UDK 621.941:311.2
Professional article/Strokovni članek
ISSN 1580-2949
MTAEC9, 43(1)55(2009)
IMPROVING THE PROCESS CAPABILITY OF A TURNING OPERATION BY THE APPLICATION OF STATISTICAL TECHNIQUES
IZBOLJŠANJE PROCESA SPOSOBNOSTI STRUŽENJA Z UPORABO STATISTIČNE TEHNIKE
Aysun Sagbas
Mersin University, Tarsus Technical Education Faculty, Department of Mechanical Education, 33400 Tarsus-Mersin/TURKEY
asagbas@mersin.edu.tr
Prejem rokopisa — received: 2008-08-05; sprejem za objavo - accepted for publication: 2008-10-22
Process-capability indices are effective tools for the continuous improvement of quality, productivity and managerial decisions. Statistical process-control techniques improve the quality in mass production. In this study, a process-capability analysis was carried out in the machining line of a medium-sized company that produces machine and spare parts. For this purpose, normal probability plots and histograms were prepared and the process-capability indices Cp and Cpk were calculated. It is shown that the process capability for the whole process was inadequate and that the mass production was unstable. In order to satisfy the process-capability measures it is necessary to improve the quality level by shifting the process mean to the target value and reducing the variations in the process.
Keywords: process capability analysis, quality improvement, turning operation
Indeksi sposobnosti so za procese učinkovita orodja za stalno izboljševanje kakovosti, produktivnosti in vodstvenih odločitev. Statistična tehnika kontrole procesa omogoči izboljšanje kakovosti pri masovni proizvodnji. V tej študiji je bila izvršena ocena procesa za obdelovalno linijo srednje velike družbe, ki izdeluje stroje in rezervne dele. Za ta namen so bili pripravljeni histogrami normalne verjetnosti in izračunani indeksi sposobnosti procesa (Cp in Cpk). Pokazalo se je, da je bila procesna sposobnost za celoten proces neprimerna in je zato bila nestalna masovna proizvodnja. Za izboljšanje stanja je bilo treba sprejeti ukrepe za dvig nivoja kakovosti s premikom povprečja procesa na ciljno vrednost in znižati njegovo variabilnost.
Ključne besede: analiza sposobnosti procesa, izboljšanje kakovosti, struženje
1 INTRODUCTION
Process-capability analysis is a technique applied in many stages of the product cycle, including process, product design, manufacturing and manufacturing planning, since it helps to determine the ability to manufacture parts within the tolerance limits and engineering values. There are several capability indices, including Cp, Cpu, Cpl and Cpk, that have been widely used in manufacturing industry to provide common quantitative measures of process potential and performance. Process-capability indices are powerful means of studying the process ability for manufacturing a product that meets specifications 1,2.
There is considerable theoretical and experimental research work on improving product quality and process efficiency using a process-capability analysis. Kane 3 described six areas of application for capability indices: the prevention of the production of nonconforming products, the continuous measure of improvement, communication, prioritization, the identification of directions for improvement, and the auditing of the quality system. Wright 4 discussed the cumulative distribution function of process-capability indexes.
The process-capability indices, including, Cp, Cpk and Cpm, have been proposed in manufacturing industry to
provide a quick indication of how a process has conformed to its specifications, which are preset by manufacturers and customers. Pearn et al.5 indicated the index of capability for monitoring the accuracy of the manufacturing process. Singhal 6 introduced the multiprocess performance-analysis chart (MPPAC) based on process-capability indices for controlling and monitoring multiple processes. The MPPAC provides an easy way to process improvement by comparing the locations on the chart of the processes before and after the impro-vemet effort. Pearn and Chen 7 proposed a modification to the MPPAC, combining the more advanced process-capability indexes Cpm and Cpmk to identify the problems causing the process failing to centre around the target. Pearn et al.5 introduced the MPPAC based on the capability index, which is a simple transformation of Cpmk. They developed the multi-process performance-analysis chart based on process-capability indices to analyze the manufacturing performance for multiple processes. Deleryd et al.8 investigated experiences of implementing statistical methods in two small companies from the ceramics industry. Motorcu and Güllü 9 used some statistical calculations to eliminate quality problems, such as undesirable tolerance limits and the out of circularity of spherodial cast-iron parts during machining. Dolinsek and Kopac 10 presented particular examples of
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A. SAGBAS: IMPROVING THE PROCESS CAPABILITY OF A TURNING OPERATION
machining crank shafts. From the results obtained from statistical process control (SPC), they identified tool wear and machine inaccuracies. Deleryd 11 performed a survey among 97 Swedish organizations that use process-capability studies. Corbett and Pan 12 described a quantitive procedure for the monitoring and evaluating of environmental performance using statistical process-control techniques. Chang and Wu 13 provided explicit formulas with efficient algorithms to obtain the lower confidence bounds and sample sizes required for the specified precision of the estimation of Cpk for processes with asymmetric tolerances. Ramakrishnan et al. 1 discussed process-capability indices and product reliability. Chen et al. 14 constructed a process-capability-monitoring chart (PCMC) for evaluating the process potential and performance for the silicon-filler product, which is designed for practical applications.
