A DMAIC approach for process capability improvement an engine crankshaft manufacturing process

Statistical process control (SPC) widely employs various process monitoring charts for determining whether the process under consideration is performing within the specified limits are not. Process monitoring charts gives a graphical description of the process performance and it instantly helps the process personnel to differentiate chance causes from assignable causes. Process capability indices are the measure of efficiency of the process to produce the product within the specified dimensional tolerance limits. To be specific, C_P is the process potential capability index and C_PK is the process performance capability index. C_P gives a measure of the variation and deviation in the process. The higher the C_P value, the less the variation and deviation in the process. C_PK, on the other hand, is obtained from C_PKU and C_PKL. As a precaution of safety, the lower value among the C_PKU and C_PKL is considered to be the value of C_PK. Elaborating on this, it can be said that centering of the process within the specification limits is done by C_PK. It provides an indication whether the process is operating at the center of the specified tolerance zone or nearer to the upper or lower specification limits.

Schilling (1994), has thrown light on the superiority of process control over the traditional sampling techniques. Locke (1994), stressed on the importance of process charts, cause and effect relationship and control charts. Lin (2004), had emphasized on process capability indices for normal distribution. Tong et al. (2004), focused on define–measure–analyze–improve–control (DMAIC) approach and its application for printed circuit board quality improvement. Li et al. (2008) adopted DMAIC approach to improve the capability of surface mount technology in solder printing process. Hwang (2006) employed the DMAIC procedure in context of application to manufacturing execution system. Gentili et al. (2006) applied the DMAIC process for a mechanical manufacturing process line, which manufactures both professional and simple kitchen knives. Sahay et al. (2011) used the DMAIC approach for analyzing the manufacturing lines of a brake lever at a Connecticut automotive component manufacturing company. Singh (2011) improved the process capability of polyjet printing for plastic components and charted the procedure for attaining the C_pk value attainment >1.33, i.e., >4 sigma level, which is considered as industrial benchmark. Lin et al. (2013) elaborated on the accurate yield assessment of the processes of multiple characteristics of the turbine blade manufacturing process. Kumaravadivel and Natarajan (2013) applied the cause and effect matrix and failure modes and effects analysis (FMEA) for solving problems associated with flywheel casting process. Mariajayaprakash et al. (2013) identified the CTQ characteristics of shock absorber manufacturing process and improved the process by minimizing the defects using Taguchi approach. Genetic algorithm was applied to optimize the parameters using Taguchi approach. Chen et al. (2013) applied Taguchi’s orthogonal array and analysis of variance (ANOVA) to find the optimal values for the nine process parameters namely, injection time, injection pressure, packing time, packing pressure, cooling time, cooling temperature, mold open time, melt temperature and mold temperature, in a plastic injection molding process. Lal et al. (2013) in their paper discussed about the performance of piston manufacturing plant through stochastic models. They concluded that the time-dependent availability of the piston manufacturing plant is affected by fixture seat machining and circlip grooving.

The literature cited here reveals that the DMAIC approach is widely used for process capability improvements across the manufacturing sector. Hence, without any iota of doubt, this paper straightaway adopts the DMAIC approach for process capability improvement of the stub-end hole boring operation of an engine crankshaft manufacturing process.

The definition stratum starts with defining the project charter and then the mapping of the machining sequence flow of the crankshaft. It is followed by identifying the CTQ characteristic of interest, for the scope of improvement study.

Process mapping

The process flow chart for machining line of the crankshaft manufacturing cell consists of the following machining operations sequence, as shown in the Fig. 1. The manufacturing sequence of the crankshaft consists a total of 15 operations. Of all the manufacturing operations, the operation number 90 is of concern. The operations from 10 to 90 constitute the roughing line operations involving mainly facing and centering, turning, whirling, drilling, tapping and chamfering. The operations from 100 to 150 constitute the finishing line operations involving mainly grinding, sursulfing and lapping.

Open image in new window

Table 2 depicts the description of the machining operations of crankshaft manufacturing cell along with the associated CTQ characteristics.

