Manufacturing Practices (BT-106) - Important Questions

Explain the concept of Statistical Process Control (SPC). How does SPC differ from Acceptance Sampling? Discuss typical applications of SPC in manufacturing processes and the advantages of using SPC for continuous improvement.

Draw the X-bar and R control charts used for monitoring a variable characteristic. Write the formulae for the center lines and control limits for both charts and explain the meaning of each term. In particular show the limits as: $$\text{UCL}_{\bar{X}} = \bar{\bar{X}} + A_2\,\bar{R},\quad \text{CL}_{\bar{X}} = \bar{\bar{X}},\quad \text{LCL}_{\bar{X}} = \bar{\bar{X}} - A_2\,\bar{R}$$ and $$\text{UCL}_R = D_4\,\bar{R},\quad \text{CL}_R = \bar{R},\quad \text{LCL}_R = D_3\,\bar{R}\,.$$

Define the process capability indices $C_p$ and $C_{pk}$. Derive their expressions and explain how each index is interpreted. Show the formulae: $$C_p = \frac{USL - LSL}{6\sigma}$$ and $$C_{pk} = \min\left(\frac{USL - \mu}{3\sigma},\;\frac{\mu - LSL}{3\sigma}\right)\,.$$ Describe the meaning of $USL$, $LSL$, $\mu$ and $\sigma$ in these formulae.

Explain the design of a single sampling plan for attribute inspection. For a lot when a sample of size $n$ is taken with acceptance number $c$ and the lot (or population) defective fraction is $p$, derive the expression for the probability of acceptance $P_a$. Use the binomial model and show: $$P_a = \sum_{i=0}^{c} \binom{n}{i} p^{i} \left(1 - p\right)^{n - i}\,.$$ Discuss limitations of the binomial approximation and when the hypergeometric distribution should be used.

Describe control charts for attributes: the $p$-chart and the $c$-chart. Give the expressions for their centre lines and control limits. In particular show for the $p$-chart: $$\text{CL}_p = \bar{p},\quad \text{UCL}_p = \bar{p} + 3\sqrt{\left(\frac{\bar{p}\left(1 - \bar{p}\right)}{n}\right)},\quad \text{LCL}_p = \bar{p} - 3\sqrt{\left(\frac{\bar{p}\left(1 - \bar{p}\right)}{n}\right)}\,,$$ and for the $c$-chart: $$\text{CL}_c = \bar{c},\quad \text{UCL}_c = \bar{c} + 3\sqrt{\bar{c}},\quad \text{LCL}_c = \max\left(0,\;\bar{c} - 3\sqrt{\bar{c}}\right)\,.$$ Explain assumptions for each chart and when to use them.

Explain Measurement System Analysis (MSA) with emphasis on Gage Repeatability and Reproducibility (Gage R&R). Describe the main components of variation in a measurement system and outline the ANOVA and average-and-range methods used to estimate repeatability and reproducibility.

Describe the key elements of ISO 9001 relevant to manufacturing practices. Explain how implementation of an ISO 9001 quality management system supports process control and continual improvement on the shop floor.

Define the Six Sigma methodology and outline the DMAIC cycle. Explain conceptually how process capability indices such as $C_p$ and $C_{pk}$ relate to Six Sigma performance levels and the goal of reducing defects.

List and explain the working principles, typical applications, advantages and limitations of common Non-Destructive Testing (NDT) methods used in manufacturing: Ultrasonic Testing (UT), Radiographic Testing (RT), Magnetic Particle Testing (MT), and Dye Penetrant Testing (PT). Include examples of defect types each method can detect.

A production process manufactures shafts with specified diameter tolerance $50.00\ \mathrm{mm} \pm 0.10\ \mathrm{mm}$ (i.e. $USL = 50.10\ \mathrm{mm}$, $LSL = 49.90\ \mathrm{mm}$). A quality engineer takes samples of size $n = 5$ at 25 subgroups. The grand mean of subgroup means is $\bar{\bar{X}} = 50.02\ \mathrm{mm}$ and the average range is $\bar{R} = 0.15\ \mathrm{mm}$. Given constants $A_2 = 0.578$, $D_3 = 0$, and $D_4 = 2.114$, construct the X-bar and R chart control limits and determine whether the process appears to be in statistical control.