The purpose of this study was to focus on the process-capability analysis in a medium-sized company to eliminate quality problems during machining. A normal distribution curve and histograms were prepared, the process-capability indices were calculated, and the number of nonconforming parts was determined.
2 PROCESS-CAPABILITY STUDIES AND PROCESS-CAPABILITY INDICES
Process-capability indices have been widely used to measure product qualities and process performance that meet specifications in the manufacturing industries. The procedure for the analysis of process performance is shown in Figure 1.
Many engineers use process-capability indices as communication indicators to evaluate the manufacturing process. The quality characteristics of items are often
measured in order to determine the capability of the production process. Usually, the customer determines a specification area or tolerance zone by setting lower and upper specification limits to require a certain quality from the supplier. Process capability is the repeatability and consistency of a manufacturing process relative to the customer's requirements 15. Since the estimated capability index is a random variable with a distribution, most engineers look at the value of the capability index calculated from the given sample and then draw a conclusion on whether the given process is capable or not and whether or not it is reliable. When a process is in a state of statistical control, and only then, the process can be evaluated with respect to its ability to produce items within specifications. Obviously, the variability of the process is a measure of the consistency of the output products. The stability of a process is an important property, since, if the process is stable in the current frame, then it is likely to stay in a stable condition in the future. Thus, the output of a stable process is in some sense predictable. There are several capability indices, including Cp, Cpu, Cpl Cpk, Cpm and Cpmk. Process variation, process departure, process yield, and process loss have been considered as crucial benchmarks for measuring process performance. The index Cp considers the overall process variability relative to the specification tolerance, and therefore it only reflects the consistency of the product's quality characteristic. The index Cpk takes the mean of the process into consideration, but it can fail to distinguish between on-target processes and off-target processes, which is a yield-based index providing lower bounds on the process yield 2. The index Cpm takes the proximity of the process mean from the target value into account, which is more sensitive to process departure than Cpk. Since the design of Cpm, is based on the average process loss relative to the specification tolerance, the index Cpm provides an upper bound of the average process loss, which is also reffered to as the Taguchi index or the loss-based index. The index Cpmk is constructed from combining the modifications to Cp that produced Cpk and Cpm, which inherits the merits of both indices. The index Cpmk indeed provides more quality assurance with respect to process yield and process loss to the customers than the other two indices, Cpk and Cpm. The most widely used capability indices in industry are defined with Eq. 1 and 2. U3.
C p =
USL - LSL 6a
. fUSL - u u - LSL C pk = min f
[ 3a
3a
d - \u - M\
3a
Cpk — Cp(l — k)
k — ■
|T-u|
05(USL - LSL)
(1)
(2)
Figure 1: Analysis procedure for process performance Slika 1 : Procedura analize lastnosti procesa
where USL is the upper specification limit, LSL is the lower specification limit, denotes the process' stan-
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dard deviation, ^ denotes the process mean, d is the half-length and M is the midpoint of the specification interval. T is the target value, and k is the variation factor. When the process is perfectly on target, k = 0 and Cpk — Cp from Eq.(2), the maximum value for Cpk is Cp. Examples of the estimation of the capability-process indices Cp and Cpk are introduced in Table 1.
Table 1: Examples of process estimation based on the indices Cp and
Cpk
Tabela 1: Dva primera ocene procesa na podlagi indeksov Cp in Cpk
Capability index	Estimation of the process
Cpk — Cp	Process is placed exactly at the centre of the specification limits
Cp< 1	Process is not adequate
1 £ Cpk < 1.33	Process is adequate
Cp > 1.33	Process is satisfactory enough
Cp > 1.66	Process is very satisfactory
Cpk Cpk	Process is inadequate, new process parameters must be chosen
3 PROCESS-CAPABILITY ANALYSIS IN TURNING
The following case is taken from a medium-sized casting and manufacturing factory, making various types machine and spare parts in Istanbul, Turkey. The workpiece was cast, spheroidal iron, cast GGG-40, using investment casting and machined using an industrial type
Figure 3: Normal probability plot for quality characteristic (0 24 ± 0.1)
Slika 3: Odvisnost normalne verjetnosti za karakteristično kakovost (0 24 ± 0,1), N — 150
lathe machine. The workpieces were machined under dry conditions, and ceramic-based cutting inserts were used. The quality characteristics considered are shown in 1, 2, and 3 in Figure 2. The dimensions and tolerance values of the workpiece and the technical drawing are shown in Figure 2.