Table 2

Machining operations of connecting rod manufacturing cell

Machining operation no.	Description of machining operation	CTQ characteristic pertaining to the machining operation
10	Facing and centering	Center to center distance
		Locating hole diameter and chamfer angle
20	Web milling	Web flatness
30	CNC rough turning of journals	Journal diameter
40	Pin whirling	Phase-out of pins
		Throw of pins
		Pin diameter after whirling
		Journal diameter after whirling
50	Finish turning of journals	Journal diameter after finish turning
60	Oil hole gun drilling	Oil hole diameter
70	Flange end finish turning	Flange diameter
		Flange circularity
80	Bolt hole PCD drilling and tapping	Bolt hole pitch circle diameter
		Thread pitch of bolt holes
90	Stub end boring and chamfering using a combination boring-cum-chamfering inserts tool bar	Stub-end-hole diameter
		Chamfer angle
100	Journal grinding	Journal finish diameter
		Journal circularity
110	Pin grinding	Pin finish diameter
		Pin circularity
120	Magnetic crack detection	Check for internal cracks
130	Sursulfing heat treatment	Hardness of journals and pins after sursulfing operation
140	Lapping of pins and journals	Surface roughness of journals and pins after lapping
150	Final inspection quality check

Identifying CTQ characteristic

Timing belt pulley is located onto the stub-end-hole of the crank shaft. Hence if the stub-end-hole is undersize or oversize, it leads to incorrect fitment of the timing belt pulley and subsequently the timing belt. Ultimately, this leads to incorrect timing of fuel combustion within the cylinders and detonation and knocking. Therefore, from functional view-point, the Stub-end-hole diameter forms a CTQ characteristic. Second, from manufacturing view-point, the stub-end hole is the last operation performed on the roughing line and it forms the locating reference for the subsequently operations in the finishing line. Any small variations in the stub-end-hole boring operations are carried to the finishing operations of journal and pin grinding. Hence, unanimously, the stub-end-hole boring operation forms the prime choice for identifying it as a CTQ characteristic. Figure 2 shows the pictorial representation of the CTQ characteristic.

Open image in new window

The analysis stratum comprises of performing the calculations for the C _P and C_PK values across each iteration. In this stratum, the root cause analysis is performed with the help of various quality control (QC) tools like cause and effect diagram and physical mechanism analysis. Prioritization of the corrective actions is extracted from the output of process FMEA. This is followed by one-way ANOVA method of investigation to test the differences between the three iterations of the data sets.

Cause and effect diagram

The cause and effect diagram, also known as Ishikawa diagram or fish-bone analysis, is a directional approach where the common as well as special causes are classified under the heading of 4 M’s, i.e., man, material, method and machine. All the causes are directed towards the common effect namely, C_P and C_PK of the CTQ being <1.33. Figure 4 below charts the detailed cause and effect diagram pertaining to this research.

Open image in new window

Through the cause and effect diagram, and the PM analysis, the various causes for the poor performance of the machining operation can be identified and corrective actions are taken upon based on the prioritization by the risk priority number (RPN) generated in the FMEA.

Analysis of variance (ANOVA)

ANOVA starts with the formulation of the hypothesis to be tested, followed by, tests for the assumption about the normality of the data and the homogeneity of variance among the sets of the data.

A post hoc analysis is required if F_STATISTIC is found to be >F_CRITICAL.

Formulating the hypothesis and testing the assumptions for normality of data and homogeneity of variance

The null hypothesis (H₀) and the alternate hypothesis (H₁) can be formulated in the present context as

$$H_0:{\mathit{\mu }}_i=\mathit{\mu }\mathrm{all}i=1,2,3,$$

$$H_1:{\mathit{\mu }}_i=\mathit{\mu }\mathrm{for}\mathrm{some}i=1,2,3,$$

where µ _i is the population mean for level i, and µ is the overall grand mean of all levels.

With respect to the data in Table 3, it is seen that there are 3 levels (i.e., 3 iterations) with each level consisting of 32 measurement readings of stub-end-hole diameter of connecting rod. The data plot for normality is captured in Fig. 5, and the histogram bar chart is captured in Fig. 6. The pre-requisite for performing one-way ANOVA test is to find departure from normality and to check the homogeneity of variance among the sets of the data. The normal probability plot is seen linear with equispaced values and this is supported by the histogram with near bell-shaped curvature. The P value is <0.005, which is less than the α value of 0.05, thereby indicating that a linear relationship exists with normality retained. The results are further strengthened by the fact that there are no unusual data points. The sample size of 32 is sufficient to detect differences among means and because all the sample sizes are >15, normality is not an issue. Also based on the data observations and alpha level of 0.05, there is at least a 90 % chance of detecting a difference of standard deviation of 0.0023297 and at most a 60 % chance of detecting a difference of standard deviation of 0.0013632.

