospective study included all patients having a TKA for varus deformities over a 36-month period. Patients with valgus deformities were excluded because a different surgical approach was used. A single surgeon (S.A.C.S.) previously experienced in nonnavigated TKA performed all the cases with the same first assistant. The scrub nurse and second assistant were drawn from a pool of 3 other members of staff. The E.motion (B. Braun Aesculap, Tuttlingen, Germany) uncemented floating platform TKA was implanted using the OrthoPilot navigation system version 4.2 (B. Braun Aesculap) with soft tissue management. The surgical technique was that recommended by the manufacturer and has been validated previously.⁷ The preimplantation and postimplantation mechanical axes in the coronal plane were recorded by the OrthoPilot and were measured throughout the procedure.

Surgery was performed using a pneumatic tourniquet with digital timing. This was done by the anesthesia staff and was not known to the surgical team until after the procedure was completed. The limb was prepped and draped. The limb was then elevated and the tourniquet inflated. After the procedure, the skin was closed. When the sterile dressing was applied, the tourniquet was deflated. This gave a definitive time (T) for the complete procedure. The patients’ weight and height were obtained preoperatively. The body mass index (BMI) was calculated by dividing the patient’s weight in kilograms by the square of the patient’s height in meters (kg/m²). To quantify the experience of the surgeon with the OrthoPilot system, the sequential case number of E.motion knees implanted was also recorded. Statistical analysis of the results was carried out using SPSS 17.0 (SPSS Inc, Chicago, Illinois).

Results

Two hundred and forty TKAs were implanted. The mean BMI was 30.2 (range, 20.1-45.7; standard deviation [SD] 4.9) (Figure 1). The mean time was 61.6 minutes (range, 39-122 minutes; SD 15.6) (Figure 2). The mean preoperative varus was 6.3°varus (range, 0-35; SD 4.8) (Figure 3). Postoperatively, varus was reduced to a mean alignment of 0.43° (range, -2-3; SD 0.94) from the neutral axis (Figure 4). The difference in the alignment of the mechanical axis is statistically significant (P<.0001, Student t test).

Figure 1: Body mass index (N=240 varus knees).

Figure 2: Operative time (N=240 varus knees).

Figure 3: Preoperative varus deformity in degrees (N=240 varus knees).

Figure 4: Postoperative varus deformity in degrees (N=240 knees).

Figure 5: Experience curve for 240 navigated uncemented TKAs.

Power curve fitting analysis gave the following power curve equation (Figure 5):

Equation 1

T=89N^-0.08

P<.001; r²=.107

Where T=tourniquet time in minutes

N=case number

This corresponds to an experience curve of 93%.

Multiple linear regression analyses on the data demonstrated a statistically significant relationship between preoperative varus, BMI, natural logarithm (Ln) N, and Ln T:

Equation 2

Ln T=4.0-0.09×Ln N+0.01×BMI+0.02Vr

P<.001; r²=.27

Ln is the natural logarithm.

Vr is the preoperative varus measured in degrees from the neutral axis.

Discussion

In this series of 240 computer-assisted TKAs, all cases were corrected to within -2° to 3° of the neutral axis despite preoperative varus deformities of up to 35°. This corroborates previous work.⁸ Because each case was corrected to the same endpoint (within 3° of neutral alignment), we had the opportunity to analyze and compare the data very accurately. Comparison with published data⁹ shows that the experience curve for navigated uncemented TKA in our clinic (93%) is similar to that for processes with 25% hand assembly and 75% machining (90%). For any manufacturing process, the greater the percentage of machining and the lower the percentage of hand assembly, the greater is the learning percent.¹⁰ This is consistent with the actual technique of uncemented TKA wherein, for example, machining is bone cutting using power instruments and hand assembly is the surgical exposure. Processes with a larger proportion of hand assembly to machining have a lesser experience curve (Table). Unlike manufacturing processes, however, there is a large spread of data points. The plotted power curve (Figure 5) accounts for only a limited fraction of the variation in the data (r²=.107). When the variation in varus deformity and BMI are taken into account (equation 2) the value of r² increases to 0.27. Therefore, approximately 70% of the variation in the data has not been accounted for by our analysis. We suggest that this variation, like any variation in data, may fall into 2 broad categories: random variation or noise and nonrandom variation. Examples of nonrandom variation that were not included in the analysis but may be relevant include day of the week, position of the case on the list, difficulty of the previous case, number of cases on the list, and experience of supporting staff in the operating theater. Inclusion of these variables in future analyses of this type may prove to account for an increased percentage of the variation found.

Table: Experience Curve for Typical Manufacturing Processes

Conclusion

The process of navigated uncemented TKA has a similar experience curve to that of manufacturing processes in general and to those with 25% hand assembly and 75% machining in particular. However, the model fits better when the patient variables, BMI, and varus deformity are considered. It is possible that investigation of other factors may further improve the mathematical model.

The economics of computer-navigated TKA have already been investigated¹¹ and found to be cost effective.¹² The mathematical relationship we describe suggests that surgeons may plan their operating lists with greater accuracy, thereby wasting less time and using fewer resources. Our mathematical model takes into account previous experience, such that the expected time taken for cases undertaken by trainees can be factored in when planning lists. Theater time is a valuable resource. In the United Kingdom under the National Health System, cases that overrun may lead to the cancellation of > cases scheduled to follow, creating a ripple effect of scheduling and cancellations. A reliable prediction of theater time would reduce the number of cancellations.

References

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Authors

Dr Sampath is from the Bluespot Knee Clinic, Lytham St Annes, and Drs Davies and Voon are from Addenbrookes Hospital NHS Trust, Cambridge, United Kingdom.

Drs Sampath, Davies, and Voon have no relevant financial relationships to disclose.

The authors would like to gratefully acknowledge the assistance of Mrs Lynsey Cumberland.

Correspondence should be addressed to: Shameem A. C. Sampath, FRCS, the Bluespot Knee Clinic, 32 Orchard Rd, Lytham St Annes, Lancashire FY8 1PF, United Kingdom.

doi: 10.3928/01477447-20090915-60