Manufacturing Practices (BT-106) - Important Questions

Explain the construction, assumptions and interpretation of the $\bar{X}$ and $R$ control charts. Show how the control limits are calculated and give the formulae for $UCL_{\bar{X}}$, $LCL_{\bar{X}}$, $UCL_{R}$ and $LCL_{R}$. Describe an example procedure to detect assignable causes using these charts.

Describe the $p$-chart and the $c$-chart. Derive the formulae for the control limits of each chart and explain the situations where each chart should be used. Include the expressions for $UCL$ and $LCL$ for both charts.

Define process capability indices $C_p$ and $C_{pk}$. Give the formulas and explain their interpretation. For a process with upper specification limit $\text{USL}$, lower specification limit $\text{LSL}$, mean $\mu$ and standard deviation $\sigma$, write the mathematical expressions for $C_p$ and $C_{pk}$.

Explain the principles of single sampling plans for lot acceptance. Define producer's risk and consumer's risk, and describe how the Operating Characteristic (OC) curve is used to select a sampling plan given an AQL and LTPD.

Derive the sample size formula for estimating a proportion with specified confidence and precision. Using the normal approximation to the binomial, present the formula $$n = \frac{Z_{1-\alpha/2}^{2}\,p(1-p)}{d^{2}}$$ and explain each term. Show how this is applied to determine sample size for inspection.

Explain the objectives of Gauge Repeatability and Reproducibility (Gauge R&R) study. Describe the range method and the ANOVA method for Gauge R&R and list the steps involved in calculating % contribution of repeatability and reproducibility to total variation.

For a process with known standard deviation $\sigma$ and subgroup size $n$, derive the control limits for the sample mean chart when the process mean is $\mu$. Present the expressions for $UCL$ and $LCL$ using the standard error of the mean.

Define the Operating Characteristic (OC) curve of an acceptance sampling plan. Explain how the OC curve reflects the discrimination power of a sampling plan and how to interpret points on the curve.

Outline the DMAIC cycle of Six Sigma. Explain the key statistical and quality tools used in the Measure and Analyze phases, and describe how these tools support process improvement.

List the common non-destructive testing (NDT) methods such as Ultrasonic Testing (UT), Radiographic Testing (RT), Magnetic Particle Testing (MT), Penetrant Testing (PT) and Eddy Current Testing (ET). For each method, briefly describe the basic principle and a typical industrial application.

Summarize the key requirements of ISO 9001 quality management system relevant to production and inspection. Describe the role of quality manuals, documented procedures and internal audits in maintaining compliance.

Define Mean Time Between Failures (MTBF) and Mean Time To Repair (MTTR). Derive the formula for system availability in terms of MTBF and MTTR and compute availability for a system with $\text{MTBF}=2000\,\text{hours}$ and $\text{MTTR}=5\,\text{hours}$.