In this study, in order to demonstrate the applicability of the proposed method and to make a clear decision about the capability of the machining process, the sample size was determined and a sufficient number of sample parts was inspected. A single sampling plan was implemented by using the lot-acceptance sampling plan. Samples were chosen randomly during the turning process. The data for the investigated characteristics were collected for 30 days in the company, determined for 150 samples, i.e., 30 % of a lot size of 500 parts. The same number of workpieces (N — 150) was measured every day. Normal probability plots and histograms were prepared and statistical parameters were calculated using the measured values taken from the workpieces that
Figure 2: The dimensions and tolerance values of the workpiece and technical drawing
Slika 2: Dimenzije in tolerance za obdelovanec in tehnični načrt
Figure 4: Normal probability plot for (010 ± 0.2)
Slika 4: Normalna verjetnostna odvisnost za (010 ± 0,2), N =
150
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Figure 5: Normal probability plot for (011 ± 0.2)
Slika 5: Normalna verjetnostna odvisnost za (011 ± 0,2), N = 150
Figure 7: Histograms and process-capability analysis for quality characteristic (010 ± 0.2)
Slika 7: Histogram analize procesne sposobnosti za karakteristično kakovost (010 ± 0,2)
represent the whole process. To receive a numerical measure of the capability, the so-called process-capability indices were calculated. In all the stages of data analysis, Minitab software was used. The validity of the normallity was verified using the Chi-square test, 2. Figures 3, 4 and 5 display the normal probability plots of the sample data and from these figures the sample data appear to be normal.
Figures 6, 7 and 8 display the histograms of the 150 observations with a density line and specification limits (LSL, T, USL) and the results of the process-capability analysis.
Figure 6 shows that the process capability deteriorated during the monitoring period to Cp and Cpk < 1, which indicates the potential risk of an increase in the number of nonconforming parts. It denotes that the process capability is inadequate. For Cp Cpk the process mean is not centred for the process width. The number of non-conforming parts out of the LSL is 120,000 and there is a none value out of the USL in the observed performance. In a short period of time, the non-conforming parts out of the LSL is 119,010 ppm and out of the USL is 1837 ■ 10-6. In a long period of time,
the number of non-conforming parts out of the LSL is 126,322 ■ 10-6 and out of the USL is 2429 ■ 10-6. This analysis shows that the specification limits should be rearranged and the process variabilty should be reduced.
Since the calculated Cp value (1.52) is bigger than 1.33 and the Cpk value (0.23) is lower than 1.00, the process is inadequate. Some measures must be taken immediately and new process parameters must be chosen. For Cp Cpk , the process mean is not centred with the process width. If the process mean is not centred relative to the specification limits, the process-capability index will give misleading results. The process mean is near to USL. The number of non-conforming parts out of the USL is 240,000 and there is no value out of the LSL in the observed performance. The number of non-conforming parts out of the USL is 246,986 ■ 10-6 in a short period of time and 259,443 ■ 10-6 in a long period of time. In the short and long periods of time the data fall out of the LSL. As the process-capability indices calculated are clearly different, there will be different percentages of non-conforming products. In short and long periods of time the number of parts produced out of the USL will be
Figure 6: Histograms and process-capability analysis for quality characteristic (024 ±0.1)
Slika 6: Histogram analize procesne sposobnosti za karakteristično kakovost (024 ±0,1), N =150
Figure 8: Histograms and process-capability analysis for quality characteristic (011 ± 0.2)
Slika 8: Histogram analize procesne sposobnosti za karakteristično kakovost (011 ± 0,2)
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increased. In order to satisfy the process capability, some actions must be taken immediately and new process parameters must be chosen.
As the calculated Cp value (Cp is larger than 1.33, the process meets the capability requirement with a 95 % confidence level, or equivalently, at the significance level a = 0.05. These product items conform to the manufacturing specifications and are considered as reliable products. For Cp Cpk, the process mean is not centred on the process width. The process mean is near to the target value. It is clear that in the observed performance no data are outside the speciffication limits. The number of non-conforming parts out of the LSL is 0.07 ■ 10-6 and the USL is 241 ppm in a short period of time. The number of non-conforming parts out of the LSL is 0.05 ■ 10-6 and the USL is 214 ■ 10-6 in a long period of time.
4 CONCLUSIONS
In recent years, process-capability analysis has become an important integrated part in the applications of statistical techniques for quality assurance. Quality assurance in mass production is achieved using statistical process-control techniques. The process-capability analysis, which is a SPC technique, helps to determine the ability for manufacturing between tolerance limits and engineering specifications. The capability analysis gives information about the changes and tendencies of the systems during production.
In this study the process-capability analysis was carried out for the elimination of the quality problems during turning operations. The number of non-conforming parts was determined in observed values, in short and long periods of time. For the elimination of the observed quality problems, some suggestions were proposed. Faults regarding manufacturing out-of-tole-rance limits were eliminated, the variability in the process and the cost due to low-quality production were reduced in the particular company.
In today's competitive market, SPC is not the most frequently used technique in small and medium-sized
companies in Turkey. The most important problems in business are that there are no trained employees to apply it and there is unsufficient investment. Consequently, SPC must be applied widely and continuously to achieve quality improvements.
5 REFERENCES
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