# Machine Breakdown and Maintenance Cost Analysis ## Problem Data - Machine operates: **300 days/year** - Probability of breakdown per day: **.02** - Preventive maintenance cost: **$100** (per maintenance) - Breakdown repair cost: **$800** (per breakdown) --- ## a) Expected Breakdown Cost Per Day **Step 1: Define Expected Value** The expected breakdown cost per day is: \[ \text{Expected Cost/Day} = (\text{Probability of Breakdown}) \times (\text{Cost per Breakdown}) \] **Step 2: Substitute Values** \[ \text{Expected Cost/Day} = .02 \times \$800 = \$16 \] **Final Answer:** **Expected breakdown cost per day is \(\$16\).** --- ## b) Is Preventive Maintenance Economically Justified? **Step 1: Annualize Breakdown Cost** Annual breakdown cost (if no preventive maintenance): \[ \text{Annual Expected Breakdown Cost} = \text{Expected Cost/Day} \times 300 = \$16 \times 300 = \$4,800 \] **Step 2: Compare with Preventive Maintenance Cost** - If preventive maintenance **eliminates all breakdowns**: - Annual preventive maintenance cost = \$100 \(\times\) 300 days = \$30,000 - However, usually, **preventive maintenance is scheduled periodically** (e.g., monthly, quarterly, yearly), not daily. **Step 3: Compare Per-Day Cost** - Daily expected breakdown cost: **\$16** - Daily preventive maintenance cost: **\$100** \[ \$16 < \$100 \] **Conclusion:** **Preventive maintenance (at \$100 per day) is not economically justified compared to the expected breakdown cost (\$16 per day).** --- ## c) Importance of Maintenance Management in Operations **Key Points:** 1. **Minimizes Downtime:** Regular maintenance reduces unexpected breakdowns, ensuring smooth operations and maximizing equipment availability. 2. **Cost Control:** Effective maintenance balances the cost of repairs and preventive measures to minimize total operating costs. 3. **Safety and Compliance:** Proper maintenance prevents accidents and ensures compliance with safety and regulatory standards. 4. **Asset Longevity:** Maintenance extends the useful life of equipment, delaying capital expenditures for replacements. 5. **Product Quality:** Well-maintained machines produce more consistent and higher-quality output. **Summary:** Maintenance management is essential for operational efficiency, cost control, safety, and long-term sustainability of assets. --- **Image Example:**  --- **Summary Table** | Option | Daily Cost | Annual Cost | Justified? | |-------------------------|-----------|-------------|------------| | Breakdown Repair Only | $16 | $4,800 | Yes | | Preventive Maintenance* | $100 | $30,000 | No | *\*Assuming daily preventive maintenance* --- **Final Answers:** - (a) **Expected breakdown cost per day: \$16** - (b) **Preventive maintenance (at \$100 per day) is not economically justified** - (c) **Maintenance management is crucial for minimizing costs, ensuring reliability, safety, and asset longevity**

# Machine Breakdown and Maintenance Cost Analysis ## Problem Data - **Machine operates:** 300 days/year - **Probability of breakdown per day:** 0.02 - **Cost of preventive maintenance:** $100 (per maintenance) - **Cost of breakdown repair:** $800 (per breakdown) --- ## a) Expected Breakdown Cost Per Day **Step 1: Define Expected Value** The expected breakdown cost per day can be calculated using the formula: \[ \text{Expected Cost/Day} = (\text{Probability of Breakdown}) \times (\text{Cost per Breakdown}) \] **Step 2: Substitute Values** \[ \text{Expected Cost/Day} = 0.02 \times 800 = 16 \] **Final Answer:** **Expected breakdown cost per day is \$16.** --- ## b) Is Preventive Maintenance Economically Justified? **Step 1: Annualize Breakdown Cost** Calculate the annual expected breakdown cost: \[ \text{Annual Expected Breakdown Cost} = \text{Expected Cost/Day} \times 300 = 16 \times 300 = 4800 \] **Step 2: Consider Preventive Maintenance Costs** - **Annual Preventive Maintenance Cost** (assuming daily maintenance): \[ \text{Annual Preventive Maintenance Cost} = 100 \times 300 = 30000 \] **Step 3: Compare Costs** - **Daily expected breakdown cost:** \$16 - **Daily preventive maintenance cost:** \$100 Since: \[ 16 < 100 \] **Conclusion:** **Preventive maintenance (at \$100 per day) is not economically justified compared to the expected breakdown cost (\$16 per day).** --- ## c) Importance of Maintenance Management in Operations **Key Points:** 1. **Minimizes Downtime:** Regular maintenance reduces unexpected breakdowns, ensuring smooth operations and maximizing equipment availability. 2. **Cost Control:** Effective maintenance strategies minimize total operating costs by balancing repair and preventive measures. 3. **Safety and Compliance:** Proper maintenance enhances safety and ensures compliance with regulatory standards. 4. **Asset Longevity:** Regular maintenance extends the useful life of equipment, delaying capital expenditures for replacements. 5. **Product Quality:** Well-maintained machines produce more consistent and higher-quality output. **Summary:** Maintenance management is essential for operational efficiency, cost control, safety, and long-term sustainability of assets. --- **Summary Table** | Option | Daily Cost | Annual Cost | Economically Justified? | |-------------------------|------------|-------------|--------------------------| | Breakdown Repair Only | \$16 | \$4,800 | Yes | | Preventive Maintenance | \$100 | \$30,000 | No | --- **Final Answers:** - (a) **Expected breakdown cost per day: \$16** - (b) **Preventive maintenance (at \$100 per day) is not economically justified.** - (c) **Maintenance management is crucial for minimizing costs, ensuring reliability, safety, and asset longevity.**