Manufacturing Practices (BT-106) - Important Questions

Explain the principles and objectives of Statistical Process Control (SPC). Discuss the main applications of SPC in a manufacturing environment and list the typical causes of variation that SPC helps to identify.

Describe the procedure for constructing $\bar{X}$ and $R$ control charts. Show the formulae for control limits and explain the role of constants such as $A_2$, $D_3$ and $D_4$. In your answer include the control limit expressions: $\bar{X}_{UCL}=\bar{\bar{X}}+A_2\,\bar{R}$ and $\bar{X}_{LCL}=\bar{\bar{X}}-A_2\,\bar{R}$, and $R_{UCL}=D_4\,\bar{R}$, $R_{LCL}=D_3\,\bar{R}$.

From 25 subgroups each of size 4, the overall process mean is $\bar{\bar{X}}=50.2$ and the average range is $\bar{R}=1.8$. Given $A_2=0.73$ for subgroup size 4, compute the upper and lower control limits for the $\bar{X}$ chart and state whether a subgroup mean of $51.8$ is in control.

Define process capability. Derive the formula for $C_p$ and $C_{pk}$ and explain the difference between them. Use the expressions $C_p=\frac{USL-LSL}{6\sigma}$ and $C_{pk}=\min\left(\frac{USL-\mu}{3\sigma},\,\frac{\mu-LSL}{3\sigma}\right)$ in your explanation and discuss their interpretation.

Explain single sampling plans for attribute inspection and define the Operating Characteristic (OC) curve. Derive the expression for the probability of accepting a lot in a single sampling plan of size $n$ with acceptance number $c$ using the binomial model: $P_a=\sum_{i=0}^{c} \binom{n}{i} p^{i} \left(1-p\right)^{n-i}$. Discuss the meanings of Producer's Risk and Consumer's Risk.

Sketch a typical Operating Characteristic (OC) curve and explain its shape. Describe how the OC curve is used to compare two sampling plans and explain the effect of increasing sample size $n$ or changing acceptance number $c$ on the OC curve.

What is Gage Repeatability and Reproducibility (Gage R&R)? Describe the purpose of Gage R&R study, outline the standard study procedure, and explain how the results are interpreted. Briefly contrast the Average and Range method with the ANOVA method of Gage R&R.

Describe the key requirements of ISO 9001 relevant to a small manufacturing unit. Explain how the requirements related to 'control of processes' and 'corrective action' contribute to product quality.

Differentiate preventive, predictive and corrective maintenance. Describe the main pillars of Total Productive Maintenance (TPM) and explain how TPM improves equipment effectiveness in manufacturing.

Define Mean Time Between Failures (MTBF) and Mean Time To Repair (MTTR). Derive the expression for availability $A$ in terms of MTBF and MTTR using $A=\frac{MTBF}{MTBF+MTTR}$ and explain its significance for production planning.