Production data evaluation analysis model: a case study of broaching machine

ABSTRACT

To increase machine tool reliability and overall product quality, process quality must be increased for all parts and components. Aside from quality, processing efficiency is also a crucial indicator of machine tools, which has brought about various customized machine tools with high processing efficiency. As broaching machines offer high production efficiency and are simple in structure and operation, we used broaching machines as a case study to construct a model for process capability evaluation, analysis, and improvement. Furthermore, the Six Sigma quality index directly reflects process yield as well as process quality levels. We then derived the relationships between the quality level of the product and those of individual quality characteristics to establish quality assessment standards and created a process quality analysis chart for products with multiple quality characteristics. We used a mathematical programming model to find the corresponding coordinate point of the upper confidence limit for Six Sigma quality indices. Process engineers need only check whether the corresponding coordinate points fall in the acceptable-quality zone or the poor-quality zone to identify critical-to-quality characteristics. Finally, we used a cause-and-effect diagram to determine the causes of poor process quality and formulate suggestions for improvement.

KEYWORDS:

• Six sigma quality indices
• upper confidence limit
• quality characteristics
• process quality analysis chart

Nomenclature

CTQscritical-to-quality characteristics

E$\bigcap _{h=1}^5{E}_h$

_ELh$\left\{LS{L}_h\le X_h\right\}$

E_Uh$\left\{X_h\le USL\right\}$

E_hevents in which process specifications are met for quality characteristic h

$E_h^C$events in which process specifications are not met for quality characteristic h

d_h(USLh − LSLh)/2

hquality characteristic

k; $k{ }^{\mathrm{\prime }}$process quality of the product

NTBnominal-the-best

LTBlarger-the-better

LSL_hlower specification limits of quality characteristic h

${\delta }_h$accuracy index of quality characteristic h

${\gamma }_h$precision index of quality characteristic h

${\mu }_h$process mean of quality characteristic h

${\sigma }_h$process standard deviation of quality characteristic h

T_hProcess target of quality characteristic h

Q_phthe assessment indices of the quality characteristic h

$q_h$defect rate of products …

$\mathrm{\Phi }(z)$the cumulative distribution function of the standard normal distribution Z

X_hrandom variable of the quality characteristic h

N$({\mu }_h,{\sigma }_h^2)$normal distribution of the quality characteristic h

_nsample size

${\bar{X}}_h$estimator of ${\mu }_h$

$S_h^2$estimator of ${\sigma }_h^2$

${\hat{Q}}_{ph}$the estimators of $Q_{ph}$

$\alpha$significance level

K$n{\hat{\gamma }}_h^2/{\gamma }_h^2$

${\chi }_{n-1}^2$chi-square distribution with n - 1 degrees of freedom

${\hat{\delta }}_h$the estimators of ${\delta }_h$

${\hat{\gamma }}_h^{\hspace{0.17em}}$the estimators of ${\gamma }_h^{\hspace{0.17em}}$

${\gamma }_{hD}$$\sqrt{\frac{n}{{\chi }_{0.5+\sqrt{1-\alpha }/2,n-1}^2}}{\hat{\gamma }}_h$

${\gamma }_{hU}$$\sqrt{\frac{n}{{\chi }_{0.5-\sqrt{1-\alpha }/2,n-1}^2}}{\hat{\gamma }}_h$

CRconfidence region

x_hjthe observed value of X_hj

${\bar{x}}_h$the observed value of ${\bar{X}}_h$

$s_h$the observed value of $S_h$

${\hat{\delta }}_{h0}$the observed value of ${\hat{\delta }}_h$

${\hat{\gamma }}_{h0}$the observed value of ${\hat{\gamma }}_h$

$L{\delta }_h$lower limit of ${\delta }_h$

$({\delta }_{h0},{\gamma }_{h0})$the corresponding coordinate point of upper confidence limit UQ_ph

p_kthe least process yield when Q_ph = k

p(E_h)probability of E_h

$p\left(E_h^C\right)$probability of $E_h^C$

$P_T$P(E)

p(E_Lh)probability of events E_Lh

p(E_Uh)probability of events E_Uh

$p\left(E_{Lh}^C\right)$$1-p\left(E_{Lh}^{\hspace{0.17em}}\right)$

$p\left(E_{Uh}^C\right)$$1-p\left(E_{Uh}^{\hspace{0.17em}}\right)$

STBsmaller-the-better

SSQISix Sigma quality index

P_hyield of products that meet process specifications for quality characteristic h

$U{\delta }_h$upper limit of ${\delta }_h$

UQ_phupper confidence limit of Q_ph

USL_hupper specification limits of quality characteristic h

_ZAa triangular acceptable-quality zone

Z$\sqrt{n}\left({\hat{\delta }}_h^{\hspace{0.17em}}-{\delta }_h^{\hspace{0.17em}}\right)/{\gamma }_h$

$Z_B^{+}$inadequate accuracy for the quality characteristic in question and is skewed to the right

$Z_B^{-}$inadequate accuracy for the quality characteristic in question and is skewed to the left

$Z_C^{\hspace{0.17em}}$inadequate precision and excessive variance for the quality characteristic in question

$Z_C^{+}$inadequate accuracy and precision for the quality characteristic in question and is skewed to the right

$Z_C^{-}$inadequate accuracy and precision for the quality characteristic in question and is skewed to the left

Disclosure of interest

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Ministry of Science and Technology, Taiwan [MOST 107-2622-E-167-003-CC3].