Open image in new window

Open image in new window

Finding the F_STATISTIC

The ANOVA Table obtained from Minitab software is captured in Table 6. Here it is seen that

$$F_{\text{STATISTIC}}=41.24.$$

(1)

Table 6

The ANOVA table

One-way ANOVA: Iteration 1, Iteration 2, Iteration 3
Source	DF	SS	MS	F	P
Factor	2	0.0004342	0.0002171	41.24	0.000
Error	93	0.0004897	0.0000053
Total	95	0.0009239

An α value of 0.05 is typically used, corresponding to 95 % confidence levels. If α is defined to be equal to 0.05, then the critical value for rejection region is F_{CRITICAL(α, K−1, N−K).} and is obtained to be 3.094. Thus,

$$F_{\text{CRITICAL}}=3.094.$$

(2)

Hence, it is seen that

$$F_{\text{STATISTIC}}>F_{\text{CRITICAL}}.$$

(3)

Therefore, the decision will be to reject the null hypothesis. If the decision from the ANOVA is to reject the null hypothesis, then it indicates that at least one of the means (µ _i ) is different from the remaining other means. In order to figure out where this difference lies, a post hoc ANOVA test is required.

Post-hoc ANOVA test

Since here the sample sizes are same, we go for the Tukey’s test for conducting the Post-hoc ANOVA test. In Tukey’s test, the honestly significant difference (HSD) is calculated as

$$\text{HSD}=q\sqrt{\frac{{\text{MST}}_{\text{E}}}{n}}=3.38\sqrt{\frac{0.53\times {10}^{-5}}{32}}=0.00137,$$

(4)

where q is the studentized range statistic which is equal to a value of 3.38, for a df of 93 and k = 3, i.e., number of levels as 3.

If “C1” denotes “Iteration 1”, “C2” denotes “Iteration 2” and “C3” denotes for “Iteration 3”, then from Minitab software, the following grouping information using Tukey method is shown in Table 7:

Table 7

Grouping information using Tukey method

Iteration column ‘C’	N	Mean	Grouping
C3	32	30.007156	A
C2	32	30.006781	A
C1	32	30.002469	B

From Table 7, it is seen that means that do not share a letter are significantly different, i.e., Iteration 1 is significantly different from Iterations 2 and 3.

The pairwise comparison using Minitab is depicted in Table 8.

Table 8

Pairwise comparisons of iterations

S. no.	Pairwise comparison	Value
1	C1 subtracted from: C2	0.004312
2	C1 subtracted from: C3	0.004687
3	C2 subtracted from: C3	0.000375

In Table 8, it is seen that the pairwise comparison between C2 and C3 is 0.000375 which is less than HSD is Eq. (3), whereas the pairwise comparison between C1 and C2 is 0.004312 and that between C1 and C3 is 0.004687, which are greater than that of the HSD in Eq. (4), with the difference 0.004687 being the largest. So, it is deduced that the differences are statistically significant. Hence, it is concluded that among all the different causes enumerated in the cause and effect diagram, the most influencing causes are the worn out cutting tool insert, insert setting v-block wear out and non-calibration of the vernier calipers and tool setting mandrel.

The improvement in the process performance is fostered by the fact that the sigma levels (standard deviation) are reduced from 0.003 to 0.002 as captured in Table 3.

This paper traces the DMAIC approach for improving the process capability levels of the stub-end-hole boring operation of the crankshaft manufacturing process. The QC tools predominantly used for tracing out the causes for poor process performance are the Ishikawa diagram, physical mechanism analysis and the failure modes and effects analysis. The process monitoring charts are employed at the workplace for monitoring the process performance and preventing it from deviations. In order to trace out the extent of influence of the causes identified, the ANOVA procedure is adopted. The predominant causes identified are worn out cutting tool inserts, worn out insert setting v-block and non-calibration of the vernier calipers and tool setting mandrel. Finally, on eliminating the causes one-by-one, the process potential capability index (C_P) showed an improvement from 1.29 to 2.02 and the process performance capability index (C_PK) improved from 0.32 to 1.45.